2.14 Solution of linear and quadratic equations Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Solve 3x + 5 = 20.

   • 15
   • 5
   • 25/3
   • 8

2. Which values of x satisfy x^2 = 49?

   • x = 7 only
   • x = ±7
   • x = ±24.5
   • x = 49

3. Solve x^2 − 5x + 6 = 0 by factorising.

   • x = −2 or x = −3
   • x = 2 or x = 3
   • x = −1 or x = −6
   • x = 1 or x = 6

4. Which formula gives the solutions of ax^2 + bx + c = 0?

   • x = (−b ± √(b^2 + 4ac))/(2a)
   • x = (−b ± √(b^2 − 4ac))/(2a)
   • x = (b ± √(b^2 − 4ac))/(2a)
   • x = −b ± √(b^2 − 4ac)

5. Solve 2x − 7 = 3x + 1.

   • x = −6
   • x = 8
   • x = −8
   • x = 6

6. Which method rewrites a quadratic as (x + p)^2 = q to solve it?

   • Substitution
   • Completing the square
   • Factorising
   • Elimination

7. Solve 2x^2 + 3x − 2 = 0.

   • x = −1/2 or x = 2
   • x = 1/2 or x = 2
   • x = −1/2 or x = −2
   • x = 1/2 or x = −2

8. Use the quadratic formula to solve x^2 − 3x − 1 = 0.

   • x = (−3 ± √13)/2
   • x = (3 ± √5)/2
   • x = (3 ± √13)/2
   • x = 3 ± √13

9. Solve 5 − 2(x + 1) = 3x − 4.

   • x = 7/5
   • x = −5/7
   • x = −7/5
   • x = 5/7

10. A rectangle has length 2 cm more than its width, and an area of 24 cm^2. What is its width?

    • 4 cm
    • 3 cm
    • 6 cm
    • 8 cm

11. Solve x/3 + 2 = 5.

    • 3
    • 15
    • 9
    • 6

12. Solve x^2 = 4 graphically, using the intersection of y = x^2 and y = 4.

    • x = 2 only
    • x = ±2
    • x = ±16
    • x = ±4

13. What is the solution to the equation x² − 6x + 9 = 0?

    • x = 9
    • x = ±3
    • x = −3
    • x = 3

14. Solve (x + 1)/2 = (x − 3)/4.

    • x = −1
    • x = −5
    • x = 5
    • x = 1

15. A taxi charges £3 plus £1.50 per mile. A journey costs £18. How many miles were travelled?

    • 6
    • 12
    • 10
    • 9

16. Solve x^2 + 4x − 5 = 0 by completing the square.

    • x = −1 or x = −5
    • x = −1 or x = 5
    • x = 2 or x = −2
    • x = 1 or x = −5

17. Solve x^2 − 2x − 2 = 0.

    • x = −1 ± √3
    • x = 2 ± √3
    • x = 1 ± √2
    • x = 1 ± √3

18. Solve x^4 − 5x^2 + 4 = 0.

    • x = ±4 or x = ±1
    • x = ±1 only
    • x = ±1 or x = ±2
    • x = ±2 only

19. Solve 3x^2 − 10x + 8 = 0.

    • x = −4/3 or x = −2
    • x = 3/4 or x = 2
    • x = 4/3 or x = 2
    • x = 4/3 or x = −2

20. For what value of k does kx^2 + 4x + 1 = 0 have equal (repeated) roots?

    • 1/4
    • 2
    • −4
    • 4

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