Mathematics Knowledge · Practice test 8

Correct answer: 162

Each term is 3 times the one before it, so this is a geometric sequence with a common ratio of 3. The next term is 54 x 3 = 162.

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Correct answer: 108

Interior angles on the same side of the transversal are supplementary, so they add to 180 degrees and the other measures 108.

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Correct answer: 5

Gather the variables on one side and the numbers on the other: 5x - 2x = 12 + 3 gives 3x = 15, so x = 5.

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Correct answer: 76 degrees

The three angles of any triangle add to 180 degrees. The two given angles total 104, so the third is 180 - 104 = 76.

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Correct answer: 6

Dividing both sides of d = rt by r gives t = d / r. Substituting gives t = 150 / 25 = 6.

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Correct answer: 4

Substitute both values: 2 x 5 = 10 and 3 x (-2) = -6, so the total is 10 - 6 = 4. Treating b as positive gives 16.

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Correct answer: 5

Dividing powers of the same base means subtracting the exponents, so 9 - 4 = 5. Adding them gives 13 and multiplying gives 36, which are the two usual slips.

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Correct answer: 135

An octagon has 8 sides, so its interior angles sum to (8 - 2) x 180 = 1080 degrees. A regular octagon splits this equally among its 8 angles, giving 1080 / 8 = 135.

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Correct answer: They are congruent

When all three corresponding sides match exactly, the triangles are not just similar but congruent, meaning they are identical in size and shape.

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Correct answer: 294

A cube has six identical square faces. Each face is 7 x 7 = 49, so the surface area is 6 x 49 = 294. The choice 343 is the volume.

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Correct answer: 27

Everything inside the bracket is raised to the power, the coefficient included. So 3 cubed gives 27 and x squared becomes x to the 6th, making the full result 27x to the 6th.

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Correct answer: 56

The angles of a triangle sum to 180 degrees. Subtracting the two known angles, 180 - 90 - 34 = 56.

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Correct answer: -2

The change in y is -5 - 5 = -10, and the change in x is 3 - (-2) = 5, so the slope is -10 / 5 = -2.

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Correct answer: 6

The y-axis is where x = 0, so the equation reduces to y = 6. The choice 3 is the x-intercept, found by setting y to 0 instead.

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Correct answer: 5

Breaking 90 down gives 2 x 3 x 3 x 5, so its prime factors are 2, 3, and 5, and the largest is 5. The choice 45 is a factor of 90 but is not prime.

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Correct answer: 5

The cube root asks which number multiplied by itself three times gives 125. Since 5 x 5 x 5 = 125, the answer is 5.

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Correct answer: 7 and 8

Since 7 squared is 49 and 8 squared is 64, and 55 lies between 49 and 64, the square root of 55 must lie between 7 and 8.

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Correct answer: 40

The two base angles of an isosceles triangle are equal and share what remains after the apex: 180 - 100 = 80, split evenly gives 40 each.

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Correct answer: 5

The horizontal gap is 3 and the vertical gap is 4, so the distance is the root of 9 + 16, which is the root of 25, or 5. Forgetting the final square root gives 25.

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Correct answer: 56

An octagon has eight sides, and in a regular polygon they are all equal, so the perimeter is 8 x 7 = 56. The choice 42 counts six sides, as for a hexagon.

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Correct answer: 70

Each term is 10 less than the one before, so this is an arithmetic sequence with a common difference of -10. The next term is 80 - 10 = 70.

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Correct answer: 2

Find two numbers multiplying to 10 and adding to -7: those are -2 and -5, so the equation factors as (x - 2)(x - 5) = 0. The solutions are 2 and 5, and the smaller is 2.

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Correct answer: 6 root 2

Pull out the largest perfect square: 72 is 36 x 2, and the root of 36 is 6, giving 6 root 2. The choices 3 root 8 and 2 root 18 both equal the same number but are not fully simplified, since 8 and 18 still contain square factors.

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Correct answer: 1

Subtracting a negative adds instead: -14 + 9 + 6. Adding left to right, -14 + 9 = -5, then -5 + 6 = 1.

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Correct answer: 3

Slope is the change in y over the change in x. Here y rises by 14 - 2 = 12 while x increases by 5 - 1 = 4, so the slope is 12 / 4 = 3.

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