ASVAB — All Questions

A train travels at a constant speed of 60 miles per hour. How long will it take to travel 180 miles?

• a.3.5 hours
• b.2 hours
• c.4 hours
• d.3 hours✓

Time equals distance divided by speed. Dividing 180 miles by 60 miles per hour gives 3 hours. Keeping the units consistent lets the miles cancel and leaves hours.

If 5 pounds of apples cost $4.00, how much do 12 pounds cost at the same rate?

• a.$8.40
• b.$12.00
• c.$10.00
• d.$9.60✓

The unit price is $4.00 divided by 5 pounds, or $0.80 per pound. Multiplying $0.80 by 12 pounds gives $9.60. Setting up a proportion produces the same result.

What is 25% of 240?

• a.80
• b.60✓
• c.72
• d.48

Twenty-five percent is the same as one quarter. Dividing 240 by 4 gives 60. You could also multiply 240 by 0.25 to reach the same value.

A recipe uses flour and sugar in a ratio of 3 to 1. If you use 9 cups of flour, how many cups of sugar are needed?

• a.6 cups
• b.12 cups
• c.1 cup
• d.3 cups✓

The ratio 3 to 1 means three parts flour for every one part sugar. Since 9 cups of flour is three times the base part of 3, the sugar is also tripled from 1 to 3 cups. Ratios scale both quantities by the same factor.

The average of four test scores is 85. Three of the scores are 80, 90, and 85. What is the fourth score?

• a.80
• b.85✓
• c.95
• d.90

An average of 85 over four tests means the total is 85 times 4, or 340. The three known scores add to 255, so the fourth score is 340 minus 255, which equals 85.

A worker can assemble 8 units per hour. How many units can 3 workers assemble in 5 hours at that rate?

• a.120 units✓
• b.40 units
• c.80 units
• d.160 units

One worker makes 8 units per hour, so 3 workers make 24 units per hour. Over 5 hours that is 24 times 5, which equals 120 units. Rate times number of workers times time gives total output.

A jacket originally priced at $80 is discounted 15%. What is the sale price?

• a.$76
• b.$65
• c.$72
• d.$68✓

Fifteen percent of $80 is $12. Subtracting the $12 discount from $80 leaves a sale price of $68. You can also multiply $80 by 0.85 to get the same answer.

You deposit $500 in an account earning 4% simple interest per year. How much interest is earned in 3 years?

• a.$80
• b.$60✓
• c.$20
• d.$40

Simple interest equals principal times rate times time. That is $500 times 0.04 times 3, which equals $60. Simple interest is calculated only on the original principal.

Two cars start from the same point and drive in opposite directions at 40 mph and 55 mph. How far apart are they after 2 hours?

• a.95 miles
• b.110 miles
• c.150 miles
• d.190 miles✓

Their combined separation speed is 40 plus 55, or 95 miles per hour. After 2 hours they are 95 times 2, which equals 190 miles apart. Opposite directions mean the speeds add.

A map uses a scale of 1 inch to 25 miles. Two towns are 4.5 inches apart on the map. What is the actual distance?

• a.90 miles
• b.125 miles
• c.112.5 miles✓
• d.100 miles

Each inch represents 25 miles, so multiply 4.5 inches by 25 miles per inch. That product is 112.5 miles. Scale problems are solved with a direct proportion.

A rectangular room is 12 feet long and 9 feet wide. If carpet costs $3 per square foot, what is the total cost to carpet the room?

• a.$108
• b.$324✓
• c.$396
• d.$252

The floor area is length times width, or 12 times 9, which equals 108 square feet. Multiplying 108 square feet by $3 per square foot gives $324.

A store sells 6 bottles of water for $9. What is the cost of one bottle?

• a.$1.75
• b.$1.20
• c.$1.50✓
• d.$2.00

Dividing the total price of $9 by 6 bottles gives $1.50 per bottle. Unit price is found by dividing total cost by the number of items.

In a class of 30 students, 3/5 are girls. How many boys are in the class?

• a.15
• b.12✓
• c.18
• d.10

Three fifths of 30 is 18 girls. Subtracting 18 girls from 30 total students leaves 12 boys. The fraction of boys is the remaining two fifths of 30, which also equals 12.

A meal costs $40 before tax. If sales tax is 8%, what is the total amount paid?

• a.$48.00
• b.$44.80
• c.$43.20✓
• d.$42.00

Eight percent of $40 is $3.20 in tax. Adding the tax to the $40 meal gives a total of $43.20. Multiplying $40 by 1.08 gives the same total.

A tank holds 240 gallons and is being filled at 8 gallons per minute. How many minutes will it take to fill the empty tank?

• a.24 minutes
• b.40 minutes
• c.30 minutes✓
• d.32 minutes

Dividing the 240-gallon capacity by the fill rate of 8 gallons per minute gives 30 minutes. Time equals total amount divided by rate.

If 168 pencils are packed equally into boxes of 12, how many boxes are needed?

• a.14✓
• b.16
• c.18
• d.12

Dividing 168 pencils by 12 pencils per box gives exactly 14 boxes. Because 12 times 14 equals 168, there is no remainder and no extra box is required.

"Abundant" most nearly means:

• a.scarce
• b.costly
• c.hidden
• d.plentiful✓

Abundant describes something existing in large quantity or great supply. Plentiful is its closest synonym. Scarce is an antonym meaning in short supply.

"Cautious" most nearly means:

• a.reckless
• b.cheerful
• c.curious
• d.careful✓

Cautious means acting with care to avoid danger or mistakes. Careful is the nearest match. Reckless is the opposite, meaning careless.

"Vacant" most nearly means:

• a.empty✓
• b.dirty
• c.locked
• d.crowded

Vacant means not occupied or containing nothing. Empty is the closest synonym. A vacant lot or apartment has no one in it.

"Fatigue" most nearly means:

• a.hunger
• b.tiredness✓
• c.anger
• d.strength

Fatigue is a state of extreme weariness or exhaustion, usually from exertion. Tiredness is its nearest meaning. It is the opposite of feeling energetic.

"Rigid" most nearly means:

• a.warm
• b.flexible
• c.stiff✓
• d.smooth

Rigid means stiff and unable to bend easily. Stiff is the closest synonym. Flexible is the antonym, describing something that bends readily.

"Conceal" most nearly means:

• a.gather
• b.clean
• c.reveal
• d.hide✓

To conceal something is to keep it out of sight or secret. Hide is its nearest synonym. Reveal is the opposite, meaning to show.

"Ample" most nearly means:

• a.sufficient✓
• b.tiny
• c.broken
• d.rapid

Ample means more than enough or fully adequate in amount. Sufficient captures this meaning of an adequate supply. It is the opposite of insufficient.

"Diminish" most nearly means:

• a.repair
• b.brighten
• c.expand
• d.decrease✓

To diminish is to make or become smaller or less. Decrease is the closest synonym. Expand, meaning to grow larger, is its antonym.

"Novice" most nearly means:

• a.expert
• b.leader
• c.traitor
• d.beginner✓

A novice is a person new to a field or activity. Beginner is the nearest match. An expert, being highly skilled, is the opposite.

"Verify" most nearly means:

• a.confirm✓
• b.delay
• c.forget
• d.deny

To verify is to check or prove that something is true or accurate. Confirm is the closest synonym. Deny is an antonym meaning to reject as untrue.

"Hostile" most nearly means:

• a.quiet
• b.unfriendly✓
• c.welcoming
• d.wealthy

Hostile describes an unfriendly or antagonistic attitude. Unfriendly is the nearest meaning. Welcoming is the opposite.

"Fragment" most nearly means:

• a.engine
• b.piece✓
• c.signal
• d.whole

A fragment is a small broken-off part of something larger. Piece is the closest synonym. It contrasts with a whole or complete object.

"Prohibit" most nearly means:

• a.measure
• b.forbid✓
• c.praise
• d.allow

To prohibit something is to formally forbid it by rule or law. Forbid is the nearest synonym. Allow is the antonym, meaning to permit.

"Sturdy" most nearly means:

• a.strong✓
• b.fragile
• c.distant
• d.gentle

Sturdy means solidly built and strong. Strong is the closest match. Fragile, meaning easily broken, is its opposite.

"Vivid" most nearly means:

• a.heavy
• b.bright✓
• c.silent
• d.dull

Vivid describes something bright, intense, or strikingly clear. Bright is the nearest synonym. Dull is the antonym, meaning lacking brightness.

"Assemble" most nearly means:

• a.sell
• b.gather✓
• c.scatter
• d.ignore

To assemble is to bring or come together into a group or whole. Gather is the closest synonym. Scatter is the opposite, meaning to spread apart.

The human body loses water constantly through breathing, sweating, and digestion. To stay healthy, this lost water must be replaced by drinking fluids and eating foods that contain water. According to the passage, why must people drink fluids?

• a.To replace water the body loses✓
• b.To improve eyesight
• c.To build stronger muscles
• d.To gain more energy

The passage states the body constantly loses water and that this loss must be replaced. The correct choice restates that idea directly. The other options are not mentioned in the passage.

Recycling reduces the amount of waste sent to landfills. It also saves energy, because making products from recycled materials often uses less power than making them from raw materials. One benefit of recycling mentioned in the passage is that it:

• a.saves energy✓
• b.raises product prices
• c.creates more landfills
• d.uses more raw materials

The passage says recycling saves energy since recycled materials often require less power. That matches the correct choice. The remaining options contradict the passage.

A good study routine includes setting a regular time and place. Studying in the same spot each day helps the brain associate that location with focus, making it easier to concentrate. The passage suggests that studying in the same place each day helps a person to:

• a.avoid taking notes
• b.finish homework faster
• c.concentrate more easily✓
• d.study fewer subjects

The passage explains that a consistent location helps the brain associate it with focus, making concentration easier. The correct answer restates this. The other choices are not supported.

Firefighters wear heavy protective suits made of flame-resistant material. These suits shield the wearer from intense heat, but they are also very hot and tiring to work in. According to the passage, one drawback of the protective suits is that they:

• a.cannot be cleaned
• b.are hot and tiring to wear✓
• c.are too thin
• d.catch fire easily

The passage notes that although the suits protect against heat, they are hot and tiring to work in. That is the drawback described. The other options are not stated.

Bees play a vital role in agriculture. As they move from flower to flower collecting nectar, they carry pollen between plants, allowing many crops to produce fruit. The passage indicates that bees help crops by:

• a.eating harmful insects
• b.keeping the ground warm
• c.carrying pollen between plants✓
• d.watering the soil

The passage states bees carry pollen from flower to flower, which allows crops to produce fruit. That matches the correct choice. The other answers are not mentioned.

Reading aloud to young children builds their vocabulary. Hearing new words in context helps children understand meanings and remember the words later. According to the passage, hearing words in context helps children to:

• a.speak more quietly
• b.read silently
• c.write neatly
• d.understand and remember words✓

The passage says that hearing new words in context helps children grasp meanings and recall the words later. The correct option restates this. The others are not supported.

Regular exercise strengthens the heart. A stronger heart pumps blood more efficiently, which can lower a person's resting heart rate over time. The passage states that a stronger heart:

• a.requires more oxygen
• b.pumps blood more efficiently✓
• c.shrinks in size
• d.beats faster at rest

The passage explains that a stronger heart pumps blood more efficiently and can lower the resting heart rate. That matches the correct choice, while the others contradict the passage.

Many plants close their leaves or flowers at night. This response helps protect the plant from cold temperatures and reduces water loss during dark hours. According to the passage, closing at night helps plants by:

• a.attracting more insects
• b.growing taller quickly
• c.reducing water loss✓
• d.producing more seeds

The passage says that closing at night protects plants from cold and reduces water loss. The correct answer reflects this. The remaining choices are not mentioned.

A budget is a plan for spending money. By listing income and expenses, a budget helps a person avoid spending more than they earn. The main purpose of a budget, according to the passage, is to:

• a.borrow more money
• b.increase a person's income
• c.plan spending and avoid overspending✓
• d.eliminate all expenses

The passage defines a budget as a spending plan that lists income and expenses to prevent overspending. The correct choice captures this purpose. The others are not stated.

Sea turtles travel thousands of miles across the ocean but often return to the same beach where they hatched to lay their eggs. Scientists believe they use the Earth's magnetic field to navigate. According to the passage, sea turtles are believed to navigate using:

• a.ocean water temperature
• b.the position of the moon
• c.the Earth's magnetic field✓
• d.the sound of waves

The passage states that scientists believe sea turtles use the Earth's magnetic field to find their way. That matches the correct choice. The other options are not mentioned.

Getting enough sleep improves memory. During deep sleep, the brain organizes and stores information learned during the day, making it easier to recall later. The passage explains that during deep sleep the brain:

• a.forgets the day's events
• b.stops all activity
• c.organizes and stores information✓
• d.grows new bones

The passage says the brain organizes and stores the day's information during deep sleep, aiding recall. The correct answer restates this. The other choices are unsupported.

Traffic roundabouts can reduce accidents at intersections. Because vehicles move in the same direction around a circle, dangerous head-on and right-angle collisions are far less likely. According to the passage, roundabouts reduce accidents because vehicles:

• a.use fewer lanes
• b.stop more often
• c.travel much faster
• d.move in the same direction✓

The passage explains that roundabouts keep vehicles moving in the same direction, reducing head-on and right-angle crashes. The correct choice restates this reason. The others are not stated.

Salt has long been used to preserve food. It draws moisture out of meat and fish, creating conditions in which the bacteria that cause spoilage cannot easily grow. The passage indicates that salt preserves food by:

• a.raising the temperature
• b.drawing out moisture✓
• c.adding vitamins
• d.adding color

The passage says salt draws moisture out of food, making it hard for spoilage bacteria to grow. That matches the correct answer. The other options are not mentioned.

Volunteering benefits both the community and the volunteer. Besides helping others, volunteers often gain new skills and build friendships that improve their own lives. According to the passage, one way volunteering benefits the volunteer is by:

• a.reducing their taxes
• b.increasing their salary
• c.helping them gain new skills✓
• d.giving them free housing

The passage states that volunteers often gain new skills and build friendships. The correct choice reflects a benefit to the volunteer. The other options are not supported by the text.

