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Year 10 Quadratics Topic Test — Answers

Answer sheet with worked solutions for the Year 10 quadratics topic test.

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Year 10 · Mathematics · Quadratics

Year 10 Quadratics Topic Test — Answers

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Part A — Expanding Brackets

1.Expand and simplify: (x − 8)(x − 7)[2 marks]

Answer: x2 − 15x + 56

  1. x × x = x2
  2. x × −7 + −8 × x = −15x
  3. −8 × −7 = 56
2.Expand and simplify: (x − 7)(x − 1)[2 marks]

Answer: x2 − 8x + 7

  1. x × x = x2
  2. x × −1 + −7 × x = −8x
  3. −7 × −1 = 7
3.Expand and simplify: (x + 1)(x − 8)[2 marks]

Answer: x2 − 7x − 8

  1. x × x = x2
  2. x × −8 + 1 × x = −7x
  3. 1 × −8 = −8
4.Expand and simplify: (x − 4)(x + 6)[2 marks]

Answer: x2 + 2x − 24

  1. x × x = x2
  2. x × 6 + −4 × x = 2x
  3. −4 × 6 = −24
5.Expand and simplify: (x − 2)(x + 4)[2 marks]

Answer: x2 + 2x − 8

  1. x × x = x2
  2. x × 4 + −2 × x = 2x
  3. −2 × 4 = −8

Part B — Factorising and Solving Quadratics

6.Factorise: x2 + x − 2[2 marks]

Answer: (x + 2)(x − 1)

  1. Find two numbers that multiply to −2 and add to 1: 2 and −1
7.Factorise: x2 − 7x − 18[2 marks]

Answer: (x + 2)(x − 9)

  1. Find two numbers that multiply to −18 and add to −7: 2 and −9
8.Factorise: x2 − 11x + 30[2 marks]

Answer: (x − 6)(x − 5)

  1. Find two numbers that multiply to 30 and add to −11: −6 and −5
9.Factorise: x2 + 12x + 35[2 marks]

Answer: (x + 7)(x + 5)

  1. Find two numbers that multiply to 35 and add to 12: 7 and 5
10.Factorise: x2 + 6x − 27[2 marks]

Answer: (x + 9)(x − 3)

  1. Find two numbers that multiply to −27 and add to 6: 9 and −3

Part C — Factorising and Solving Quadratics

11.Solve: x2 + 8x + 15 = 0[2 marks]

Answer: x = −5 or x = −3

  1. Factorise: (x + 5)(x + 3) = 0
  2. Null factor law: x + 5 = 0 or x + 3 = 0
  3. x = −5 or x = −3
12.Solve: x2 − 11x + 30 = 0[2 marks]

Answer: x = 6 or x = 5

  1. Factorise: (x − 6)(x − 5) = 0
  2. Null factor law: x − 6 = 0 or x − 5 = 0
  3. x = 6 or x = 5
13.Solve: x2 − 3x − 10 = 0[2 marks]

Answer: x = −2 or x = 5

  1. Factorise: (x + 2)(x − 5) = 0
  2. Null factor law: x + 2 = 0 or x − 5 = 0
  3. x = −2 or x = 5
14.Solve: x2 − 8x + 7 = 0[2 marks]

Answer: x = 7 or x = 1

  1. Factorise: (x − 7)(x − 1) = 0
  2. Null factor law: x − 7 = 0 or x − 1 = 0
  3. x = 7 or x = 1
15.Solve: x2 − 3x − 4 = 0[2 marks]

Answer: x = 4 or x = −1

  1. Factorise: (x − 4)(x + 1) = 0
  2. Null factor law: x − 4 = 0 or x + 1 = 0
  3. x = 4 or x = −1

Part D — Factorising and Solving Quadratics

16.Solve: 2x2 − 11x − 21 = 0[2 marks]

Answer: x = − or x = 7

  1. Factorise: (2x + 3)(x − 7) = 0
  2. 2x + 3 = 0 gives x = −
  3. x − 7 = 0 gives x = 7
17.Solve: 2x2 + 2x − 12 = 0[2 marks]

Answer: x = 2 or x = −3

  1. Factorise: (2x − 4)(x + 3) = 0
  2. 2x − 4 = 0 gives x = 2
  3. x + 3 = 0 gives x = −3
18.Solve: 2x2 − 22x + 56 = 0[2 marks]

Answer: x = 4 or x = 7

  1. Factorise: (2x − 8)(x − 7) = 0
  2. 2x − 8 = 0 gives x = 4
  3. x − 7 = 0 gives x = 7
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