CSLB General Building (B) — All Questions
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If 3x + 7 = 22, what is the value of x?
- a.3
- b.7
- c.5✓
- 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.25
- b.37
- c.49
- d.43✓
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.16
- c.60
- d.45
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.13
- b.36✓
- c.18
- d.45
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.3
- b.7
- c.9✓
- d.12
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.15.7
- b.25.0
- c.78.5
- d.31.4✓
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.120✓
- b.25
- c.60
- d.720
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.2
- b.8✓
- c.5
- d.16
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.11
- b.14
- c.12✓
- d.72
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.270 degrees
- c.360 degrees
- d.180 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.7
- c.5
- d.-11
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.0.34
- b.0.75✓
- c.0.43
- d.1.33
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.6
- c.5✓
- d.9
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.6x
- c.2x
- 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.12✓
- b.3
- c.6
- d.0.083
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.9
- b.27✓
- c.18
- 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.