If 3x + 7 = 22, what is the value of x?

• a.5✓
• b.3
• c.7
• d.9

Subtracting 7 from both sides gives 3x equals 15. Dividing both sides by 3 gives x equals 5. You can check by substituting 5 back into the equation.

What is the value of 4 squared plus 3 cubed?

• a.43✓
• b.25
• c.49
• d.37

Four squared is 16 and three cubed is 27. Adding 16 and 27 gives 43. Exponents are evaluated before addition.

The area of a triangle with base 10 and height 6 is:

• a.30✓
• b.60
• c.45
• d.16

The area of a triangle equals one half times base times height. That is 0.5 times 10 times 6, which equals 30 square units. Forgetting the one-half factor gives the incorrect value 60.

What is the value of x if x/4 = 9?

• a.45
• b.18
• c.36✓
• d.13

To isolate x, multiply both sides of the equation by 4. That gives x equals 9 times 4, or 36. Dividing 36 by 4 returns 9, which confirms the answer.

Simplify: 2(3 + 4) - 5.

• a.12
• b.7
• c.9✓
• d.3

Following order of operations, first add inside the parentheses to get 7. Multiply by 2 to get 14, then subtract 5 to reach 9.

A circle has a radius of 5. What is its circumference? (Use pi is about 3.14.)

• a.78.5
• b.15.7
• c.31.4✓
• d.25.0

Circumference equals 2 times pi times the radius. That is 2 times 3.14 times 5, which equals 31.4. The value 78.5 is the area, not the circumference.

What is the value of the expression 5! (5 factorial)?

• a.720
• b.120✓
• c.60
• d.25

A factorial multiplies all whole numbers from the number down to 1. So 5 factorial is 5 times 4 times 3 times 2 times 1, which equals 120.

Solve for y: 2y - 6 = 10.

• a.8✓
• b.2
• c.16
• d.5

Adding 6 to both sides gives 2y equals 16. Dividing both sides by 2 gives y equals 8. Substituting 8 back confirms the solution.

What is the square root of 144?

• a.12✓
• b.72
• c.11
• d.14

The square root of a number is the value that, multiplied by itself, gives that number. Since 12 times 12 equals 144, the square root of 144 is 12.

The sum of the interior angles of a triangle is:

• a.90 degrees
• b.180 degrees✓
• c.360 degrees
• d.270 degrees

The interior angles of any triangle always add up to 180 degrees. This is a fundamental rule of Euclidean geometry. A quadrilateral, by contrast, totals 360 degrees.

If a = 3 and b = -2, what is the value of a squared minus b?

• a.-11
• b.5
• c.11✓
• d.7

First, a squared is 3 times 3, which equals 9. Subtracting b, which is negative 2, means adding 2, giving 9 plus 2, or 11.

What is 3/4 written as a decimal?

• a.1.33
• b.0.75✓
• c.0.43
• d.0.34

Dividing the numerator 3 by the denominator 4 gives 0.75. Fractions are converted to decimals by dividing the top number by the bottom number.

A rectangle has a length of 8 and a perimeter of 26. What is its width?

• a.4
• b.5✓
• c.9
• d.6

The perimeter equals twice the length plus twice the width. So 26 minus 2 times 8, which is 16, leaves 10 for the two widths. Dividing 10 by 2 gives a width of 5.

Simplify the expression 3x + 2x - x.

• a.5x
• b.2x
• c.6x
• d.4x✓

Combining like terms, 3x plus 2x equals 5x, and subtracting x leaves 4x. Only the coefficients are added and subtracted since all terms share the variable x.

What is the value of 6 divided by 0.5?

• a.3
• b.6
• c.0.083
• d.12✓

Dividing by 0.5 is the same as multiplying by 2. So 6 divided by 0.5 equals 12. Dividing by a number less than 1 produces a result larger than the original.

A cube has edges of length 3. What is its volume?

• a.27✓
• b.18
• c.9
• d.81

The volume of a cube equals the edge length raised to the third power. Three cubed is 3 times 3 times 3, which equals 27 cubic units.

Which part of the plant cell carries out photosynthesis?

• a.Mitochondrion
• b.Chloroplast✓
• c.Ribosome
• d.Nucleus

Chloroplasts contain chlorophyll, the green pigment that captures light energy to make sugar during photosynthesis. The nucleus stores genetic material, while mitochondria release energy from food.

What is the chemical symbol for water?

• a.H2O✓
• b.O2
• c.NaCl
• d.CO2

Water is made of two hydrogen atoms bonded to one oxygen atom, giving the formula H2O. CO2 is carbon dioxide and NaCl is table salt.

Which gas do humans need to breathe in to survive?

• a.Helium
• b.Oxygen✓
• c.Carbon dioxide
• d.Nitrogen

The human respiratory system takes in oxygen, which cells use to release energy from food. Carbon dioxide is the waste gas that people breathe out.

The force that pulls objects toward the center of the Earth is called:

• a.Friction
• b.Magnetism
• c.Gravity✓
• d.Inertia

Gravity is the attractive force that pulls objects toward the Earth's center, giving them weight. Friction opposes motion between surfaces, and magnetism acts between magnetic materials.

Which planet is closest to the Sun?

• a.Mars
• b.Venus
• c.Mercury✓
• d.Earth

Mercury is the innermost planet, orbiting nearest to the Sun. Venus is second, Earth third, and Mars fourth.

What is the basic unit of heredity that carries traits from parents to offspring?

• a.Tissue
• b.Gene✓
• c.Cell
• d.Organ

A gene is a segment of DNA that carries the instructions for inherited traits. Cells, tissues, and organs are structural levels of the body, not units of heredity.

At what temperature does pure water freeze at sea level, in degrees Celsius?

• a.100 degrees
• b.-10 degrees
• c.32 degrees
• d.0 degrees✓

Pure water freezes at 0 degrees Celsius at standard sea-level pressure. That same point is 32 degrees on the Fahrenheit scale, while water boils at 100 degrees Celsius.

Which blood cells help fight infection in the body?

• a.Plasma proteins
• b.White blood cells✓
• c.Red blood cells
• d.Platelets

White blood cells are part of the immune system and defend the body against germs and infection. Red blood cells carry oxygen, and platelets help blood clot.

The process by which liquid water turns into water vapor is called:

• a.Freezing
• b.Precipitation
• c.Condensation
• d.Evaporation✓

Evaporation is the change of a liquid into a gas as molecules gain enough energy to escape the surface. Condensation is the reverse, when vapor turns back into liquid.

Which of these is an example of a chemical change?

• a.Tearing paper
• b.Water boiling
• c.Iron rusting✓
• d.Ice melting

Rusting forms a new substance, iron oxide, so it is a chemical change. Melting, boiling, and tearing are physical changes that do not create new substances.

The Richter scale is used to measure the strength of:

• a.Earthquakes✓
• b.Floods
• c.Tornadoes
• d.Hurricanes

The Richter scale measures the magnitude, or energy released, of earthquakes. Hurricanes and tornadoes are rated on different scales based on wind speed.

Which organ system is responsible for pumping blood throughout the body?

• a.Circulatory system✓
• b.Respiratory system
• c.Digestive system
• d.Nervous system

The circulatory system, centered on the heart and blood vessels, pumps blood to deliver oxygen and nutrients. The respiratory system handles breathing, and the digestive system processes food.

What type of energy is stored in a stretched rubber band?

• a.Thermal energy
• b.Sound energy
• c.Potential energy✓
• d.Kinetic energy

A stretched rubber band stores potential energy because of its position or state. When released, that stored energy converts into kinetic energy, the energy of motion.

Which part of the atom carries a negative electric charge?

• a.Electron✓
• b.Nucleus
• c.Neutron
• d.Proton

Electrons carry a negative charge and orbit the atom's nucleus. Protons carry a positive charge and neutrons have no charge, both residing in the nucleus.

Photosynthesis produces oxygen and which sugar?

• a.Lactose
• b.Glucose✓
• c.Sucrose
• d.Fructose

During photosynthesis, plants use carbon dioxide and water to make glucose and release oxygen. Glucose is the simple sugar plants use for energy and growth.

The layer of gases surrounding the Earth is called the:

• a.Atmosphere✓
• b.Lithosphere
• c.Biosphere
• d.Hydrosphere

The atmosphere is the envelope of gases held around Earth by gravity. The lithosphere is the solid crust, and the hydrosphere includes the planet's water.

According to Ohm's law, voltage equals current multiplied by:

• a.power
• b.resistance✓
• c.frequency
• d.capacitance

Ohm's law states that voltage equals current times resistance, written as V equals I times R. This relationship links the three basic quantities in a circuit.

The unit used to measure electrical resistance is the:

• a.watt
• b.ohm✓
• c.volt
• d.ampere

Resistance is measured in ohms, symbolized by the Greek letter omega. The volt measures voltage, the ampere measures current, and the watt measures power.

A device that stores electrical charge is a:

• a.inductor
• b.resistor
• c.transformer
• d.capacitor✓

A capacitor stores electrical energy in an electric field between two plates. A resistor limits current, while an inductor stores energy in a magnetic field.

In a circuit, current is measured in:

• a.farads
• b.ohms
• c.amperes✓
• d.volts

Electric current, the flow of charge, is measured in amperes, often shortened to amps. Ohms measure resistance, volts measure voltage, and farads measure capacitance.

What is the total resistance of two 10-ohm resistors connected in series?

• a.10 ohms
• b.5 ohms
• c.100 ohms
• d.20 ohms✓

In a series circuit, resistances add together directly. Ten ohms plus ten ohms equals 20 ohms. In parallel, the total would instead be lower than either resistor.

Electrical power in watts is calculated by multiplying voltage by:

• a.current✓
• b.resistance
• c.capacitance
• d.time

Power equals voltage times current, written as P equals V times I. This gives the rate at which electrical energy is used, measured in watts.

A component that allows current to flow in only one direction is a:

• a.diode✓
• b.switch
• c.resistor
• d.capacitor

A diode conducts current in one direction and blocks it in the other, acting like a one-way valve. This property makes diodes useful for converting AC to DC.

The abbreviation AC stands for:

• a.alternating current✓
• b.active charge
• c.ampere current
• d.automatic circuit

AC stands for alternating current, in which the direction of electron flow reverses periodically. DC, or direct current, flows steadily in one direction.

Which material is the best conductor of electricity?

• a.Copper✓
• b.Glass
• c.Rubber
• d.Wood

Copper is an excellent conductor and is widely used in electrical wiring. Rubber, glass, and wood are insulators that resist the flow of current.

A transformer is used to change the level of:

• a.resistance
• b.current direction
• c.voltage✓
• d.frequency

A transformer increases or decreases AC voltage using two coils of wire. Stepping voltage up or down helps electricity travel efficiently and power different devices.

If voltage is 12 volts and resistance is 4 ohms, what is the current?

• a.3 amperes✓
• b.48 amperes
• c.4 amperes
• d.2 amperes

Using Ohm's law, current equals voltage divided by resistance. That is 12 volts divided by 4 ohms, which equals 3 amperes.

A material that strongly resists the flow of electric current is called a(n):

• a.semiconductor
• b.battery
• c.conductor
• d.insulator✓

An insulator resists the flow of electricity and is used to protect and separate conductors. Rubber and plastic are common insulators used to coat wires.

The component that provides a source of stored electrical energy in a portable device is the:

• a.battery✓
• b.fuse
• c.switch
• d.antenna

A battery stores chemical energy and converts it to electrical energy to power a device. A fuse protects the circuit, and a switch simply opens or closes it.

A fuse protects a circuit by:

• a.increasing the voltage
• b.breaking the circuit when current is too high✓
• c.reversing the current
• d.storing extra charge

A fuse contains a thin wire that melts and breaks the circuit when current exceeds a safe level. This prevents overheating and damage to the rest of the circuit.

Which simple machine is a doorknob an example of?

• a.Wheel and axle✓
• b.Wedge
• c.Pulley
• d.Inclined plane

A doorknob turns a shaft, so the large knob and thin spindle form a wheel and axle. Turning the larger wheel produces a stronger turning force on the smaller axle.

A lever is used mainly to:

• a.reduce weight
• b.increase force✓
• c.store electricity
• d.produce heat

A lever multiplies the force applied to it, making it easier to move a load. Placing the fulcrum closer to the load increases this mechanical advantage.

If two people push on a box from opposite sides with equal force, the box will:

• a.move toward the stronger side
• b.speed up
• c.stay still✓
• d.spin in place

Equal and opposite forces cancel out, producing a net force of zero. With no net force, the box remains at rest, an example of balanced forces.

A pulley system is used to:

• a.reduce friction to zero
• b.change the direction of a force✓
• c.increase temperature
• d.create electricity

A single fixed pulley lets you pull down to lift a load up, changing the direction of the applied force. Adding more pulleys can also reduce the effort needed.

Which of these is an example of an inclined plane?

• a.A ramp✓
• b.A seesaw
• c.A wheelbarrow
• d.A ceiling fan

A ramp is a flat surface set at an angle, which is the definition of an inclined plane. It makes raising a load easier by spreading the effort over a longer distance.

The force that opposes the motion of two surfaces sliding against each other is:

• a.buoyancy
• b.friction✓
• c.gravity
• d.tension

Friction acts between contacting surfaces and resists their relative sliding motion. Rougher surfaces generally produce more friction than smooth ones.

In a class-one lever, the fulcrum is located:

• a.outside the lever
• b.between the effort and the load✓
• c.at the effort end only
• d.at the load end only

A class-one lever, such as a seesaw, has its fulcrum between the effort and the load. A crowbar prying a nail is another common example.

Two gears mesh together. If the driving gear turns clockwise, the driven gear will turn:

• a.clockwise
• b.not at all
• c.in both directions
• d.counterclockwise✓

When two gears mesh directly, they turn in opposite directions. So if the driving gear turns clockwise, the meshed driven gear turns counterclockwise.

A smaller gear driving a larger gear will cause the larger gear to turn:

• a.more slowly✓
• b.backward only
• c.faster
• d.at the same speed

A small gear driving a large gear reduces speed but increases turning force, or torque. The larger gear turns more slowly because it has more teeth to move per revolution.

