MATHEMATICS - QUADRATIC FORMULA

Quadratic Formula Worksheet

  • 10 questions
  • Solve quadratic equations by factorisation, completing the square and by use of the quadratic formula.
  • Difficulty: Hard
  • Board: CAIE
  • Attempt online on the examination portal

Here are the first 3 questions. Click “View all questions” to see the complete assessment.

Q1.

Solve 15x² − 14x − 8 = 0 by factorisation.

  1. A) x = 2/3 or x = − 4/5
  2. B) x = − 4/3 or x = 2/5
  3. C) x = 4/5 or x = − 2/3
  4. D) x = 4/3 or x = − 2/5

Q2.

Solve x² − 8x + 5 = 0 by completing the square.

  1. A) x = − 4 ± √(11)
  2. B) x = 4 ± √(21)
  3. C) x = 8 ± √(11)
  4. D) x = 4 ± √(11)

Q3.

Use the quadratic formula to solve 3x² + 4x − 2 = 0.

  1. A) x = frac − 2 ± √(10)3
  2. B) x = frac2 ± √(10)3
  3. C) x = frac − 2 ± √(5)3
  4. D) x = frac − 4 ± √(10)3

Q4.

Solve 0.24x² − 1.1x + 1 = 0 by first clearing the decimals and then factorising.

  1. A) x = 5/3 or x = 5/2
  2. B) x = 10/3 or x = − 5/4
  3. C) x = − 10/3 or x = − 5/4
  4. D) x = 10/3 or x = 5/4

Q5.

Solve the equation 3x(x − 2) = 2x + 7.

  1. A) x = frac4 ± √(21)3
  2. B) x = frac − 4 ± √(37)3
  3. C) x = frac8 ± √(37)3
  4. D) x = frac4 ± √(37)3

Q6.

Solve 2x² + 12x + 7 = 0 by completing the square.

  1. A) x = − 6 ± √(22)
  2. B) x = − 3 ± frac√(22)2
  3. C) x = − 3 ± frac√(11)2
  4. D) x = 3 ± frac√(22)2

Q7.

Solve (3x − 2)² = 4x + 9, giving the exact solutions.

  1. A) x = frac − 8 ± √(109)9
  2. B) x = frac16 ± √(109)9
  3. C) x = frac8 ± √(109)9
  4. D) x = frac8 ± √(61)9

Q8.

Solve 7x² − 5x − 9 = 0. Give both solutions correct to three significant figures.

  1. A) x ≈ 1.45 or x ≈ − 0.732
  2. B) x ≈ 0.832 or x ≈ − 1.55
  3. C) x ≈ 2.26 or x ≈ − 0.569
  4. D) x ≈ 1.55 or x ≈ − 0.832

Q9.

The diagram shows a rectangular garden. Using the dimensions and area marked on the diagram, which value of x is geometrically valid?

Diagram for question 9: The diagram shows a rectangular garden. Using the dimensions and area marked on the diagram, which value of…
  1. A) x = frac − 5 − √(329)4
  2. B) x = frac5 + √(329)4
  3. C) x = frac − 5 + √(305)4
  4. D) x = frac − 5 + √(329)4

Q10.

The diagram shows a straight line and a parabola. What are the x-coordinates of their points of intersection?

Diagram for question 10: The diagram shows a straight line and a parabola. What are the x-coordinates of their points of intersection?
  1. A) x = − 3 ± √(13)
  2. B) x = 6 ± √(13)
  3. C) x = 3 ± √(13)
  4. D) x = 3 ± √(5)

What this assessment covers

Concepts Tested

  • quadratic formula
  • Solve quadratic equations by factorisation, completing the square and by use of the quadratic formula.

Question Mix

  • Hard questions included

Skills you build

  • Apply

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