Mathematics Knowledge · Practice test 4

Correct answer: 5

The y-intercept occurs where x = 0. Substituting gives -2y = -10, so y = 5, and the intercept is the point (0, 5).

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Correct answer: x is less than 7

Solve it like an equation: add 5 to get 3x < 21, then divide by 3 to get x < 7. The direction of the sign only flips when you multiply or divide by a negative, which does not happen here.

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Correct answer: 3

Average the two y values: (-1 + 7) / 2 = 3. The choice 4 is half the length of the segment rather than the midpoint's coordinate.

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Correct answer: 55 degrees

Complementary angles add to 90 degrees, so the other is 90 - 35 = 55. The choice 145 comes from using 180, which is the rule for supplementary angles.

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Correct answer: 5

Subtracting the second equation from the first cancels x: 2y = 10, so y = 5.

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Correct answer: 150

A cube has six identical square faces. Each face is 5 x 5 = 25, so the surface area is 6 x 25 = 150. The choice 125 is the volume.

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Correct answer: 5

Undo the addition first: 22 - 7 = 15. Then undo the multiplication: 15 / 3 = 5.

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Correct answer: 8

Squaring a binomial gives x squared plus twice the product of the terms plus the square of the second, so the expansion is x squared + 8x + 16. Forgetting the middle term entirely is the classic error.

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Correct answer: 65

The rectangle contributes 8 x 5 = 40. The semicircle contributes half of pi times radius squared: 3.14 x 16 / 2 = 25.12. Adding gives about 65.

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Correct answer: a right triangle

Test the Pythagorean relationship: 25 + 144 = 169, which is 13 squared, so the triangle has a right angle. When the squares of the two shorter sides add to the square of the longest, the triangle is right-angled.

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Correct answer: 16

Work inside the bracket first: 7 - 3 = 4, and 4 squared is 16. Squaring each term separately and subtracting gives 40, which is why that choice is offered.

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Correct answer: equal in measure

Alternate interior angles sit on opposite sides of the transversal between the parallel lines and are always equal. The interior angles on the same side are the supplementary pair.

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Correct answer: 64

A power raised to a power multiplies the exponents: 3 x 2 = 6, and 2 to the 6th is 64. Working inside out gives the same result, since 2 cubed is 8 and 8 squared is 64.

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Correct answer: 62 degrees

Supplementary angles add to 180 degrees, so the other is 180 - 118 = 62.

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Correct answer: 94

Surface area sums the areas of all six faces, which come in three matching pairs: 2 x (4x3 + 4x5 + 3x5) = 2 x (12 + 20 + 15) = 2 x 47 = 94.

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Correct answer: 126

Area of a rectangle is length times width, so 14 x 9 = 126. The choice 46 is the perimeter, 2 x (14 + 9).

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Correct answer: 28

Subtract 3 from both sides to get x / 4 = 7, then multiply by 4 to get x = 28. Multiplying before subtracting gives 40, the usual order-of-operations slip.

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Correct answer: 46

Substitute 4 for x: 4 squared is 16, and 3 x 16 = 48. Then 48 - 2 = 46. Squaring 3x instead of x alone gives 94, the common slip.

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Correct answer: 23000

A positive exponent of 4 moves the decimal point four places right, turning 2.3 into 23000. Multiplying 2.3 by 4 instead gives 9.2, the common slip.

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Correct answer: 34

Perimeter of a rectangle is twice the sum of length and width, so 2 x (11 + 6) = 34.

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Correct answer: 87.92

The circular base has an area of 3.14 x 2 squared = 12.56, and multiplying by the height of 7 gives 87.92. Using the radius rather than the radius squared gives 43.96.

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Correct answer: equal in measure

Opposite, or vertical, angles are always equal. The angles next to each other in the same figure are supplementary, adding to 180, which is a separate rule.

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Correct answer: 8

Substitute 3 for x: 5 x 3 = 15, and 15 - 7 = 8.

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Correct answer: 720 degrees

For a polygon with n sides the interior angles sum to (n - 2) x 180. A hexagon has 6 sides, so the sum is 4 x 180 = 720 degrees. The choice 360 is the sum of the exterior angles, which is the same for every polygon.

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Correct answer: Quadrant IV

Quadrants are numbered counterclockwise starting at the upper right. A positive x with a negative y puts the point down and to the right, which is Quadrant IV.

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