Which object has the most gravitational potential energy?

• a.A rock resting in a valley
• b.A rock rolling on flat ground
• c.A rock at the top of a hill✓
• d.A rock at the bottom of a hill

Gravitational potential energy increases with height. A rock at the top of a hill is highest, so it has the greatest stored energy ready to convert to motion.

Increasing the length of a lever's effort arm will:

• a.reduce the load
• b.decrease the force output
• c.have no effect
• d.increase the mechanical advantage✓

A longer effort arm gives more leverage, increasing the mechanical advantage. This lets a smaller effort force lift a larger load.

Air pressure is greatest at:

• a.high in the atmosphere
• b.the edge of space
• c.the top of a mountain
• d.sea level✓

Air pressure is highest at sea level because the full weight of the atmosphere presses down there. Pressure decreases with altitude as less air remains above.

A wedge is used to:

• a.lift objects with a rope
• b.reduce electrical current
• c.split or separate objects✓
• d.store rotational energy

A wedge is a moving inclined plane that concentrates force to split or separate materials. An axe head and a knife blade are common wedges.

When a compressed spring is released, the stored energy is converted mainly into:

• a.sound only
• b.electricity
• c.heat only
• d.motion✓

A compressed spring stores elastic potential energy. When released, that energy is converted mainly into kinetic energy, causing the spring or an attached object to move.

Which engine component converts the up-and-down motion of the pistons into rotating motion?

• a.Radiator
• b.Spark plug
• c.Camshaft
• d.Crankshaft✓

The crankshaft is connected to the pistons and turns their linear up-and-down motion into rotational motion that drives the wheels. The camshaft instead controls the valves.

What is the main purpose of engine oil?

• a.To lubricate moving parts✓
• b.To inflate the tires
• c.To power the lights
• d.To cool the cabin

Engine oil lubricates moving metal parts to reduce friction and wear. It also helps carry away heat and keep internal components clean.

A spark plug is used to:

• a.ignite the fuel-air mixture✓
• b.charge the battery
• c.cool the engine
• d.filter the oil

In a gasoline engine, the spark plug produces an electric spark that ignites the compressed fuel-air mixture in the cylinder. This controlled ignition powers the piston stroke.

Which tool is best for measuring the gap of a spark plug?

• a.Hacksaw
• b.Feeler gauge✓
• c.Pipe wrench
• d.Torque wrench

A feeler gauge has thin blades of known thickness used to measure small gaps, such as a spark plug gap. A torque wrench instead measures tightening force.

The part of the car that keeps the engine from overheating by circulating coolant is the:

• a.radiator✓
• b.alternator
• c.distributor
• d.muffler

The radiator transfers heat from the circulating coolant to the outside air, keeping the engine at a safe temperature. The alternator, by contrast, generates electricity.

A Phillips screwdriver is designed to fit a screw head shaped like a:

• a.hexagon
• b.square
• c.cross✓
• d.straight slot

A Phillips screwdriver has a cross-shaped, or X-shaped, tip that matches a screw head with a cross-shaped recess. A flat-blade screwdriver instead fits a single straight slot.

Which part of a car stores electrical energy to start the engine?

• a.Muffler
• b.Fuel pump
• c.Carburetor
• d.Battery✓

The battery supplies the electrical current needed to power the starter motor and start the engine. Once running, the alternator recharges the battery.

The device that reduces engine exhaust noise is the:

• a.alternator
• b.clutch
• c.radiator
• d.muffler✓

The muffler is part of the exhaust system and dampens the loud noise created by the engine's exhaust gases. It does not affect engine cooling or charging.

A torque wrench is used to:

• a.measure voltage
• b.cut metal pipe
• c.tighten bolts to a specific tightness✓
• d.sand wood surfaces

A torque wrench applies a precise, measured amount of turning force to a bolt or nut. This prevents fasteners from being too loose or over-tightened and damaged.

Which type of saw is designed for cutting metal?

• a.Crosscut saw
• b.Hacksaw✓
• c.Chainsaw
• d.Coping saw

A hacksaw has a fine-toothed blade held under tension in a frame and is made for cutting metal and plastic. A crosscut saw and chainsaw are intended for wood.

The system that allows a car to slow down and stop is the:

• a.fuel system
• b.exhaust system
• c.braking system✓
• d.cooling system

The braking system uses friction, typically pads pressing on discs or rotors, to slow the wheels and stop the vehicle. The fuel and exhaust systems handle power, not stopping.

Which tool would you use to drive a nail into wood?

• a.Pliers
• b.Wrench
• c.Hammer✓
• d.Level

A hammer delivers a strong impact to drive nails into wood. Wrenches turn bolts, pliers grip objects, and a level checks whether a surface is horizontal.

In a four-stroke engine, which stroke immediately follows the compression stroke?

• a.Intake stroke
• b.Cooling stroke
• c.Exhaust stroke
• d.Power stroke✓

The four-stroke cycle runs intake, compression, power, then exhaust. After the fuel-air mixture is compressed, the spark plug fires and the power stroke pushes the piston down.

The purpose of a vehicle's transmission is to:

• a.cool the engine oil
• b.transfer engine power to the wheels✓
• c.store fuel
• d.clean the exhaust gases

The transmission uses gears to transfer the engine's power to the wheels while matching engine speed to driving conditions. Lower gears provide more force, higher gears more speed.

A mechanic charges $85 for the first hour of labor and $60 for each additional hour. What is the labor charge for a job that takes 5 hours?

• a.$265
• b.$325✓
• c.$385
• d.$425

The first hour costs $85 and the remaining four hours cost $60 each, so 4 x $60 = $240. Adding $85 + $240 gives $325.

A delivery truck averages 18 miles per gallon. How many gallons of fuel will it use on a 468-mile route?

• a.32 gallons
• b.28 gallons
• c.24 gallons
• d.26 gallons✓

Gallons equal miles divided by miles per gallon: 468 / 18 = 26. Checking the other way, 18 x 26 = 468.

A jacket priced at $72 is marked down 25 percent. What is the sale price?

• a.$60
• b.$48
• c.$58
• d.$54✓

A 25 percent discount removes 72 x 0.25 = $18, leaving 72 - 18 = $54. You can also take 75 percent of $72 directly.

A student scored 82, 91, 76, and 95 on four tests. What is the average score?

• a.84
• b.88
• c.86✓
• d.91

The four scores total 344, and 344 / 4 = 86. The average must fall between the lowest and highest scores, which 86 does.

A recipe calls for flour and sugar in a ratio of 5 to 2. If a baker uses 20 cups of flour, how much sugar is needed?

• a.50 cups
• b.10 cups
• c.4 cups
• d.8 cups✓

Twenty cups of flour is four times the 5 in the ratio, so the sugar is four times the 2, or 8 cups. The ratio 20 to 8 reduces back to 5 to 2.

A runner covers 2 miles in 14 minutes 30 seconds. At the same pace, how long will 5 miles take?

• a.33 minutes 45 seconds
• b.42 minutes 30 seconds
• c.36 minutes 15 seconds✓
• d.38 minutes 45 seconds

Fourteen and a half minutes for 2 miles is 7.25 minutes per mile, and 7.25 x 5 = 36.25 minutes, which is 36 minutes 15 seconds.

How much simple interest does $2,400 earn in 3 years at an annual rate of 6 percent?

• a.$864
• b.$432✓
• c.$504
• d.$144

Simple interest is principal x rate x time: 2400 x 0.06 = $144 per year, and $144 x 3 = $432.

An empty crate weighs 18 pounds. It is packed with 24 cans that each weigh 14 ounces. What is the packed weight?

• a.39 pounds✓
• b.42 pounds
• c.33 pounds
• d.36 pounds

The cans weigh 24 x 14 = 336 ounces, and 336 / 16 = 21 pounds. Adding the 18-pound crate gives 39 pounds.

One painter can finish a room in 6 hours and another can finish the same room in 12 hours. Working together, how long will the room take?

• a.5 hours
• b.4 hours✓
• c.9 hours
• d.3 hours

In one hour the pair completes 1/6 + 1/12 = 3/12 = 1/4 of the room, so the whole room takes 4 hours. Averaging the two times would be wrong.

A car bought for $18,000 is worth $12,600 one year later. By what percent did its value fall?

• a.42 percent
• b.25 percent
• c.32 percent
• d.30 percent✓

The drop is 18,000 - 12,600 = $5,400, and 5,400 / 18,000 = 0.30. Percent change is always measured against the original amount.

A tank that holds 240 gallons is five-eighths full. How many gallons are needed to fill it?

• a.90 gallons✓
• b.150 gallons
• c.96 gallons
• d.60 gallons

If the tank is 5/8 full, it is 3/8 empty. One-eighth of 240 is 30, so 3/8 is 3 x 30 = 90 gallons.

Three pounds of coffee cost $26.85. At the same rate, what do 7 pounds cost?

• a.$53.70
• b.$71.60
• c.$80.55
• d.$62.65✓

One pound costs 26.85 / 3 = $8.95, and 8.95 x 7 = $62.65. Multiplying the 3-pound price by 7 would overcount.

A rectangular field measures 120 feet by 75 feet. Fencing costs $4 per foot. What is the cost to fence the field?

• a.$1,170
• b.$1,950
• c.$1,560✓
• d.$2,340

The perimeter is 2 x (120 + 75) = 390 feet, and 390 x $4 = $1,560. Fencing follows the perimeter, not the area.

A stock recipe calls for 2.5 quarts of broth. How many cups is that?

• a.8 cups
• b.20 cups
• c.10 cups✓
• d.5 cups

One quart equals 4 cups, so 2.5 x 4 = 10 cups.

Twelve people share equally the cost of a $282 rental plus a $54 cleaning fee. How much does each person pay?

• a.$33.60
• b.$23.50
• c.$32.00
• d.$28.00✓

The total is 282 + 54 = $336, and 336 / 12 = $28.00. The cleaning fee has to be added before dividing.

Enrollment in a program rose from 250 students to 320 students. What was the percent increase?

• a.25%
• b.22%
• c.35%
• d.28%✓

The increase is 320 - 250 = 70 students, and 70 / 250 = 0.28. Dividing by the new total instead of the old one is the common error.

A machine produces 45 parts per hour. How many parts does it produce in 7 hours 20 minutes?

• a.330 parts✓
• b.315 parts
• c.345 parts
• d.320 parts

Twenty minutes is one-third of an hour, so the run is 7 1/3 hours. That gives 45 x 7 = 315 parts plus 15 more, or 330.

A convoy leaves at 0800 and arrives at 1345 after covering 322 miles. What was its average speed?

• a.62 mph
• b.58 mph
• c.52 mph
• d.56 mph✓

From 0800 to 1345 is 5 hours 45 minutes, or 5.75 hours. Then 322 / 5.75 = 56, and 56 x 5.75 = 322 confirms it.

A $60 item is discounted 20 percent, and then 8 percent sales tax is added to the discounted price. What is the final total?

• a.$49.92
• b.$54.24
• c.$51.84✓
• d.$55.20

The discount brings the price to 60 x 0.80 = $48.00. Tax adds 48 x 0.08 = $3.84, for a total of $51.84.

Renting a ladder costs $22 for the first day and $9.50 for each day after that. What is the charge for 6 days?

• a.$69.50✓
• b.$57.00
• c.$84.50
• d.$79.00

Five days follow the first, so 5 x $9.50 = $47.50. Adding the $22 first day gives $69.50.

A 40-pound bag of trail mix is 15 percent peanuts by weight. How many pounds of peanuts does it contain?

• a.8 pounds
• b.15 pounds
• c.4 pounds
• d.6 pounds✓

Ten percent of 40 is 4 pounds and 5 percent is 2 pounds, so 15 percent is 6 pounds.

A worker earns $2,150 per month before deductions, and 18 percent is withheld. What is the monthly take-home pay?

• a.$2,537
• b.$1,935
• c.$1,763✓
• d.$1,802

The withholding is 2,150 x 0.18 = $387, and 2,150 - 387 = $1,763. Taking 82 percent of $2,150 directly gives the same figure.

A board 9 1/2 feet long is cut into pieces 1 1/4 feet long. How many whole pieces can be cut?

• a.9 pieces
• b.6 pieces
• c.8 pieces
• d.7 pieces✓

Dividing 9.5 by 1.25 gives 7.6, so only 7 full pieces come out of the board and a remainder is left over.

On a map, 1 inch represents 24 miles. Two towns are 3.75 inches apart on the map. How far apart are they?

• a.72 miles
• b.84 miles
• c.96 miles
• d.90 miles✓

Multiply the map distance by the scale: 24 x 3.75 = 90 miles. That is 24 x 3 = 72 plus 24 x 0.75 = 18.

A store sells pens at 3 for $2.10. What is the cost of 14 pens at the same rate?

• a.$9.80✓
• b.$10.50
• c.$8.40
• d.$9.10

Each pen costs 2.10 / 3 = $0.70, and 0.70 x 14 = $9.80.

Five deliveries averaged 62 pounds. Four of them weighed 55, 71, 48, and 66 pounds. What did the fifth weigh?

• a.60 pounds
• b.68 pounds
• c.70 pounds✓
• d.74 pounds

Five deliveries averaging 62 pounds total 310 pounds. The four listed weigh 240 pounds, so the fifth is 310 - 240 = 70 pounds.

A pump moves 12 gallons per minute. How long will it take to fill a 1,080-gallon tank?

• a.90 minutes✓
• b.120 minutes
• c.75 minutes
• d.108 minutes

Time equals volume divided by rate: 1,080 / 12 = 90 minutes. Checking, 12 x 90 = 1,080.

A town of 8,000 people grows 5 percent in one year and another 5 percent the next year. What is the population after two years?

• a.8,800
• b.9,000
• c.8,400
• d.8,820✓

After the first year the town has 8,000 x 1.05 = 8,400 people. The second 5 percent is taken on 8,400, adding 420 for a total of 8,820.

A generator uses 3/4 gallon of coolant for every 6 hours it runs. How much does it use in 10 hours?

