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Year 11 Quadratics Topic Test — Answers

Answer sheet with worked solutions for the Year 11 quadratics topic test.

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Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Quadratics

Year 11 Quadratics Topic Test — Answers

Part A: Expanding Brackets

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

Answer: x2 − 6x − 16

  1. x × x = x2
  2. x × 2 + −8 × x = −6x
  3. −8 × 2 = −16
2.Expand and simplify: (x + 5)(x − 5)[2 marks]

Answer: x2 − 25

  1. x × x = x2
  2. x × −5 + 5 × x = 0
  3. 5 × −5 = −25
3.Expand and simplify: (x + 8)(x + 3)[2 marks]

Answer: x2 + 11x + 24

  1. x × x = x2
  2. x × 3 + 8 × x = 11x
  3. 8 × 3 = 24
4.Expand and simplify: (x + 9)(x + 4)[2 marks]

Answer: x2 + 13x + 36

  1. x × x = x2
  2. x × 4 + 9 × x = 13x
  3. 9 × 4 = 36
5.Expand and simplify: (x − 5)(x − 7)[2 marks]

Answer: x2 − 12x + 35

  1. x × x = x2
  2. x × −7 + −5 × x = −12x
  3. −5 × −7 = 35

Part B: Factorising and Solving Quadratics

6.Factorise: x2 + 4x + 3[2 marks]

Answer: (x + 1)(x + 3)

  1. Find two numbers that multiply to 3 and add to 4: 1 and 3
7.Factorise: x2 − 9x + 20[2 marks]

Answer: (x − 4)(x − 5)

  1. Find two numbers that multiply to 20 and add to −9: −4 and −5
8.Factorise: x2 − 5x + 4[2 marks]

Answer: (x − 1)(x − 4)

  1. Find two numbers that multiply to 4 and add to −5: −1 and −4
9.Factorise: x2 − 3x − 4[2 marks]

Answer: (x + 1)(x − 4)

  1. Find two numbers that multiply to −4 and add to −3: 1 and −4
10.Factorise: x2 + 14x + 48[2 marks]

Answer: (x + 6)(x + 8)

  1. Find two numbers that multiply to 48 and add to 14: 6 and 8

Part C: Factorising and Solving Quadratics

11.Solve: x2 + 6x + 8 = 0[2 marks]

Answer: x = −4 or x = −2

  1. Factorise: (x + 4)(x + 2) = 0
  2. Null factor law: x + 4 = 0 or x + 2 = 0
  3. x = −4 or x = −2
12.Solve: x2 − 4x − 45 = 0[2 marks]

Answer: x = 9 or x = −5

  1. Factorise: (x − 9)(x + 5) = 0
  2. Null factor law: x − 9 = 0 or x + 5 = 0
  3. x = 9 or x = −5
13.Solve: x2 − 11x + 30 = 0[2 marks]

Answer: x = 5 or x = 6

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

Answer: x = −1 or x = −1

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

Part D: Factorising and Solving Quadratics

16.Solve: 2x2 + 16x + 24 = 0[2 marks]

Answer: x = -2 or x = −6

  1. Factorise: (2x + 4)(x + 6) = 0
  2. 2x + 4 = 0 gives x = -2
  3. x + 6 = 0 gives x = −6
17.Solve: 2x2 + 14x − 16 = 0[2 marks]

Answer: x = 1 or x = −8

  1. Factorise: (2x − 2)(x + 8) = 0
  2. 2x − 2 = 0 gives x = 1
  3. x + 8 = 0 gives x = −8
18.Solve: 3x2 + 19x + 28 = 0[2 marks]

Answer: x = − or x = −4

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