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10th Grade Quadratics Topic Test — Answers

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

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Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Quadratics

10th Grade Quadratics Topic Test — Answers

Part A: Expanding Expressions (Distributive Property)

1.Expand and simplify: (x − 2)(x − 9)[2 marks]

Answer: x2 − 11x + 18

  1. x × x = x2
  2. x × −9 + −2 × x = −11x
  3. −2 × −9 = 18
2.Expand and simplify: (x − 6)(x + 8)[2 marks]

Answer: x2 + 2x − 48

  1. x × x = x2
  2. x × 8 + −6 × x = 2x
  3. −6 × 8 = −48
3.Expand and simplify: (x + 7)(x − 1)[2 marks]

Answer: x2 + 6x − 7

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

Answer: x2 − 7x + 6

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

Answer: x2 − 5x − 24

  1. x × x = x2
  2. x × 3 + −8 × x = −5x
  3. −8 × 3 = −24

Part B: Factoring and Solving Quadratics

6.Factor: x2 + x − 42[2 marks]

Answer: (x + 7)(x − 6)

  1. Find two numbers that multiply to −42 and add to 1: 7 and −6
7.Factor: x2 + 18x + 81[2 marks]

Answer: (x + 9)(x + 9)

  1. Find two numbers that multiply to 81 and add to 18: 9 and 9
8.Factor: x2 + x − 72[2 marks]

Answer: (x − 8)(x + 9)

  1. Find two numbers that multiply to −72 and add to 1: −8 and 9
9.Factor: x2 − 8x + 15[2 marks]

Answer: (x − 3)(x − 5)

  1. Find two numbers that multiply to 15 and add to −8: −3 and −5
10.Factor: 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

Part C: Factoring and Solving Quadratics

11.Solve: x2 − 4x − 21 = 0[2 marks]

Answer: x = 7 or x = −3

  1. Factor: (x − 7)(x + 3) = 0
  2. Zero product property: x − 7 = 0 or x + 3 = 0
  3. x = 7 or x = −3
12.Solve: x2 + 3x − 18 = 0[2 marks]

Answer: x = 3 or x = −6

  1. Factor: (x − 3)(x + 6) = 0
  2. Zero product property: x − 3 = 0 or x + 6 = 0
  3. x = 3 or x = −6
13.Solve: x2 − 13x + 36 = 0[2 marks]

Answer: x = 9 or x = 4

  1. Factor: (x − 9)(x − 4) = 0
  2. Zero product property: x − 9 = 0 or x − 4 = 0
  3. x = 9 or x = 4
14.Solve: x2 − 2x − 48 = 0[2 marks]

Answer: x = 8 or x = −6

  1. Factor: (x − 8)(x + 6) = 0
  2. Zero product property: x − 8 = 0 or x + 6 = 0
  3. x = 8 or x = −6
15.Solve: x2 + 2x + 1 = 0[2 marks]

Answer: x = −1 or x = −1

  1. Factor: (x + 1)(x + 1) = 0
  2. Zero product property: x + 1 = 0 or x + 1 = 0
  3. x = −1 or x = −1

Part D: Factoring and Solving Quadratics

16.Solve: 3x2 + 23x + 40 = 0[2 marks]

Answer: x = − or x = −5

  1. Factor: (3x + 8)(x + 5) = 0
  2. 3x + 8 = 0 gives x = −
  3. x + 5 = 0 gives x = −5
17.Solve: 3x2 + 15x − 18 = 0[2 marks]

Answer: x = 1 or x = −6

  1. Factor: (3x − 3)(x + 6) = 0
  2. 3x − 3 = 0 gives x = 1
  3. x + 6 = 0 gives x = −6
18.Solve: 3x2 + 5x + 2 = 0[2 marks]

Answer: x = − or x = −1

  1. Factor: (3x + 2)(x + 1) = 0
  2. 3x + 2 = 0 gives x = −
  3. x + 1 = 0 gives x = −1
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