• a.1.00 gallons
• b.1.50 gallons
• c.2.00 gallons
• d.1.25 gallons✓

Per hour the generator uses 0.75 / 6 = 0.125 gallon, and 0.125 x 10 = 1.25 gallons.

A shift begins at 2245 and ends at 0715 the following morning. How long is the shift?

• a.8 hours 15 minutes
• b.9 hours 30 minutes
• c.7 hours 30 minutes
• d.8 hours 30 minutes✓

From 2245 to midnight is 1 hour 15 minutes, and midnight to 0715 is 7 hours 15 minutes. Together that is 8 hours 30 minutes.

A vendor buys 200 shirts for $6 each and sells 175 of them at $14 each. What is the profit?

• a.$1,450
• b.$2,450
• c.$1,250✓
• d.$1,050

Revenue is 175 x $14 = $2,450, but the cost covers all 200 shirts at $6, or $1,200. Profit is 2,450 - 1,200 = $1,250.

An award of $840 is divided among three people in the ratio 3 to 4 to 5. How much does the person with the largest share receive?

• a.$210
• b.$420
• c.$350✓
• d.$280

The ratio has 3 + 4 + 5 = 12 parts, so each part is 840 / 12 = $70. The largest share is 5 x $70 = $350.

A generator burns 0.8 gallon of fuel per hour and runs from 0600 until 1830. How much fuel does it burn?

• a.11.2 gallons
• b.12.5 gallons
• c.9.6 gallons
• d.10.0 gallons✓

From 0600 to 1830 is 12.5 hours, and 12.5 x 0.8 = 10.0 gallons.

Brand A sells 18 ounces for $4.32 and Brand B sells 24 ounces for $5.52. How much less per ounce is the cheaper brand?

• a.$0.01✓
• b.$0.03
• c.$0.02
• d.$0.05

Brand A costs 4.32 / 18 = $0.24 per ounce and Brand B costs 5.52 / 24 = $0.23 per ounce, a difference of $0.01 per ounce.

A room measures 14 feet by 18 feet. Carpet is sold by the square yard. How many square yards are needed?

• a.32 square yards
• b.24 square yards
• c.36 square yards
• d.28 square yards✓

The floor is 14 x 18 = 252 square feet. One square yard is 9 square feet, so 252 / 9 = 28 square yards.

Five machines fill 300 boxes in 2 hours. At the same rate, how many boxes will 8 machines fill in 3 hours?

• a.640 boxes
• b.480 boxes
• c.900 boxes
• d.720 boxes✓

One machine fills 300 / (5 x 2) = 30 boxes per hour. Eight machines for 3 hours give 30 x 8 x 3 = 720 boxes.

What is a 15 percent tip on a bill of $46.40?

• a.$9.28
• b.$7.42
• c.$5.80
• d.$6.96✓

Ten percent of $46.40 is $4.64 and 5 percent is half of that, $2.32. Together the tip is $6.96.

A saver deposits $45 the first week and increases the deposit by $5 each following week. How much has been deposited after six weeks?

• a.$315
• b.$370
• c.$330
• d.$345✓

The deposits are 45, 50, 55, 60, 65, and 70. That is six deposits of $45 plus 5 x (1+2+3+4+5) = $75, for $345.

A car with a 16-gallon tank averages 27 miles per gallon. How far can it travel on a full tank?

• a.405 miles
• b.432 miles✓
• c.448 miles
• d.486 miles

Range equals gallons times miles per gallon: 16 x 27 = 432 miles.

Of 450 recruits, 60 percent are men, and 20 percent of the men wear glasses. How many men wear glasses?

• a.54 recruits✓
• b.108 recruits
• c.45 recruits
• d.90 recruits

There are 450 x 0.60 = 270 men, and 20 percent of 270 is 54. The second percentage applies to the men only, not to all 450.

A shipment of 1,250 items has a defect rate of 4 percent. How many items are not defective?

• a.1,200 items✓
• b.1,206 items
• c.1,150 items
• d.1,246 items

Four percent of 1,250 is 50 defective items, so 1,250 - 50 = 1,200 are good.

A driver travels 2 hours at 55 miles per hour and then 3 hours at 65 miles per hour. What was the average speed for the whole trip?

• a.63 mph
• b.61 mph✓
• c.60 mph
• d.58 mph

The distance is 110 + 195 = 305 miles over 5 hours, so 305 / 5 = 61 mph. Averaging 55 and 65 ignores that more time was spent at the faster speed.

A shopper pays with a $50 bill for items costing $12.75, $8.40, and $19.99. How much change is due?

• a.$9.16
• b.$7.86
• c.$8.86✓
• d.$8.14

The items total $41.14, and 50.00 - 41.14 = $8.86.

A batch that feeds 48 people uses 6 pounds of rice. How much rice is needed for 20 people?

• a.2.0 pounds
• b.2.5 pounds✓
• c.3.0 pounds
• d.3.5 pounds

Each person needs 6 / 48 = 0.125 pound, and 0.125 x 20 = 2.5 pounds.

An account pays 0.5 percent simple interest per month. How much interest does $500 earn in 8 months?

• a.$25.00
• b.$20.00✓
• c.$12.50
• d.$40.00

Each month earns 500 x 0.005 = $2.50, and $2.50 x 8 = $20.00.

A truck has a load limit of 2,000 pounds and is carrying 46 crates weighing 38 pounds each. How many more pounds may it carry?

• a.152 pounds
• b.232 pounds
• c.252 pounds✓
• d.348 pounds

The crates weigh 46 x 38 = 1,748 pounds, so 2,000 - 1,748 = 252 pounds remain.

Two-fifths of a class of 35 students chose the morning shift and the rest chose evenings. How many chose evenings?

• a.21 students✓
• b.25 students
• c.18 students
• d.14 students

If 2/5 chose mornings, then 3/5 chose evenings. One-fifth of 35 is 7, so 3/5 is 21 students.

A copier prints 22 pages per minute for 9 minutes, jams for 4 minutes, then prints at the same rate for 6 more minutes. How many pages are printed?

• a.264 pages
• b.330 pages✓
• c.198 pages
• d.418 pages

The copier actually prints for 9 + 6 = 15 minutes, so 22 x 15 = 330 pages. The 4-minute jam produces nothing.

After a 20 percent discount, a coat costs $96. What was the original price?

• a.$108.00
• b.$124.80
• c.$120.00✓
• d.$115.20

The sale price is 80 percent of the original, so the original is 96 / 0.80 = $120.00. Checking, 20 percent of $120 is $24, and 120 - 24 = 96.

A garden 20 feet by 30 feet is bordered by a walkway 3 feet wide on all sides. What is the area of the walkway alone?

• a.396 square feet
• b.276 square feet
• c.306 square feet
• d.336 square feet✓

The walkway adds 3 feet on each side, making the outer rectangle 26 by 36, or 936 square feet. Subtracting the 600-square-foot garden leaves 336.

A driver covers 60 miles at 30 miles per hour and returns over the same 60 miles at 60 miles per hour. What is the average speed for the round trip?

• a.40 mph✓
• b.45 mph
• c.36 mph
• d.48 mph

The outbound leg takes 2 hours and the return takes 1 hour, so 120 miles are covered in 3 hours, or 40 mph. Averaging 30 and 60 to get 45 ignores the unequal times.

A box holds 24 red markers, 16 blue markers, and 40 green markers. What percent of the markers are blue?

• a.25%
• b.20%✓
• c.16%
• d.18%

There are 80 markers in all, and 16 / 80 = 0.20.

Abate most nearly means

• a.subside✓
• b.conclude
• c.repeat
• d.enlarge

To abate is to lessen or die down, as a storm abates. Enlarge is its opposite, and the other choices describe different actions entirely.

The sergeant gave a terse reply. Terse most nearly means

• a.brief✓
• b.loud
• c.rude
• d.long-winded

Terse describes speech that is short and to the point. It can sound abrupt, but the meaning is about length rather than politeness or volume.

Lenient most nearly means

• a.punctual
• b.tolerant✓
• c.strict
• d.unforgiving

A lenient supervisor is easygoing about the rules and slow to punish. Strict and unforgiving both point the other way.

Candid most nearly means

• a.hidden
• b.clumsy
• c.formal
• d.frank✓

A candid remark is honest and unguarded. Hidden is the reverse, and formal describes tone rather than honesty.

Deter most nearly means

• a.determine
• b.deteriorate
• c.postpone
• d.discourage✓

To deter is to prevent someone from acting by making the action unattractive. Postponing an act only delays it, and the other choices concern deciding and decaying.

Frugal most nearly means

• a.thrifty✓
• b.hungry
• c.careless
• d.wealthy

A frugal person spends sparingly. Wealth is unrelated, since a rich person may be frugal and a poor person may not be.

The bridge was declared obsolete. Obsolete most nearly means

• a.unstable
• b.crowded
• c.outdated✓
• d.expensive

Something obsolete has been replaced by something newer and is no longer in use. An obsolete item may still be perfectly sound structurally.

Meager most nearly means

• a.scant✓
• b.steady
• c.bright
• d.heavy

Meager means small in amount and less than is needed, as in a meager portion.

Placid most nearly means

• a.sour
• b.flat
• c.calm✓
• d.tense

Placid describes something untroubled and still, such as a placid lake or a placid temperament. Tense is its opposite.

Taut most nearly means

• a.tight✓
• b.sudden
• c.damp
• d.hollow

A taut rope is pulled tight with no slack left in it. The word says nothing about moisture, weight, or speed.

Vigilant most nearly means

• a.truthful
• b.cheerful
• c.restless
• d.watchful✓

A vigilant sentry stays alert for danger. Restless describes an inability to keep still, which is a different idea.

Fledgling most nearly means

• a.soldier
• b.specialist
• c.beginner✓
• d.teacher

A fledgling bird has only just left the nest, and the word carries over to anyone just starting out. A specialist sits at the opposite end of the same scale.

Fog began to shroud the harbor. Shroud most nearly means

• a.carry
• b.clean
• c.find
• d.hide✓

To shroud something is to cover it so that it cannot be seen. Find is roughly its opposite.

Diligent most nearly means

• a.forgetful
• b.talkative
• c.hardworking✓
• d.unpredictable

A diligent worker applies steady, careful effort. The word describes effort, not results or personality.

The corporal's account of the incident was accurate. Accurate most nearly means

• a.correct✓
• b.recent
• c.lengthy
• d.unusual

An accurate account matches the facts. Its length and how recently it was given say nothing about whether it is right.

Adjacent most nearly means

• a.distant
• b.neighboring✓
• c.concealed
• d.crooked

Adjacent things lie next to each other, as in adjacent rooms. Distant is its opposite.

Potent most nearly means

• a.gentle
• b.clever
• c.hollow
• d.strong✓

A potent dose or a potent argument carries great force or effect. Gentle suggests the opposite kind of strength.

Perilous most nearly means

• a.risky✓
• b.doubtful
• c.pleasant
• d.lengthy

A perilous route is one that puts a traveler at risk. Doubtful concerns uncertainty rather than danger.

Halt most nearly means

• a.climb
• b.join
• c.rush
• d.stop✓

To halt is to bring movement to an end, as a column halts on command. Rush points the opposite way.

Reluctant most nearly means

• a.prompt
• b.capable
• c.hesitant✓
• d.enthusiastic

A reluctant volunteer holds back. Enthusiastic is its opposite, and capable concerns ability rather than willingness.

Lethargy most nearly means

• a.irritation
• b.tiredness✓
• c.hunger
• d.muscle

Lethargy is a heavy lack of energy and unwillingness to move. Hunger and irritation are different states entirely.

Void most nearly means

• a.narrow
• b.hidden
• c.filled
• d.empty✓

A void space contains nothing at all. Filled is its opposite, and the other choices describe shape and visibility.

Summit most nearly means

• a.border
• b.peak✓
• c.valley
• d.meadow

The summit is the highest point of a mountain. Valley is the low ground between mountains.

Ponder most nearly means

• a.consider✓
• b.release
• c.forget
• d.measure

To ponder is to think something over carefully before acting.

Legible most nearly means

• a.breakable
• b.lawful
• c.spoken
• d.readable✓

Legible handwriting can be made out easily. Lawful sounds similar to legal but is a different word family from legible.

Barren most nearly means

• a.bare✓
• b.rocky
• c.muddy
• d.green

Barren land produces little or no vegetation. Rocky ground can still support plants, so it is not the same idea.

Congregate most nearly means

• a.inspect
• b.deliver
• c.disperse
• d.gather✓

To congregate is to come together in a crowd. Disperse is its opposite, describing a crowd breaking up.

The colonel issued a stern warning. Stern most nearly means

• a.vague
• b.final
• c.harsh✓
• d.brief

A stern warning is severe and unsmiling in tone. It may be short, but shortness is not what the word means.

Prudent most nearly means

• a.generous
• b.wealthy
• c.sensible✓
• d.stubborn

A prudent decision shows good judgment and forethought about consequences.

Detect most nearly means

• a.gather
• b.forbid
• c.notice✓
• d.repair

To detect is to discover the presence of something, often something faint or concealed.

Endorse most nearly means

• a.question
• b.support✓
• c.delay
• d.cancel

To endorse a plan is to give it public backing. The word also means to sign the back of a check, which is a form of approval.

Sever most nearly means

• a.soak
• b.bend
• c.cut✓
• d.join

To sever is to cut something apart completely. Join is its opposite.

Robust most nearly means

• a.sturdy✓
• b.fragile
• c.hollow
• d.hasty

Robust means strong and healthy, or strongly built. Fragile is its opposite.

Ration most nearly means

• a.shortage
• b.container
• c.surplus
• d.allotment✓

A ration is a fixed share handed out to one person. A shortage may be the reason rations are issued, but the word names the share itself.

Erratic most nearly means

• a.gradual
• b.precise
• c.permanent
• d.unsteady✓

Erratic behavior is irregular and unpredictable. Gradual describes a steady rate of change, which is nearly the reverse.

Comply most nearly means

• a.argue
• b.boast
• c.plead
• d.obey✓

To comply is to act in accordance with an order or a rule. Argue points the other way.

