Edutest Year 9 Mathematics Practice

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

1. 1.Expand and simplify: (x + 3)(x - 5)

   • Ax² - 2x - 15
   • Bx² + 2x - 15
   • Cx² - 8x - 15
   • Dx² - 15
   Show answer and working

   Answer: A (x² - 2x - 15)

   Multiply every term in the first bracket by every term in the second (FOIL): x × x = x², x × −5 = −5x, 3 × x = 3x and 3 × −5 = −15. Collect the middle terms: −5x + 3x = −2x. So the answer is x² − 2x − 15. Option B gets the sign of the x-term wrong.

2. 2.Solve for x: x² - 5x + 6 = 0

   • A2, 3
   • B-2, -3
   • C1, 6
   • D-1, -6
   Show answer and working

   Answer: A (2, 3)

   Factorise by finding two numbers that multiply to +6 and add to −5. Those are −2 and −3, so x² − 5x + 6 = (x − 2)(x − 3) = 0. A product is zero only if one factor is zero, so x = 2 or x = 3. Check: 2² − 5(2) + 6 = 0. Option B has the signs reversed.

3. 3.Calculate the surface area of a cube with side length 4cm.

   • A64 cm²
   • B96 cm²
   • C16 cm²
   • D24 cm²
   Show answer and working

   Answer: B (96 cm²)

   A cube has 6 identical square faces. Each face has area 4 × 4 = 16 cm², so the total surface area is 6 × 16 = 96 cm². The answer 64 cm² is the volume (4 × 4 × 4), which measures space inside rather than the area of the outside, and 16 cm² is only one face.

4. 4.Simplify: (2x³)²

   • A4x⁵
   • B4x⁶
   • C2x⁶
   • D2x⁵
   Show answer and working

   Answer: B (4x⁶)

   Squaring means multiplying the whole expression by itself, so square both the 2 and the x³. 2² = 4. For (x³)², multiply the indices: 3 × 2 = 6, giving x⁶. So (2x³)² = 4x⁶. Adding the indices (3 + 2 = 5) is a common mistake, and forgetting to square the 2 gives 2x⁶.

5. 5.Find the gradient of the line passing through (1, 2) and (3, 6).

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

   Answer: B (2)

   Gradient = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). Using (1, 2) and (3, 6): rise = 6 − 2 = 4 and run = 3 − 1 = 2. So the gradient is 4 ÷ 2 = 2. This means y increases by 2 for every increase of 1 in x. Keep the points in the same order on top and bottom.

6. 6.What is the probability of rolling a sum of 7 with two dice?

   • A1/6
   • B1/12
   • C1/36
   • D5/36
   Show answer and working

   Answer: A (1/6)

   Two dice give 6 × 6 = 36 equally likely outcomes. A sum of 7 can be made six ways: (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1). So the probability is 6/36 = 1/6. The answer 1/12 counts each pair only once, but (1,6) and (6,1) are different outcomes.

7. 7.Trig: sin(30)

   • A0
   • B0.5
   • C1
   • D0.866
   Show answer and working

   Answer: B (0.5)

   sin 30° = 0.5 is a standard exact value worth memorising. It comes from an equilateral triangle cut in half: the side opposite the 30° angle is exactly half the hypotenuse, so opposite ÷ hypotenuse = 1/2. The value 0.866 is sin 60° (or cos 30°), which is a common mix-up.

8. 8.Value of 2⁻²

   • A-4
   • B0.25
   • C-0.25
   • D4
   Show answer and working

   Answer: B (0.25)

   A negative index means 'one over' the positive power: 2⁻² = 1/2² = 1/4 = 0.25. A negative index does not make the answer negative, so −4 and −0.25 are traps. Think of it as dividing by 2 twice, starting from 1: 1 ÷ 2 ÷ 2 = 0.25.

9. 9.Scientific notation of 0.003

   • A3x10⁻³
   • B3x10³
   • C0.3x10⁻²
   • D30x10⁻⁴
   Show answer and working

   Answer: A (3x10⁻³)

   Scientific notation writes a number as a value from 1 up to (but not including) 10, multiplied by a power of 10. To turn 0.003 into 3, move the decimal point 3 places right, so the power is −3: 3 × 10⁻³. Option C uses 0.3, which is less than 1, so it is not in correct scientific notation.

10. 10.Sum of angles in pentagon

    • A360
    • B540
    • C720
    • D180
    Show answer and working

    Answer: B (540)

    The interior angles of a polygon with n sides add to (n − 2) × 180°. A pentagon has 5 sides, so (5 − 2) × 180° = 3 × 180° = 540°. You can see why by splitting the pentagon into 3 triangles from one corner, each worth 180°. 720° is the sum for a hexagon.