Mathematics Knowledge · Practice test 2

Correct answer: 188.4

The circular base has area 3.14 x 4 = 12.56, and multiplying by the height gives 12.56 x 15 = 188.4.

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Correct answer: 5

The distance formula comes from the Pythagorean theorem: the horizontal leg is 4 - 1 = 3 and the vertical leg is 5 - 1 = 4, so the distance is the root of 9 + 16, which is the root of 25, or 5.

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Correct answer: 0

Zero divided by any nonzero number is always zero, since zero groups of 15 make nothing. Note that 15 divided by 0 is undefined, which is a different situation.

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Correct answer: 54

The rectangle's area is 10 x 6 = 60. The triangle removed has area 4 x 3 / 2 = 6. Subtracting gives 60 - 6 = 54.

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Correct answer: -7

The common difference is -3. The 6th term is the 1st term plus 5 times the common difference: 8 + 5 x (-3) = 8 - 15 = -7.

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Correct answer: 12

Similar triangles have proportional sides, so 6 is to 9 as 8 is to x. Cross-multiplying gives 6x = 72, so x = 12. Adding 2 to keep the difference the same gives 11, which is the trap.

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Correct answer: 0

Both points have the same y value, so the line is horizontal and rises not at all: the change in y is 0, and 0 divided by 7 is 0. A vertical line, by contrast, has an undefined slope.

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Correct answer: 9

Divide both sides by 5 to isolate x: x = 45 / 5 = 9.

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Correct answer: 16

Everything inside the bracket is raised to the outer power, the coefficient included. So 2 to the 4th gives 16 and x cubed becomes x to the 12th.

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Correct answer: 80

The ratio parts sum to 9, and 180 degrees divided into 9 parts gives 20 degrees per part. The largest angle has 4 parts, so 4 x 20 = 80.

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Correct answer: 40

Average the two parallel sides: (7 + 13) / 2 = 10. Multiply by the height: 10 x 4 = 40.

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Correct answer: 18

Add 2 to both sides to get x / 3 = 6, then multiply by 3 to get x = 18. Multiplying before adding gives 10.

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Correct answer: x is greater than or equal to -5

Subtract 4 to get -3x <= 15. Dividing by -3 flips the inequality sign, giving x >= -5.

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Correct answer: -1

Since the line crosses the y-axis at 5, its equation is y = -2x + 5. Substituting x = 3 gives -6 + 5 = -1. Missing the negative slope gives 11.

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Correct answer: 31.4

Circumference is 2 times pi times the radius, so 2 x 3.14 x 5 = 31.4. The choice 78.5 is the area, pi times the radius squared, a common mix-up.

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Correct answer: x is greater than 6

Solve it like an equation: subtract 6 to get 2x > 12, then divide by 2 to get x > 6. Dividing by a positive number never flips the inequality.

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Correct answer: 5

Add the exponents: 3 + 0 + 2 = 5. Since x to the 0 equals 1, that factor changes nothing, which is why treating it as a zero that wipes out the product is wrong.

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Correct answer: 52

The box has three pairs of matching faces measuring 6, 8, and 12. Their total is 26, and doubling for both of each pair gives 52. The choice 24 is the volume.

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Correct answer: 10

The distance formula is the Pythagorean theorem in disguise: the horizontal leg is 6 and the vertical leg is 8, so the distance is the root of 36 + 64, which is the root of 100, or 10.

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Correct answer: 15

Similar triangles have proportional sides, so 4 is to 10 as 6 is to x. Cross-multiplying gives 4x = 60, so x = 15.

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Correct answer: 4

The midpoint averages each coordinate separately, so the x-coordinate is (1 + 7) / 2 = 4. The full midpoint is (4, 7).

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Correct answer: -4

Group the constants separately from the p terms: 5 - 9 = -4. The p terms combine to 4p, giving 4p - 4 overall.

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Correct answer: 24

Since 36 + 64 = 100, this is a right triangle, so the legs of 6 and 8 serve as base and height. The area is half of 6 x 8, or 24. Forgetting to halve gives 48.

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Correct answer: 6

The factors of 12 are 1, 2, 3, 4, 6, 12 and those of 18 are 1, 2, 3, 6, 9, 18, so the greatest they share is 6. The choice 36 is the least common multiple instead.

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Correct answer: 314

Area is pi times the radius squared, so 3.14 x 100 = 314. The choice 62.8 is the circumference, 2 x 3.14 x 10.

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