Ascend most nearly means

• a.fall
• b.drift
• c.rise✓
• d.pause

To ascend is to move upward. Fall is its opposite, and drift carries no sense of direction.

Hoist most nearly means

• a.lift✓
• b.clamp
• c.drop
• d.twist

To hoist is to raise a load, usually with a rope, pulley, or crane.

Immerse most nearly means

• a.submerge✓
• b.evaporate
• c.decorate
• d.sprinkle

To immerse is to put something completely under a liquid. Sprinkling wets only the surface.

Sparse most nearly means

• a.rough
• b.dense
• c.plain
• d.thin✓

Sparse describes things thinly scattered, such as sparse vegetation. Dense is its opposite.

The recruit showed remarkable poise under pressure. Poise most nearly means

• a.determination
• b.talent
• c.composure✓
• d.strength

Poise is calm self-possession in a difficult moment. Strength and talent describe capability rather than steadiness.

Hasten most nearly means

• a.stroll
• b.hurry✓
• c.delay
• d.linger

To hasten is to move or act quickly, or to make something happen sooner. Delay and linger both point the opposite way.

Obstruct most nearly means

• a.block✓
• b.repair
• c.permit
• d.follow

To obstruct is to get in the way of movement or progress. Permit is its opposite.

Trivial most nearly means

• a.dangerous
• b.expensive
• c.temporary
• d.unimportant✓

A trivial detail carries little weight. Temporary concerns duration, not importance.

Wary most nearly means

• a.cautious✓
• b.good-natured
• c.weary
• d.reckless

To be wary is to be on guard against trouble. Weary looks almost identical but means tired.

Convene most nearly means

• a.postpone
• b.announce
• c.assemble✓
• d.adjourn

To convene a meeting is to bring it together. Adjourn is the opposite act of ending one.

A crew chief keeps a maintenance log for every aircraft in the squadron. The log records not only repairs but also the hours flown since each part was installed. Because parts are replaced on a schedule tied to flight hours rather than to the calendar, an aircraft that flies rarely may keep a part far longer than one flown daily. According to the passage, replacement of parts is scheduled by

• a.hours flown✓
• b.repair history
• c.squadron size
• d.calendar date

The passage states that parts are replaced on a schedule tied to flight hours rather than to the calendar. Repairs are recorded in the log but are not what sets the schedule.

Sea fog forms when warm, moist air drifts over water that is colder than the air. The water chills the lowest layer of air until the moisture in it condenses into droplets. This is why fog is common where a warm current meets a cold one, and why it often burns off once the sun warms the air above the dew point. The passage indicates that sea fog requires

• a.water warmer than the air
• b.a steady offshore wind
• c.rain earlier in the day
• d.air warmer than the water✓

The first sentence says fog forms when warm, moist air drifts over colder water. Wind and rain are not mentioned as requirements.

Many people believe that a heavier bat will always drive a baseball farther. In practice, a bat that is too heavy slows a batter's swing enough to cancel the advantage. The best bat for any given player is the heaviest one that the player can still swing at full speed. The main point of the passage is that

• a.the right bat weight varies✓
• b.heavier bats hit the ball farther
• c.light bats suit most players
• d.swing speed is not important

The passage rejects the blanket rule about heavy bats and concludes that the right weight depends on the individual batter's swing speed.

The first lighthouses burned wood in open baskets, and their keepers spent the night hauling fuel up the tower stairs. Oil lamps replaced the baskets, and lenses were added to gather the light into a narrow beam. Modern towers use electric lamps and need no keeper at all. Each step made the light stronger and the labor of tending it smaller. The passage is mainly about

• a.the daily life of a keeper
• b.why lighthouses were built
• c.the danger of rocky coasts
• d.lighthouse light over time✓

Each sentence traces a stage in how the light itself was produced, from wood fires to electric lamps. The keeper's labor is mentioned only in support of that history.

A supervisor who corrects a worker in front of the whole crew may win the argument and lose the worker. Criticism delivered privately is far more likely to be acted on, because the worker is not defending his standing in front of others at the same time. The passage suggests that public criticism fails mainly because it

• a.takes too much of the day
• b.goes unheard by the whole crew
• c.is usually factually wrong
• d.forces the worker to save face✓

The passage explains that a publicly corrected worker is simultaneously defending his standing before others, which is what blocks the correction from being acted on.

Concrete gains strength for weeks after it is poured, but it gains that strength only while it stays damp. A slab left to dry in hot sun may reach less than half the strength of one kept wet for a week. Crews therefore cover fresh slabs with plastic sheeting or spray them at intervals. According to the passage, covering a fresh slab is done to

• a.protect it from traffic
• b.keep the surface level
• c.speed up the pour
• d.keep the concrete damp✓

The passage says concrete gains strength only while it stays damp, and that sheeting and spraying are the crew's response to that fact.

Bamboo is a grass, not a tree, though some species grow taller than a four-story building. Because a grass stem is hollow and jointed, bamboo bends far more than a solid trunk of the same thickness, which is one reason it survives storms that break hardwoods. The passage explains that bamboo survives storms because it

• a.bends instead of breaking✓
• b.grows back very quickly
• c.has unusually deep roots
• d.is shorter than hardwoods

The passage attributes the survival to the hollow, jointed stem that lets bamboo bend more than a solid trunk. Root depth and regrowth are not discussed.

A clerk was told to file the invoices by vendor, then by date within each vendor. She filed them by date alone, reasoning that it would be faster to find a recent invoice that way. When the accounting office asked for every invoice from one supplier, the whole file had to be searched. The passage best illustrates that

• a.dates are poor labels
• b.orders can have a reason✓
• c.clerks resent extra work
• d.filing wastes office time

The clerk's shortcut looked reasonable until the request that the original instruction anticipated arrived. The passage is about the hidden reason behind the order.

Salt lowers the temperature at which water freezes, which is why crews spread it on winter roads. Below about minus 10 degrees Fahrenheit, however, salt loses most of its effect, and crews switch to sand. Sand does not melt anything; it simply gives tires something to grip. According to the passage, sand is used on very cold roads because

• a.salt loses its effect✓
• b.sand melts ice faster
• c.sand is much less costly
• d.salt damages the pavement

The passage says salt loses most of its effect below about minus 10 degrees, which is why crews switch to sand. Sand is described as providing grip rather than melting.

The word budget once meant a leather pouch. An English official who presented the year's finances was said to open his budget, meaning that he opened the bag holding his papers. Over time the name of the bag came to mean the plan inside it. In this passage, the word budget originally referred to

• a.a public speech
• b.a yearly report
• c.a leather bag✓
• d.a tax collector

The first sentence states directly that budget once meant a leather pouch, and the rest explains how the meaning shifted to the plan.

Night vision depends on rod cells, which sit mostly around the edge of the retina rather than at its center. That is why a dim star is easier to see when you look slightly to one side of it than when you stare straight at it. Sailors and astronomers both learn this trick early. The passage suggests that to see a faint object at night you should

• a.stare directly at it
• b.use a brighter light
• c.look slightly aside✓
• d.close one eye first

Because rod cells cluster away from the center of the retina, the passage says a dim star is easier to see when you look slightly to one side.

Apprenticeship differs from classroom training in one important way: the apprentice produces real work from the first week. The work is slow and closely supervised at first, and the employer accepts that cost in exchange for a worker trained to the shop's own methods. According to the passage, the employer's return on an apprenticeship is

• a.lower insurance premiums
• b.a worker trained to its methods✓
• c.a shorter training period
• d.cheap labor from the very first day

The passage names the exchange explicitly: the employer accepts early inefficiency in return for a worker trained to the shop's own methods.

A rip current is a narrow channel of water flowing away from the beach. Swimmers who try to fight one head-on tire quickly, because the current can move faster than a person can swim. Swimming parallel to the shore takes the swimmer out of the narrow channel within a short distance. The passage indicates that a swimmer caught in a rip current should

• a.dive beneath the current
• b.swim parallel to the shore✓
• c.swim straight toward dry land
• d.float until it weakens

The passage contrasts fighting the current head-on with swimming parallel to the shore, which leaves the narrow channel quickly.

In a factory that runs three shifts, the machines never cool down. Tools that would last a year in a single-shift shop wear out in four months, and a breakdown on the night shift costs as much as one at noon. Maintenance in such a plant is scheduled rather than waited for. The passage explains that maintenance is scheduled in three-shift plants because

• a.night crews are less skilled
• b.spare parts are scarce
• c.machines are more complex
• d.wear accumulates far faster✓

The passage gives continuous running and the resulting rapid tool wear as the reason maintenance cannot simply wait for failures.

Sourdough bread rises without commercial yeast. A baker keeps a starter, a mixture of flour and water in which wild yeast and bacteria live, and feeds it with fresh flour. The bacteria produce the acids that give the bread its tang, and the yeast produces the gas that lifts the loaf. According to the passage, the sour taste comes from

• a.bacteria in the starter✓
• b.the flour that is used
• c.the yeast in the starter
• d.a long slow bake time

The passage divides the work: the bacteria make the acids that give the tang, while the yeast makes the gas that lifts the loaf.

Anyone who has moved a heavy chest alone knows that pushing it is harder than sliding it on a rug. The rug does not make the chest lighter. It replaces the grip between wood and floor with a much smaller grip between rug and floor. The passage says the rug helps because it

• a.spreads the load
• b.reduces friction✓
• c.protects the floor
• d.reduces weight

The passage states that the rug does not make the chest lighter and that it replaces a large grip with a much smaller one, which is a description of reduced friction.

Written safety rules are often blamed for slowing work down. In fact most were written after an injury, and each one marks a specific accident that someone did not walk away from. A rule that seems pointless usually seems that way because the accident behind it has been forgotten. The author's attitude toward safety rules is best described as

• a.scornful
• b.alarmed
• c.positive✓
• d.undecided

The author answers the criticism by explaining that each rule records a real injury, which is a defense of the rules rather than a complaint about them.

A carpenter measuring a long wall in stages will accumulate a small error at every mark. Measuring from a single fixed end each time avoids this, because each mark is then taken from the same starting point and no error is passed along. The passage recommends measuring from one fixed end in order to

• a.save some measuring time
• b.avoid accumulated error✓
• c.mark the wall more lightly
• d.use a much shorter tape

The passage contrasts staged measurement, which passes each small error along, with measuring from a single fixed point, which does not.

Aluminum resists corrosion not because it is unreactive but because it is extremely reactive. It combines with oxygen almost instantly, and the thin oxide layer that forms seals the metal underneath. Scratch the surface and a new layer forms in seconds. According to the passage, aluminum is protected by

• a.a layer of its own oxide✓
• b.its low reactivity
• c.a coat of applied paint
• d.the density of the metal

The passage says the thin oxide layer formed when aluminum meets oxygen seals the metal underneath and reforms when scratched.

The clerk's report contained no errors of fact, yet the committee sent it back twice. Figures appeared in one order in the tables and another in the summary, and two sections used different names for the same account. Accuracy, the chairman noted, is not the same thing as clarity. The report was returned because it was

• a.inaccurate
• b.unsubstantiated
• c.inconsistent✓
• d.incomplete

The passage states the facts were correct but that the ordering and the naming disagreed between sections, which is an inconsistency rather than an error.

Desert animals rarely drink. Many get all the water they need from their food, and some produce water inside their own bodies by breaking down fat. The kangaroo rat can live its whole life without taking a single drink. According to the passage, some desert animals obtain water by

• a.digging for shallow wells
• b.breaking down body fat✓
• c.licking dew from plants
• d.storing rain in burrows

The passage names two sources, food and the breakdown of fat inside the body. Dew and stored rain are not mentioned.

A ship's compass is thrown off by the iron in the ship itself. Navigators correct for this with small magnets and iron spheres placed near the compass, adjusted until the error nearly disappears. The remaining error is written on a card and consulted on every heading. The passage indicates that compass error on a steel ship is

• a.ignored in everyday practice
• b.eliminated altogether
• c.different for each crew
• d.reduced and then recorded✓

The correction reduces the error until it nearly disappears, and what remains is written on a card for use on every heading.

Coral reefs cover less than one percent of the ocean floor but shelter roughly a quarter of all marine species. The coral animal builds a stone skeleton, and generations of skeletons stack into a structure full of crevices. It is the crevices, more than the coral itself, that make the reef so crowded. The passage attributes the variety of reef life mainly to

• a.the many hiding places✓
• b.the warmth of the water
• c.the clarity of the water
• d.the coral animal's diet

The final sentence says it is the crevices, more than the coral itself, that make the reef so crowded.

A driver who brakes hard for every red light burns more fuel than one who lifts off the accelerator early and coasts. Braking turns motion into heat and throws it away. Coasting converts the same motion into distance covered. The passage explains that hard braking wastes fuel because it

• a.wastes energy as heat✓
• b.requires a lower gear
• c.wears the brake pads
• d.shortens the trip time

The passage says braking turns motion into heat and throws it away, while coasting converts the same motion into distance.

The Roman army marched on roads built for its own supply wagons, not for trade. Merchants used them anyway, and towns grew where the roads crossed. Within two centuries the network built to move soldiers had reshaped where ordinary people lived. The passage suggests that the roads' most lasting effect was

• a.on military victories
• b.on settlement patterns✓
• c.on wagon design
• d.on Roman legal practice

The passage ends by noting that the network reshaped where ordinary people lived, which is the lasting effect it identifies.

A thermos keeps coffee hot with a vacuum between two walls of glass or steel. Heat cannot travel by conduction or convection through a vacuum because there is nothing there to carry it. The silvered surfaces handle the third route by reflecting radiant heat back inside. According to the passage, the silvering of a thermos deals with

• a.escaping steam
• b.radiant heat✓
• c.convected heat
• d.conducted heat

The vacuum stops conduction and convection; the passage assigns the silvering to the third route, radiant heat.

New employees are often told to ask questions freely, and then find that the people they must ask are the busiest in the building. A better practice is to name one person whose job explicitly includes answering them, so that the newcomer is not weighing his own confusion against someone else's deadline. The passage recommends that an employer

• a.shorten the training period
• b.assign a designated helper✓
• c.hire more experienced staff
• d.reduce the questions asked

The passage proposes naming one person whose job explicitly includes answering a newcomer's questions.

