Mathematics Knowledge · Practice test 1

Correct answer: 41

Square first, then multiply: 4 squared is 16, and 3 x 16 = 48. Then 48 - 8 + 1 = 41. Squaring 3x instead of x alone gives 137, the common slip.

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Correct answer: -2

Multiplying out gives x squared - 5x + 3x - 15, and the two middle terms combine to -2x. When both brackets start with plain x, the middle coefficient is simply the sum of the two constants: 3 + (-5) = -2.

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Correct answer: 47

Multiplying any number by 1 leaves it unchanged, so 47 x 1 = 47. This is called the identity property of multiplication.

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Correct answer: 10

Multiplying powers of the same base means adding the exponents, so 4 + 6 = 10.

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Correct answer: 7

Breaking 84 down gives 2 x 2 x 3 x 7, so its prime factors are 2, 3, and 7 and the largest is 7. The choices 21 and 42 divide 84 but are not prime.

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Correct answer: x is less than -4

Dividing both sides by -2 gives -4, but dividing by a negative reverses the inequality sign, so the answer is x < -4 rather than x > -4. This sign flip is the single most missed rule in inequalities.

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Correct answer: 113.0

A sphere's volume is four thirds times pi times the radius cubed. That is 4/3 x 3.14 x 27, which comes out to about 113.0. Using one third instead of four thirds gives 28.3.

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Correct answer: 7

Subtracting a negative is the same as adding a positive, so -5 - (-12) becomes -5 + 12, which is 7.

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Correct answer: 56

The area of a triangle is half the base times the height, so 16 x 7 = 112 and half of that is 56. Forgetting to halve gives 112, which is the area of the surrounding rectangle.

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Correct answer: -5

Look for two numbers multiplying to -10 and adding to -3. They are 2 and -5, so the factorisation is (x + 2)(x - 5) and the smaller value is -5. One number must be negative because the product is negative.

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Correct answer: 9

A difference of two squares factors into the sum and the difference of their roots. The root of 81 is 9, so the factors are (x + 9)(x - 9).

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Correct answer: 113.04

A sphere's volume is four thirds pi times the radius cubed. The radius cubed is 27, and four thirds of 3.14 x 27 gives 113.04. Leaving out the four thirds gives 84.78.

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Correct answer: 8

The midpoint averages each coordinate separately, so the y-coordinate is (2 + 14) / 2 = 8.

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Correct answer: 6 root 3

Pull out the largest perfect square: 108 is 36 x 3, and the root of 36 is 6, giving 6 root 3. The other choices equal the same number but still contain a square factor under the radical.

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Correct answer: -4

The y-axis is where x = 0, so substituting gives y = -4. In slope-intercept form y = mx + b, the constant b is always the y-intercept and m is the slope.

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Correct answer: 110 degrees

The exterior angle theorem gives 50 + 60 = 110 degrees directly. Checking the long way agrees: the third interior angle is 180 - 110 = 70, and the exterior angle beside it is 180 - 70 = 110.

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Correct answer: 6

The x-intercept occurs where y = 0. Substituting gives 2x = 12, so x = 6, and the intercept is the point (6, 0).

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Correct answer: 113.04

The radius is half the diameter, or 6. Area is pi times the radius squared, so 3.14 x 36 = 113.04. Using the diameter instead of the radius gives the wrong answer, 452.16.

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Correct answer: 169

The area of a square is the side length squared, so 13 x 13 = 169. The choice 52 is the perimeter, 4 x 13.

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Correct answer: 17

Function notation means substitute 6 wherever x appears: 2 x 6 + 5 = 17. The notation f(6) does not mean f multiplied by 6, which is the usual misreading.

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Correct answer: 2

Only terms with the same variable combine. The n terms give -4n + 6n = 2n, so the coefficient of n is 2.

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Correct answer: 8

A square's area is the side squared, so the side is the square root of 64, which is 8. The choice 16 is a quarter of the area, and 32 is the perimeter.

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Correct answer: 8

Adding the two equations cancels y: 2x = 16, so x = 8. Substituting back gives y = 4, which is why 4 appears as a choice.

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Correct answer: 24

Two negatives multiplied give a positive, so the answer is 24. A negative times a positive would give a negative.

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Correct answer: 15

By the Pythagorean theorem the hypotenuse squared equals 81 + 144 = 225, so the hypotenuse is 15. This is the 3-4-5 triangle scaled up by three.

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