Mathematics Knowledge · Practice test 5

Correct answer: 729

A power raised to a power multiplies the exponents: 2 x 3 = 6, and 3 to the 6th is 729. Adding the exponents instead of multiplying gives 18, a common mistake.

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Correct answer: 12

List the factors each number shares. Both 36 and 48 divide evenly by 12, and no larger number works, so the greatest common factor is 12. The choice 144 is their least common multiple, not the greatest common factor.

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Correct answer: 1

Any non-zero number raised to the power of zero equals 1. It follows from the quotient rule, since 5 to the 3rd divided by 5 to the 3rd is both 1 and 5 to the 0.

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Correct answer: 7

Find two numbers multiplying to -21 and adding to -4: those are -7 and 3, so the equation factors as (x - 7)(x + 3) = 0. The solutions are 7 and -3, and the positive one is 7.

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Correct answer: 24

List the multiples of 8: 8, 16, 24. The first one that 6 also divides is 24. The choice 48 is a common multiple but not the least, and 2 is the greatest common factor.

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Correct answer: 7

Distribute the 3: 3x - 6 = x + 8. Move x terms together: 3x - x = 8 + 6 gives 2x = 14, so x = 7.

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Correct answer: 48

Corresponding angles formed by a transversal crossing parallel lines are always equal, so the corresponding angle also measures 48 degrees.

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Correct answer: 14

The square root asks which number multiplied by itself gives 196. Since 14 x 14 = 196, the answer is 14.

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Correct answer: 25

Add 9 to both sides to undo the subtraction: x = 16 + 9 = 25.

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Correct answer: 5

Volume is the edge cubed, so the edge is the cube root of 125. Since 5 x 5 x 5 = 125, the edge is 5. Taking the square root instead gives about 11.2.

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Correct answer: 10

Absolute value strips the sign, giving the distance from zero. So |-7| is 7 and |3| is 3, and 7 + 3 = 10.

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Correct answer: 14

Brackets first: 10 - 6 = 4. Then multiply and divide left to right: 3 x 4 = 12 and 12 / 2 = 6. Finally add: 8 + 6 = 14. Adding before multiplying gives 22, the usual error.

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Correct answer: 6

Gather the variables on one side: 8x - 5x = 15 + 3 gives 3x = 18, so x = 6.

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Correct answer: 107

Supplementary angles add to 180 degrees, so the other is 180 - 73 = 107.

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Correct answer: 126

The area of a parallelogram is base times height, so 14 x 9 = 126. Halving it would give the area of the triangle formed by cutting it diagonally, not the whole parallelogram.

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Correct answer: Quadrant III

A negative x with a negative y puts the point down and to the left of the origin, which is Quadrant III.

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Correct answer: 26

Work the bracket and the exponent first: (6 + 4) = 10 and 2 squared = 4. Then 10 x 3 = 30, and 30 - 4 = 26.

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Correct answer: 452.16

A cylinder's volume is the area of its circular base times its height. The base is 3.14 x 16 = 50.24, and multiplying by 9 gives 452.16.

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Correct answer: 22

Square first: -2 squared is 4, and 4 x 4 = 16. Then subtract 3 times -2, which is subtracting -6, so 16 + 6 = 22.

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Correct answer: 5

Only terms with the same variable combine, so the a terms give 7a - 2a = 5a and the b terms give 8b separately. The expression simplifies to 5a + 8b.

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Correct answer: 5

Split 50 into 25 x 2. The root of 25 comes out of the radical as 5, leaving the root of 2 behind, so the answer is 5 root 2.

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Correct answer: 169

Each side of the square is 52 / 4 = 13. The area is the side squared, so 13 x 13 = 169.

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Correct answer: 9

Divide both sides by 2 to get x - 4 = 5, then add 4 to get x = 9. Distributing first gives 2x - 8 = 10 and the same answer.

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Correct answer: Equilateral

A triangle with all three angles equal also has all three sides equal, which makes it equilateral.

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Correct answer: 8

Multiplying powers of the same base means adding the exponents, so 5 + 3 = 8. Multiplying the exponents to get 15 is the standard mistake; that rule belongs to a power raised to a power.

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