Standard time zones did not exist until the railroads demanded them. Before that each town set its clocks by the local noon, so a traveler moving west found the clock behind him at every stop. Timetables were impossible to print until the country agreed on shared time. According to the passage, time zones were adopted because of

• a.railroad timetables✓
• b.shipping routes
• c.telegraph service
• d.astronomical research

The passage says the railroads demanded standard time and that timetables could not be printed until the country agreed on shared time.

A good tourniquet is applied tightly enough to stop the bleeding entirely. One applied halfway may block the veins returning blood to the heart while leaving the arteries open, so that the limb keeps filling and the bleeding grows worse rather than better. The passage warns that a loosely applied tourniquet may

• a.damage the nerves
• b.increase the bleeding✓
• c.slip out of its position
• d.become contaminated

The passage explains that blocking the veins while leaving the arteries open makes the bleeding worse rather than better.

For fifty years the standard advice was to keep a wound dry and open to the air. Studies then showed that cells rebuilding skin move faster across a moist surface, and covered wounds began to be seen as healing better than uncovered ones. The advice reversed on the strength of evidence. The passage is mainly concerned with

• a.the structure of skin
• b.the cost of bandages
• c.a change in advice✓
• d.the causes of infection

The passage traces how the standard recommendation reversed once evidence about moist healing appeared.

Solve for x: 3x - 7 = 20

• a.9✓
• b.7
• c.11
• d.13

Add 7 to both sides to get 3x = 27, then divide by 3 to get x = 9. Substituting back, 3(9) - 7 = 20.

Solve for x: 5(x + 2) = 45

• a.9
• b.11
• c.7✓
• d.5

Divide both sides by 5 to get x + 2 = 9, so x = 7. Checking, 5(7 + 2) = 5(9) = 45.

What is the value of 4 cubed minus 2 to the fourth power?

• a.56
• b.32
• c.48✓
• d.40

Four cubed is 64 and 2 to the fourth is 16, so 64 - 16 = 48.

Simplify: (x^5)(x^3)

• a.x^15
• b.x^2
• c.2x^8
• d.x^8✓

Multiplying powers of the same base adds the exponents, so 5 + 3 = 8 and the product is x^8. Testing with x = 2 gives 32 x 8 = 256, which is 2^8.

What is the area of a triangle with a base of 14 inches and a height of 9 inches?

• a.126 square inches
• b.46 square inches
• c.63 square inches✓
• d.105 square inches

The area of a triangle is one-half base times height: 0.5 x 14 x 9 = 63 square inches.

Using 22/7 for pi, what is the circumference of a circle whose diameter is 14 inches?

• a.154 inches
• b.22 inches
• c.44 inches✓
• d.88 inches

Circumference equals pi times the diameter: (22/7) x 14 = 44 inches. The value 154 would be the area, not the circumference.

Solve for y: 2y/3 = 12

• a.24
• b.12
• c.8
• d.18✓

Multiply both sides by 3 to get 2y = 36, then divide by 2 to get y = 18.

Which of the following is the factored form of x^2 - 9?

• a.(x + 3)(x - 3)✓
• b.(x - 3)(x - 3)
• c.(x + 3)(x + 3)
• d.(x + 9)(x - 1)

A difference of two squares factors as (x + 3)(x - 3). Testing at x = 5, the original is 16 and the factored form is 8 x 2 = 16.

What is 25 percent of three-fifths of 200?

• a.40
• b.50
• c.24
• d.30✓

Three-fifths of 200 is 120, and 25 percent of 120 is 30.

If a = 3 and b = -2, what is the value of a^2 - 2ab?

• a.-3
• b.9
• c.33
• d.21✓

a^2 is 9, and 2ab is 2(3)(-2) = -12. Subtracting a negative adds, so 9 + 12 = 21.

What is the slope of the line passing through the points (-1, 2) and (3, 14)?

• a.4
• b.2
• c.3✓
• d.6

Slope is the change in y over the change in x: (14 - 2) / (3 - (-1)) = 12 / 4 = 3.

What is the volume of a rectangular box measuring 5 inches by 4 inches by 3 inches?

• a.60 cubic inches✓
• b.47 cubic inches
• c.120 cubic inches
• d.12 cubic inches

Volume is length times width times height: 5 x 4 x 3 = 60 cubic inches.

Solve the inequality: 4x + 3 < 19

• a.x > 4
• b.x < 5.5
• c.x > 5.5
• d.x < 4✓

Subtract 3 to get 4x < 16, then divide by 4 to get x < 4. Dividing by a positive number leaves the inequality sign unchanged.

What is the square root of 144 plus the square root of 25?

• a.19
• b.169
• c.17✓
• d.13

The square root of 144 is 12 and the square root of 25 is 5, so the sum is 17.

A square has an area of 81 square feet. What is its perimeter?

• a.18 feet
• b.27 feet
• c.36 feet✓
• d.40 feet

The side of the square is the square root of 81, or 9 feet. The perimeter is 4 x 9 = 36 feet.

Simplify: 3(2x - 4) + 5x

• a.11x - 4
• b.11x - 12✓
• c.6x - 12
• d.11x + 12

Distributing gives 6x - 12, and adding 5x gives 11x - 12. Testing at x = 7, the original is 65 and 11(7) - 12 is also 65.

If 3^x = 81, what is the value of x?

• a.3
• b.4✓
• c.27
• d.9

Because 3 x 3 x 3 x 3 = 81, x is 4.

What is the sum of the interior angles of a pentagon?

• a.360 degrees
• b.720 degrees
• c.450 degrees
• d.540 degrees✓

The interior angles of an n-sided polygon sum to (n - 2) x 180 degrees, so a pentagon gives 3 x 180 = 540 degrees.

Which of the following numbers is prime?

• a.57
• b.61✓
• c.51
• d.69

The other three all divide by 3: 51 = 3 x 17, 57 = 3 x 19, and 69 = 3 x 23. Only 61 has no factors besides 1 and itself.

What is 3/8 written as a decimal?

• a.0.375✓
• b.0.625
• c.0.325
• d.0.380

Dividing 3 by 8 gives 0.375. The value 0.625 is 5/8, the complement of this fraction.

If x + y = 10 and x - y = 4, what is the value of y?

• a.7
• b.3✓
• c.6
• d.4

Subtracting the second equation from the first gives 2y = 6, so y = 3 and x = 7.

A right triangle has legs measuring 9 inches and 12 inches. How long is the hypotenuse?

• a.21 inches
• b.18 inches
• c.15 inches✓
• d.13 inches

By the Pythagorean theorem, 9^2 + 12^2 = 81 + 144 = 225, and the square root of 225 is 15.

Reduce the ratio 18:24 to lowest terms.

• a.3:4✓
• b.6:8
• c.2:3
• d.4:5

Both terms divide by 6, giving 3:4. The ratio 6:8 has the same value but is not in lowest terms.

What is the value of 5 factorial?

• a.20
• b.25
• c.720
• d.120✓

Five factorial is 5 x 4 x 3 x 2 x 1 = 120. The value 720 is 6 factorial.

Which values of x satisfy x^2 - 5x + 6 = 0?

• a.x = 2 or x = 3✓
• b.x = 5 or x = 6
• c.x = -2 or x = -3
• d.x = 1 or x = 6

The expression factors as (x - 2)(x - 3), so the roots are 2 and 3. Both must be positive because their product is +6 and their sum is +5.

Using 3.14 for pi, what is the area of a circle with a diameter of 10 inches?

• a.314.0 square inches
• b.62.8 square inches
• c.78.5 square inches✓
• d.31.4 square inches

The radius is half the diameter, or 5 inches. Area is pi times the radius squared: 3.14 x 25 = 78.5 square inches.

What is 8 percent of 350?

• a.28✓
• b.32
• c.42
• d.24

One percent of 350 is 3.5, so 8 percent is 8 x 3.5 = 28.

Simplify: (2x^3y^2)(4xy^4)

• a.8x^3y^8
• b.6x^4y^6
• c.2x^4y^6
• d.8x^4y^6✓

Multiply the coefficients, 2 x 4 = 8, and add the exponents of each variable: x^(3+1) and y^(2+4). Testing at x = 2 and y = 3 gives 93,312 both ways.

A rectangle has a perimeter of 46 inches and a length of 14 inches. What is its width?

• a.9 inches✓
• b.16 inches
• c.18 inches
• d.32 inches

Half the perimeter is one length plus one width, or 23 inches. Subtracting the 14-inch length leaves a width of 9 inches.

What is the median of the numbers 3, 11, 7, 2, and 9?

• a.6
• b.8
• c.9
• d.7✓

Put the numbers in order as 2, 3, 7, 9, 11 and take the middle value, which is 7. The mean of the same list is 6.4, not the median.

Solve for x: x/4 + 3 = 11

• a.32✓
• b.56
• c.24
• d.8

Subtract 3 to get x/4 = 8, then multiply by 4 to get x = 32.

Which of these fractions has the greatest value?

• a.7/12
• b.2/3✓
• c.3/5
• d.5/8

Written over a common denominator of 120 they are 75/120, 80/120, 70/120, and 72/120, so 2/3 is the largest.

What is the distance between the points (1, 2) and (7, 10)?

• a.14 units
• b.100 units
• c.10 units✓
• d.8 units

The horizontal change is 6 and the vertical change is 8, so the distance is the square root of 36 + 64 = 100, which is 10.

What is the square root of 50 in simplest radical form?

• a.2 times the square root of 5
• b.25 times the square root of 2
• c.5 times the square root of 2✓
• d.10 times the square root of 5

Since 50 = 25 x 2 and 25 is a perfect square, the root becomes 5 times the square root of 2, or about 7.07.

A number increased by 25 percent equals 90. What is the number?

• a.65
• b.70
• c.75
• d.72✓

The result is 125 percent of the number, so the number is 90 / 1.25 = 72. Checking, 25 percent of 72 is 18, and 72 + 18 = 90.

What is the value of (3^2)^3?

• a.27
• b.729✓
• c.243
• d.81

Raising a power to a power multiplies the exponents, giving 3^6 = 729.

In a right triangle, one acute angle measures 35 degrees. What does the other acute angle measure?

• a.55 degrees✓
• b.65 degrees
• c.45 degrees
• d.145 degrees

The two acute angles of a right triangle add to 90 degrees, so the second is 90 - 35 = 55 degrees.

What is the value of 8 + 2 x (6 - 2)^2 / 4?

• a.16✓
• b.12
• c.40
• d.24

Work inside the parentheses first: 6 - 2 = 4, and 4 squared is 16. Then 2 x 16 = 32, 32 / 4 = 8, and 8 + 8 = 16.

What is the reciprocal of 2/7?

• a.7/2✓
• b.1/7
• c.2/7
• d.-2/7

A reciprocal flips the numerator and denominator, so 2/7 becomes 7/2. Their product is 1.

Two triangles are similar. The smaller has sides of 3, 4, and 5 inches, and the larger has a shortest side of 12 inches. How long is the larger triangle's longest side?

• a.20 inches✓
• b.25 inches
• c.15 inches
• d.16 inches

The scale factor is 12 / 3 = 4, so every side is multiplied by 4. The longest side becomes 5 x 4 = 20 inches.

Solve for x: 2(x - 3) = x + 5

• a.16
• b.8
• c.14
• d.11✓

Distributing gives 2x - 6 = x + 5. Subtracting x from both sides and adding 6 gives x = 11.

Using 3.14 for pi, what is the volume of a cylinder with a radius of 3 inches and a height of 10 inches?

• a.282.6 cubic inches✓
• b.314.0 cubic inches
• c.188.4 cubic inches
• d.94.2 cubic inches

Volume equals pi times radius squared times height: 3.14 x 9 x 10 = 282.6 cubic inches.

What is 5/4 expressed as a percent?

• a.125%✓
• b.145%
• c.45%
• d.80%

Dividing 5 by 4 gives 1.25, and moving the decimal two places right gives 125 percent. Any fraction greater than 1 exceeds 100 percent.

If f(x) = 2x^2 - 3x, what is f(4)?

• a.20✓
• b.26
• c.12
• d.44

Substituting 4 gives 2(16) - 3(4) = 32 - 12 = 20.

The sum of three consecutive even integers is 78. What is the largest of the three?

• a.24
• b.28✓
• c.26
• d.30

Calling the smallest x gives 3x + 6 = 78, so x = 24 and the integers are 24, 26, and 28. Their sum checks out at 78.

What is 3/4 divided by 2/3?

• a.8/9
• b.1/2
• c.3/2
• d.9/8✓

Dividing by a fraction means multiplying by its reciprocal: 3/4 x 3/2 = 9/8.

Two angles are supplementary, and one is three times the size of the other. How large is the smaller angle?

• a.45 degrees✓
• b.60 degrees
• c.135 degrees
• d.30 degrees

Supplementary angles add to 180 degrees. Splitting 180 into 4 equal parts gives 45 for the smaller angle and 135 for the larger.

For x not equal to 3, simplify (x^2 - x - 6) / (x - 3).

• a.x + 3
• b.x - 6
• c.x + 2✓
• d.x - 2

The numerator factors as (x - 3)(x + 2), and the (x - 3) terms cancel. Testing at x = 10 gives 84 / 7 = 12, which matches 10 + 2.

What is the least common multiple of 12 and 18?

• a.216
• b.54
• c.36✓
• d.6

Multiples of 18 are 18, 36, 54, and 36 is the first one that 12 also divides. The value 6 is the greatest common factor, not the least common multiple.

A cube has a volume of 216 cubic inches. How long is one edge?

• a.36 inches
• b.6 inches✓
• c.12 inches
• d.8 inches

The edge is the cube root of the volume, and 6 x 6 x 6 = 216 inches.

Which component of blood carries oxygen to the tissues?

• a.white blood cells
• b.platelets
• c.blood plasma
• d.red blood cells✓

Red blood cells contain hemoglobin, the iron-bearing protein that binds oxygen. Platelets are involved in clotting and white cells in immune defense.

Which cell structure releases most of the energy a cell uses?

