Edutest Year 10 Mathematics Practice

Try each question first, then open the worked solution to check your answer and see how to reach it.

1. 1.A right-angled triangle has a hypotenuse of 13cm and one side of 5cm. What is the length of the other side?

   • A10cm
   • B11cm
   • C12cm
   • D14cm
   Show answer and working

   Answer: C (12cm)

   Rearrange Pythagoras' theorem to find a shorter side: a² = c² − b². Here a² = 13² − 5² = 169 − 25 = 144, so a = √144 = 12 cm. This is the 5-12-13 Pythagorean triple. The answer 14 cm would be longer than the hypotenuse, which is impossible in a right-angled triangle.

2. 2.In a right-angled triangle, the angle is 30° and the opposite side is 5cm. What is the length of the hypotenuse?

   • A5cm
   • B8.66cm
   • C10cm
   • D15cm
   Show answer and working

   Answer: C (10cm)

   Use SOH: sin θ = opposite ÷ hypotenuse. So sin 30° = 5 ÷ h. Since sin 30° = 0.5, we have 0.5 = 5 ÷ h, giving h = 5 ÷ 0.5 = 10 cm. A quick check: in a 30° right triangle the side opposite 30° is always half the hypotenuse. 8.66 cm is the adjacent side.

3. 3.Calculate the surface area of a cylinder with radius 5cm and height 10cm. (Leave in terms of π)

   • A100π cm²
   • B125π cm²
   • C150π cm²
   • D200π cm²
   Show answer and working

   Answer: C (150π cm²)

   A closed cylinder's surface area is two circular ends plus the curved side: 2πr² + 2πrh. The ends give 2 × π × 5² = 50π, and the curved surface gives 2 × π × 5 × 10 = 100π. Total: 50π + 100π = 150π cm². The answer 100π includes only the curved side.

4. 4.Simplify √75.

   • A3√5
   • B5√3
   • C15√5
   • D25√3
   Show answer and working

   Answer: B (5√3)

   Look for the largest square factor of 75. Since 75 = 25 × 3 and 25 is a perfect square, √75 = √25 × √3 = 5√3. The answer 3√5 swaps the numbers, and 25√3 forgets to take the square root of 25. Check: (5√3)² = 25 × 3 = 75.

5. 5.Two dice are rolled. What is the probability of getting a sum of 9?

   • A1/36
   • B2/36
   • C3/36
   • D4/36
   Show answer and working

   Answer: D (4/36)

   Two dice have 36 equally likely outcomes. A sum of 9 comes from (3,6), (4,5), (5,4) and (6,3), which is 4 outcomes. So the probability is 4/36, which simplifies to 1/9. Remember that (3,6) and (6,3) are different outcomes, because each die is separate.

6. 6.Find the size of an interior angle of a regular octagon.

   • A108°
   • B120°
   • C135°
   • D144°
   Show answer and working

   Answer: C (135°)

   The interior angles of a polygon add to (n − 2) × 180°. An octagon has 8 sides: (8 − 2) × 180° = 1080°. A regular octagon has 8 equal angles, so each is 1080° ÷ 8 = 135°. Another method: each exterior angle is 360° ÷ 8 = 45°, and 180° − 45° = 135°.

7. 7.If f(x) = 3x - 5, find f(f(2)).

   • A-2
   • B-1
   • C1
   • D2
   Show answer and working

   Answer: A (-2)

   Work from the inside out. First find f(2) = 3 × 2 − 5 = 1. Then substitute that result back in: f(1) = 3 × 1 − 5 = −2. So f(f(2)) = −2. The answer 1 stops after the first step. Composite functions always use the output of the inner function as the input of the outer one.

8. 8.Find the interquartile range of the data set: 2, 5, 5, 6, 7, 9, 12, 15.

   • A5
   • B5.5
   • C6
   • D7
   Show answer and working

   Answer: B (5.5)

   The data has 8 values: 2, 5, 5, 6 | 7, 9, 12, 15. The lower quartile (Q1) is the median of the lower half: (5 + 5) ÷ 2 = 5. The upper quartile (Q3) is the median of the upper half: (9 + 12) ÷ 2 = 10.5. The IQR is Q3 − Q1 = 10.5 − 5 = 5.5.

9. 9.A bag contains 5 red and 3 blue balls. Two balls are drawn without replacement. What is the probability they are both red?

   • A25/64
   • B20/56
   • C20/64
   • D25/56
   Show answer and working

   Answer: B (20/56)

   Without replacement, the second draw has one fewer ball. P(first red) = 5/8. After removing a red ball, 4 of the remaining 7 are red, so P(second red) = 4/7. Multiply: 5/8 × 4/7 = 20/56, which simplifies to 5/14. The answer 25/64 wrongly assumes the first ball is put back.

10. 10.Two similar triangles have corresponding sides in the ratio 1:3. If the area of the smaller triangle is 10 cm², what is the area of the larger one?

    • A30 cm²
    • B60 cm²
    • C90 cm²
    • D100 cm²
    Show answer and working

    Answer: C (90 cm²)

    When lengths are scaled by a factor k, areas are scaled by k². Here the side ratio is 1:3, so the area ratio is 1²:3² = 1:9. The larger triangle's area is 10 × 9 = 90 cm². The answer 30 cm² scales the area by 3, the length factor, which is the most common error.