• a.the mitochondria✓
• b.the cell membrane
• c.the ribosomes
• d.the nucleus

Mitochondria carry out the reactions that convert food energy into ATP. Ribosomes build proteins and the nucleus stores genetic information.

At sea level, water boils at approximately what Fahrenheit temperature?

• a.180 degrees
• b.273 degrees
• c.100 degrees
• d.212 degrees✓

Water boils at 212 degrees Fahrenheit, which is 100 degrees Celsius. The figure 273 belongs to the Kelvin scale, where 273 K is the freezing point.

Which planet orbits closest to the sun?

• a.Jupiter
• b.Neptune
• c.Venus
• d.Mercury✓

Mercury holds the innermost orbit, with Venus next and Jupiter and Neptune far beyond Earth. Venus is the hotter planet even though it orbits farther out.

Which gas do plants take in from the air during photosynthesis?

• a.free oxygen gas
• b.nitrogen gas
• c.carbon dioxide✓
• d.hydrogen

Photosynthesis uses carbon dioxide and water to build sugar, releasing oxygen as a by-product. Plants take oxygen in for respiration, not for photosynthesis.

Which element makes up the greatest share of the Earth's crust by mass?

• a.oxygen✓
• b.silicon
• c.aluminum
• d.iron

Oxygen accounts for roughly 46 percent of the crust by mass, bound up in silicate and oxide minerals. Silicon is second at about 28 percent.

How many chromosomes are found in a normal human body cell?

• a.46✓
• b.64
• c.32
• d.23

A body cell holds 23 pairs, or 46 chromosomes. A sperm or egg cell carries half that number, 23.

Which of these animals is a vertebrate?

• a.earthworm
• b.frog✓
• c.jellyfish
• d.octopus

A vertebrate has a backbone, and a frog does. Earthworms, jellyfish, and octopuses have no internal skeleton of bone or cartilage.

Frequency is measured in which unit?

• a.hertz✓
• b.newtons
• c.watts
• d.joules

One hertz is one cycle per second. Newtons measure force, joules measure energy, and watts measure power.

About how fast does sound travel through air at room temperature?

• a.110,000 feet per second
• b.110 feet per second
• c.11,000 feet per second
• d.1,100 feet per second✓

Sound moves through air at roughly 1,100 feet per second, or about 760 miles per hour. That is why thunder lags several seconds behind the lightning flash.

Which of the following is a chemical change rather than a physical change?

• a.a rock being crushed
• b.iron rusting✓
• c.water boiling
• d.ice melting

Rusting produces a new substance, iron oxide, so it is a chemical change. Melting, boiling, and crushing change form or state without changing the substance.

A trait that appears only when an individual inherits two copies of the gene is described as

• a.environmental
• b.recessive✓
• c.acquired
• d.dominant

A recessive trait is masked whenever a dominant copy is present, so it shows only when both copies are recessive.

What causes the phases of the moon?

• a.its position relative to Earth and the sun✓
• b.changes in the moon's own brightness
• c.clouds in the Earth's own atmosphere
• d.the shadow of the Earth as it falls on it

Half the moon is lit at all times, and the phase is simply how much of that lit half faces Earth. The Earth's shadow causes a lunar eclipse, which is a separate event.

Nearly all of the Earth's weather occurs in which layer of the atmosphere?

• a.the thermosphere
• b.the stratosphere
• c.the troposphere✓
• d.the mesosphere

The troposphere is the lowest layer and holds most of the atmosphere's water vapor, so clouds and storms form there. The ozone layer sits above it in the stratosphere.

Through which of the following can sound not travel?

• a.liquid water
• b.humid air
• c.a vacuum✓
• d.solid steel

Sound is a pressure wave and needs particles to carry it, so it cannot cross a vacuum. It actually travels faster in water and steel than in air.

Which vitamin does the body make in skin exposed to sunlight?

• a.vitamin C
• b.vitamin K
• c.vitamin A
• d.vitamin D✓

Ultraviolet light converts a compound in the skin into vitamin D, which the body needs to absorb calcium.

What is the pH of a neutral solution?

• a.10
• b.7✓
• c.0
• d.14

On the 0 to 14 pH scale, 7 is neutral. Values below 7 are acidic and values above 7 are basic.

An animal that holds its body temperature steady regardless of its surroundings is called

• a.warm-blooded✓
• b.cold-blooded
• c.nocturnal
• d.invertebrate

Warm-blooded animals such as mammals and birds generate and regulate their own heat. Cold-blooded animals take on the temperature of their surroundings.

Which organ produces insulin?

• a.the pancreas✓
• b.the liver
• c.the kidneys
• d.the gall bladder

Cells in the pancreas release insulin, which lets the body's cells take up glucose from the blood.

Igneous rock is formed from

• a.cooled magma✓
• b.layers of compressed sediment
• c.existing rock under heat and pressure
• d.minerals left by evaporating water

Igneous rock solidifies from molten rock. Compressed sediment forms sedimentary rock, and heat and pressure on existing rock form metamorphic rock.

What force holds a satellite in orbit around the Earth?

• a.friction
• b.gravity✓
• c.magnetism
• d.air pressure

Gravity continuously pulls the satellite toward Earth while its forward motion carries it past, and the combination is an orbit.

What is the largest artery in the human body?

• a.the femoral
• b.the vena cava
• c.the carotid
• d.the aorta✓

The aorta leaves the left side of the heart and supplies every other artery. The vena cava is the body's largest vein, not an artery.

A solar eclipse occurs when

• a.the Earth passes between the moon and the sun
• b.the moon moves into the Earth's own shadow
• c.the moon passes between the Earth and the sun✓
• d.the sun passes behind the far side of Earth

In a solar eclipse the moon blocks the sun from part of the Earth's surface. When the moon moves into Earth's shadow instead, the result is a lunar eclipse.

Which of the following is a chemical element?

• a.bronze
• b.air
• c.helium✓
• d.water

Helium appears on the periodic table as a single kind of atom. Bronze is an alloy, water is a compound, and air is a mixture of gases.

In the human lung, gas exchange with the blood takes place in the

• a.diaphragm
• b.trachea
• c.alveoli✓
• d.bronchi

The alveoli are the tiny air sacs at the ends of the airways, where oxygen and carbon dioxide cross into and out of the blood. The bronchi and trachea only carry air.

The process by which water moves from a plant's leaves into the air is called

• a.germination
• b.precipitation
• c.condensation
• d.transpiration✓

Transpiration is evaporation through the pores of a leaf, and it pulls water upward from the roots. Condensation and precipitation are stages of the weather cycle.

On the Celsius scale, at what temperature does fresh water freeze?

• a.0 degrees✓
• b.32 degrees
• c.273 degrees
• d.100 degrees

Water freezes at 0 degrees Celsius, which is the same temperature as 32 degrees Fahrenheit.

A stretched spring holds which kind of energy?

• a.kinetic
• b.potential✓
• c.thermal
• d.electrical

Energy stored by position or deformation is potential energy. It becomes kinetic energy of motion when the spring is released.

A 12-volt source is connected across a 4-ohm resistor. How much current flows?

• a.48 amperes
• b.3 amperes✓
• c.8 amperes
• d.0.33 ampere

Ohm's law gives current as voltage divided by resistance: 12 / 4 = 3 amperes. Multiplying instead of dividing would give the 48 in one of the wrong choices.

Electrical resistance is measured in which unit?

• a.ohms✓
• b.watts
• c.volts
• d.amperes

Resistance is measured in ohms. Volts measure potential difference, amperes measure current, and watts measure power.

Three resistors are wired in series. How does the current through the second resistor compare with the current through the first?

• a.it is one-third as large
• b.it is the same✓
• c.it is three times as large
• d.it is twice as large

A series circuit offers only one path, so the same current passes through every element. It is the voltage that divides among series resistors.

What is the total resistance of two 6-ohm resistors connected in parallel?

• a.12 ohms
• b.3 ohms✓
• c.36 ohms
• d.6 ohms

Two equal resistors in parallel give half the resistance of one, so 6 / 2 = 3 ohms. Parallel resistance is always less than the smallest branch.

What is the total resistance of a 4-ohm and an 8-ohm resistor connected in series?

• a.4 ohms
• b.32 ohms
• c.2.67 ohms
• d.12 ohms✓

Series resistances add directly: 4 + 8 = 12 ohms. The 2.67 figure would be the result if they were in parallel.

A device draws 5 amperes from a 120-volt supply. How much power does it use?

• a.24 watts
• b.1,200 watts
• c.600 watts✓
• d.125 watts

Power equals voltage times current: 120 x 5 = 600 watts.

Which of these materials is the best conductor of electricity?

• a.rubber
• b.copper✓
• c.dry wood
• d.window glass

Copper has many free electrons and is used for most wiring. Rubber, wood, and glass are insulators.

How does a fuse protect a circuit?

• a.a metal strip melts and opens the circuit✓
• b.a coil stores the excess current safely
• c.a switch closes to divert the current
• d.a resistor absorbs the extra voltage

Excess current heats the fuse element until it melts, breaking the circuit. A fuse can only open a circuit; it cannot store or absorb current.

What is the main function of a transformer?

• a.to measure circuit current
• b.to convert AC into DC
• c.to store electrical charge
• d.to raise or lower AC voltage✓

A transformer couples two coils magnetically to change voltage. It needs a changing current, so it does not work on steady DC, and converting AC to DC is the job of a rectifier.

What does a diode do in a circuit?

• a.it increases the voltage across a load
• b.it converts current into magnetism
• c.it stores charge between its two plates
• d.it passes current in one direction only✓

A diode conducts when forward biased and blocks when reverse biased, which is why diodes are used to rectify alternating current.

A capacitor stores energy in

• a.a mechanical spring
• b.a magnetic field
• c.a chemical reaction
• d.an electric field✓

Charge collects on the capacitor's plates and the energy resides in the electric field between them. An inductor stores energy in a magnetic field instead.

What is the frequency of standard household alternating current in the United States?

• a.50 hertz
• b.120 hertz
• c.60 hertz✓
• d.110 hertz

United States utilities supply 60 hertz. Much of Europe and Asia uses 50 hertz instead.

What is the nominal voltage of a standard household outlet in the United States?

• a.12 volts
• b.120 volts✓
• c.480 volts
• d.24 volts

Ordinary branch circuits supply about 120 volts. Large appliances such as electric ranges use a 240-volt circuit.

In United States residential wiring, which insulation color identifies the equipment grounding conductor?

• a.black
• b.green✓
• c.red
• d.white

Grounding conductors are green, green with a yellow stripe, or bare copper. White marks the grounded neutral, and black and red mark ungrounded hot conductors.

Four lamps are wired in parallel across a supply. If one lamp burns out, what happens to the others?

• a.they all go dark
• b.they keep burning✓
• c.they burn much brighter
• d.they burn much dimmer

Each branch of a parallel circuit has its own path to the source, so an open branch does not interrupt the others. In a series string, one failure would darken them all.

Which change would increase the resistance of a length of copper wire?

• a.making the wire thicker
• b.making the wire longer✓
• c.cooling the wire down
• d.coiling the wire loosely

Resistance rises with length and falls as cross-sectional area increases. Cooling a metal conductor also lowers its resistance.

How is an ammeter connected in order to read the current in a circuit?

• a.across the supply terminals
• b.in parallel with the load
• c.between the load and ground
• d.in series with the load✓

The current to be measured has to pass through the ammeter, so it goes in series. An ammeter placed in parallel presents a near short circuit.

How is a voltmeter connected in order to read the voltage across a component?

• a.in parallel with the component✓
• b.in series with the component
• c.in series with the supply
• d.between the two supply fuses

Voltage is a difference between two points, so the meter bridges those two points in parallel. A voltmeter has very high resistance so it draws almost no current.

Which material is the basis of most modern semiconductor devices?

• a.aluminum
• b.silicon✓
• c.rubber
• d.copper

Silicon conducts far better than an insulator and far worse than a metal, and doping it controls that conduction precisely.

A circuit carries 2 amperes when 24 volts is applied. What is its resistance?

• a.12 ohms✓
• b.2 ohms
• c.48 ohms
• d.26 ohms

Resistance equals voltage divided by current: 24 / 2 = 12 ohms.

What is the main purpose of a resistor in a circuit?

• a.to boost voltage
• b.to rectify current
• c.to store charge
• d.to limit current✓

A resistor opposes current flow, which sets the current in a branch and divides voltage. Storing charge is a capacitor's job.

Electrical power is measured in which unit?

• a.ohms
• b.amperes
• c.watts✓
• d.coulombs

One watt is one joule per second. Ohms measure resistance, coulombs measure charge, and amperes measure current.

A step-down transformer has which winding arrangement?

• a.equal turns on both windings
• b.more turns on the secondary
• c.no winding on the secondary
• d.fewer turns on the secondary✓

Output voltage follows the turns ratio, so fewer secondary turns give a lower output voltage and a proportionally higher output current.

Two 1.5-volt cells are connected in series. What is the voltage across the pair?

• a.0.75 volt
• b.3.0 volts✓
• c.4.5 volts
• d.1.5 volts

Cells in series add their voltages: 1.5 + 1.5 = 3.0 volts. Connecting them in parallel would keep the voltage at 1.5 while doubling the available current.

In which of these is the fulcrum located between the effort and the load?

• a.a wheelbarrow being lifted up
• b.a nutcracker being squeezed
• c.a claw hammer pulling a nail✓
• d.a pair of tweezers gripping

The hammer head rests on the board as a fulcrum, with the hand above it and the nail below, which makes it a first-class lever. A wheelbarrow and a nutcracker put the load between fulcrum and effort, and tweezers put the effort in the middle.

A crowbar is pivoted so that the effort arm is 6 feet and the load arm is 2 feet. How much effort is needed to lift a 300-pound load?

• a.100 pounds✓
• b.900 pounds
• c.150 pounds
• d.75 pounds

Balancing moments gives effort x 6 = 300 x 2, so the effort is 100 pounds. The bar multiplies force three times, and the hand must move three times as far.

What does a single fixed pulley accomplish?

• a.it changes the direction of the pull✓
• b.it cuts the required force in half
• c.it doubles the load that can be lifted
• d.it shortens the distance the rope moves

A fixed pulley has a mechanical advantage of one, so the effort equals the load. Its value is that a downward pull can raise a load upward.

A single movable pulley is used to raise a load. Compared with lifting the load directly, the effort needed is

• a.twice as large
• b.four times as large
• c.half as large✓
• d.exactly the same

Two rope sections support the movable pulley, so each carries half the load. The trade is that the rope must be pulled twice as far.

A 20-tooth gear turning at 90 revolutions per minute drives a meshed 60-tooth gear. How fast does the larger gear turn?

• a.90 revolutions per minute
• b.270 revolutions per minute
• c.30 revolutions per minute✓
• d.45 revolutions per minute

Speed is inversely proportional to tooth count, so a gear with three times the teeth turns one-third as fast: 90 x 20 / 60 = 30 rpm.

Two external gears of different sizes are meshed directly together. How do they turn?

• a.at the same speed
• b.in the same direction
• c.in opposite directions✓
• d.at exactly the same torque

Where the teeth meet, the surfaces move together, which forces the two gears to rotate opposite ways. Adding a third idler gear between them restores the same direction.

A ramp 12 feet long is used to raise a 200-pound crate to a platform 3 feet high. Ignoring friction, how much force is needed to push the crate up the ramp?

• a.50 pounds✓
• b.75 pounds
• c.25 pounds
• d.150 pounds

The ramp's mechanical advantage is length divided by height, or 12 / 3 = 4, so the force is 200 / 4 = 50 pounds. The work is unchanged: a quarter of the force over four times the distance.

In a hydraulic press, a 50-pound force is applied to a piston with an area of 2 square inches. What force appears at a second piston of 20 square inches?

• a.50 pounds
• b.500 pounds✓
• c.200 pounds
• d.1,000 pounds

The pressure is 50 / 2 = 25 pounds per square inch throughout the fluid, and 25 x 20 = 500 pounds at the larger piston. The large piston moves only one-tenth as far.

A block presses down with 120 pounds over a contact area of 4 square inches. What pressure does it exert?

• a.480 pounds per square inch
• b.4 pounds per square inch
• c.116 pounds per square inch
• d.30 pounds per square inch✓

Pressure is force divided by area: 120 / 4 = 30 pounds per square inch.

Two tanks are filled with water to the same depth, but one is much wider than the other. How does the water pressure at the bottom compare?

• a.it is greater in the wide tank
• b.it is greater in the narrow tank
• c.it is the same in both✓
• d.it depends on the tank material

Pressure in a liquid at rest depends on depth and density, not on the shape or the total volume of the container.

A 180-pound crate hangs from a 10-foot pole carried by two workers at its ends. If the crate hangs 3 feet from the first worker, how much of the load does that worker carry?

• a.126 pounds✓
• b.90 pounds
• c.54 pounds
• d.150 pounds

Taking moments about the far worker, the near worker's share is 180 x 7 / 10 = 126 pounds. The worker closer to the load always carries more of it.

A mechanic switches from a 10-inch wrench to a 20-inch wrench and pulls with the same force. The torque applied to the bolt is

• a.four times as great
• b.half as great
• c.the same
• d.twice as great✓

Torque is force multiplied by the distance from the pivot, so doubling the handle length doubles the torque for an unchanged pull.

A screw thread is best described as which simple machine?

• a.a first-class lever
• b.a wheel and axle
• c.an inclined plane✓
• d.a pulley

A thread is an inclined plane wrapped around a cylinder, which is why turning the screw many times advances it a short distance with great force.

Two screws are the same diameter, but one has finer threads than the other. Compared with the coarse screw, the fine screw offers

• a.less holding force per turn
• b.much less mechanical advantage
• c.greater mechanical advantage✓
• d.greater advance per turn

A finer thread advances a shorter distance per turn, so the same turning effort produces more force. The trade is that more turns are required.

Which change would make a loaded hand truck harder to tip over?

• a.using smaller wheels
• b.lowering the center of gravity✓
• c.narrowing the wheel base
• d.raising the center of gravity

Stability improves as the center of gravity drops and as the base of support widens, because the load must be tilted farther before its weight falls outside the base.

What is the purpose of a flywheel on an engine?

• a.to reverse the direction of rotation
• b.to smooth out changes in speed✓
• c.to cool the moving parts
• d.to increase the fuel supply

A heavy flywheel stores rotational energy during the power stroke and gives it back during the others, evening out the shaft speed.

Two pulleys of different sizes are joined by an ordinary uncrossed belt. How do they turn?

• a.with equal torque
• b.in opposite directions
• c.in the same direction✓
• d.at the same speed

An open belt carries motion around both wheels the same way. Crossing the belt reverses the driven pulley.

The property that allows a metal to be drawn out into wire is called

• a.brittleness
• b.hardness
• c.ductility✓
• d.conductivity

Ductility is the ability to deform under tension without breaking. Hardness resists scratching and denting, and a brittle metal would snap instead of stretching.

The property that allows a metal to be hammered into thin sheets is called

• a.elasticity
• b.malleability✓
• c.hardness
• d.brittleness

Malleability is the ability to deform under compression without cracking. Elasticity instead describes a material that springs back to its original shape.

A beam is supported at both ends and loaded at its midpoint. Where does the greatest bending occur?

• a.at the left support
• b.just inside each support
• c.at the right support
• d.at the midpoint✓

Bending moment in a simply supported beam builds from zero at each support to a maximum under the load at midspan.

Which shape gives a framework its rigidity without relying on stiff joints?

• a.the square
• b.the hexagon
• c.the triangle✓
• d.the rectangle

A triangle cannot change shape unless a side changes length, so trusses are built from triangles. A square frame can rack into a parallelogram.

Why is it easier to move a heavy crate on rollers than to slide it across the floor?

• a.the floor becomes smoother
• b.gravity is reduced
• c.rolling friction is lower✓
• d.the crate weighs less

Rolling contact deforms very little and produces far less resistance than sliding contact. The crate's weight is unchanged.

A block and tackle is rigged with four rope sections supporting the movable block. Ignoring friction, how much effort raises a 480-pound load?

• a.120 pounds✓
• b.480 pounds
• c.60 pounds
• d.240 pounds

Four supporting sections share the load, so the effort is 480 / 4 = 120 pounds. The rope must be pulled four feet for every foot the load rises.

A small gear drives a much larger gear. At the larger gear, compared with the smaller one, the output has

• a.less torque and more speed
• b.less torque and less speed
• c.more torque and more speed
• d.more torque and less speed✓

Gearing trades speed for turning force. Power stays roughly constant, so the slower shaft carries the greater torque.

A cam and follower are used to produce which kind of motion?

• a.back-and-forth motion from rotation✓
• b.a steady increase in speed
• c.rotation from back-and-forth motion
• d.rotation at a constant torque

A rotating cam lobe pushes the follower out and lets it return, converting rotary motion into reciprocating motion. Engine valves are opened this way.

One spring stretches 4 inches under a load. If two identical springs share the same load side by side, how far does each stretch?

• a.4 inches
• b.2 inches✓
• c.8 inches
• d.1 inch

Each spring now carries half the load, so each stretches half as far, or 2 inches. Springs sharing a load this way behave as one stiffer spring.

What is the main job of the alternator?

• a.to regulate the flow of fuel to the engine
• b.to store current for the starter motor
• c.to start the engine when the driver turns the key
• d.to recharge the battery while the engine runs✓

The alternator is driven by the engine and supplies the electrical system while replacing the charge the starter drew from the battery. Cranking the engine is the starter motor's job.

What does the thermostat in a cooling system do?

• a.it warns the driver of an overheated engine
• b.it pumps coolant through the engine block
• c.it blocks coolant flow until the engine warms up✓
• d.it cools the coolant before it reaches the engine

A closed thermostat keeps coolant out of the radiator so the engine reaches operating temperature quickly, then opens to let heat escape. The water pump does the pumping.

Besides lubricating, which of the following does engine oil also do?

• a.it carries heat away from moving parts✓
• b.it raises the compression in the cylinders
• c.it improves the spark at the plug gap
• d.it cools the passenger compartment

Oil films the bearings and rings, but it also carries heat out of the engine and suspends contaminants until the filter traps them.

What is the correct order of the strokes in a four-stroke gasoline engine?

• a.intake, compression, power, exhaust✓
• b.intake, power, compression, exhaust
• c.power, intake, compression, exhaust
• d.compression, intake, power, exhaust

The piston draws in the mixture, compresses it, is driven down by the burning charge, and then pushes the spent gases out.

How is the fuel mixture ignited in a diesel engine?

• a.by exhaust gas recirculation
• b.by a heated glow plug
• c.by a spark plug
• d.by the heat of compression✓

A diesel compresses air until it is hot enough to ignite the fuel injected into it, so no spark or arc is needed. Glow plugs, where fitted, only warm the chamber for cold starting.

What does the clutch do in a manual transmission vehicle?

• a.it holds the vehicle still on a hill
• b.it chooses which gear ratio will be used
• c.it locks the drive wheels together
• d.it disconnects engine and transmission✓

Pressing the clutch pedal separates the flywheel from the transmission input shaft so gears can be changed without the engine driving them. Choosing the ratio is the gearbox's job, not the clutch's.

In a disc brake, the pads are squeezed against which part?

• a.the rotor✓
• b.the axle
• c.the drum
• d.the wheel rim

A caliper presses the pads onto both faces of the rotor that spins with the wheel. Drums belong to the other main brake design.

What is the purpose of the catalytic converter?

• a.it makes exhaust gases less harmful✓
• b.it quiets the noise of the exhaust
• c.it increases engine power output
• d.it cools the exhaust manifold

The converter promotes reactions that turn carbon monoxide and unburned fuel into carbon dioxide and water. The muffler is what quiets the exhaust.

What does the differential allow the drive wheels to do?

• a.turn at different speeds in a corner✓
• b.turn at exactly the same speed
• c.spin freely when the car is parked
• d.reverse without shifting gears

In a turn the outside wheel travels farther than the inside wheel, and the differential lets them rotate at different rates while both receive power.

A tire that is consistently underinflated will usually show wear

• a.evenly across the entire tread width
• b.on one edge of the tread only
• c.on both outer edges of the tread✓
• d.down the center of the tread

Low pressure lets the tread bow upward in the middle so the shoulders carry the load. Overinflation produces the opposite pattern, wear down the center.

What does antifreeze added to the cooling system do?

• a.it thickens the coolant to improve the heat transfer
• b.it protects against freezing but not boiling over
• c.it protects against both freezing and boiling over✓
• d.it protects against boiling over but not freezing

A glycol and water mixture protects against freezing in winter and against boil-over in summer, which is why it stays in the system year round.

What component builds the hydraulic pressure when the brake pedal is pressed?

• a.the master cylinder✓
• b.the proportioning valve
• c.the brake booster
• d.the wheel bearing

The pedal pushes a piston in the master cylinder, which sends pressurized fluid to each wheel. The booster only reduces the pedal effort required.

A saw designed to cut across the grain of a board is called

• a.a crosscut saw✓
• b.a coping saw
• c.a rip saw
• d.a metal hacksaw

Crosscut teeth are filed to sever wood fibers across the grain, while rip teeth act like tiny chisels for cutting along the grain. A hacksaw is for metal.

Which tool measures to the nearest thousandth of an inch?

• a.a framing square
• b.a folding rule
• c.a tape measure
• d.a micrometer✓

A micrometer's precision screw and vernier scale resolve 0.001 inch. A rule or tape measure is generally read to a sixteenth of an inch.

What is a hand plane used for?

• a.driving fasteners in flush
• b.boring holes through a board
• c.cutting joints in sheet metal
• d.smoothing a wood surface✓

A plane's blade projects slightly below the sole and removes a thin shaving with each pass, flattening and smoothing the surface.

A hand file cuts on which stroke?

• a.neither, it only polishes
• b.both strokes equally
• c.the return stroke
• d.the forward stroke✓

File teeth point forward, so cutting happens on the push. Dragging the file back under pressure dulls the teeth.

A wood chisel should be struck with

• a.a claw hammer
• b.a ball-peen hammer
• c.a mallet✓
• d.a heavy wrench

A wooden or soft-faced mallet drives the chisel without mushrooming its handle. Steel hammer faces damage the chisel and can chip.

Which tool cuts internal threads inside a drilled hole?

• a.a countersink
• b.a tap✓
• c.a reamer
• d.a die

A tap cuts threads inside a hole and a die cuts threads on the outside of a rod. A reamer only sizes and smooths an existing hole.

Why is a countersink used before driving a flat-head screw?

• a.so the head finishes flush✓
• b.so the screw grips harder
• c.so the hole is sealed against water
• d.so the screw comes out faster

The countersink cuts a cone-shaped recess that matches the underside of a flat head, letting it finish level with the surface.

Why is a pilot hole drilled before driving a wood screw into hardwood?

• a.to keep the screw from rusting
• b.to make the screw hold more tightly
• c.to allow the screw to be countersunk
• d.to keep the wood from splitting✓

The screw's shank displaces wood as it enters, and in dense hardwood that pressure can split the board. A pilot hole removes that material in advance.

On sandpaper, a higher grit number indicates

• a.a wider sheet
• b.a finer abrasive✓
• c.a coarser abrasive
• d.a tougher backing

Grit numbers count the particles that pass a screen, so a larger number means smaller particles and a finer finish.

A ball-peen hammer is intended mainly for

• a.metalwork✓
• b.setting tile
• c.driving nails
• d.shaping stone

The rounded peen is used for riveting and shaping metal. Nails are driven with a claw hammer, which also pulls them.

What is a miter box used for?

• a.storing chisels in order
• b.measuring the board thickness
• c.clamping the stock to a bench
• d.guiding a saw at an angle✓

The slots in a miter box hold the saw at a fixed angle, commonly 45 or 90 degrees, so repeated cuts match.

A plumb bob is used to check

• a.that a corner is square
• b.that a line is vertical✓
• c.that a board is flat
• d.that a line is horizontal

A weight hanging on a string settles along the direction of gravity, which is by definition vertical. A spirit level checks horizontal, and a square checks corners.