A18 solve quadratic equations (including those that require rearrangement) algebraically... Quiz: Pearson Edexcel Maths, Unit 2

The 20 questions

1. The quadratic formula gives the solutions of ax^2 + bx + c = 0 as

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

2. The standard form of a quadratic equation is

   • ax^2 + bx + c = 0
   • a/x + b = c
   • ax + b = 0
   • ax^3 + bx + c = 0

3. The solutions of x^2 + 5x + 6 = 0 are

   • x = -1 or x = -6
   • x = -2 or x = -3
   • x = -5 or x = -6
   • x = 2 or x = 3

4. What must you do before factorising a quadratic equation to solve it?

   • Isolate x squared
   • Square root
   • Equals zero
   • Divide by two

5. Completing the square turns x^2 + 6x into

   • (x + 3)^2 - 9
   • (x + 3)^2 + 9
   • (x + 6)^2 - 36
   • (x - 3)^2 - 9

6. The equation x^2 - 4x = 0 has how many solutions?

   • one
   • three
   • none
   • two

7. A quadratic equation has at most how many solutions?

   • one
   • three
   • four
   • two

8. How should you solve x^2 = 16 to find all values of x?

   • Only 4
   • Only -4
   • 8 and -8
   • Plus or minus 4

9. The solutions of x^2 - 7x + 12 = 0 are

   • x = 1 or x = 12
   • x = -3 or x = -4
   • x = 2 or x = 6
   • x = 3 or x = 4

10. The solutions of x^2 + 4x - 5 = 0 are

    • x = -1 or x = 5
    • x = 4 or x = -5
    • x = 1 or x = -5
    • x = 5 only

11. The solutions of 2x^2 - 8 = 0 are

    • x = 1 or x = -1
    • x = 2 or x = -2
    • x = 8
    • x = 4 or x = -4

12. Solving x^2 + 6x + 2 = 0 by completing the square gives

    • x = -3 ± √7
    • x = -6 ± √2
    • x = -3 ± 7
    • x = 3 ± √7

13. Using the quadratic formula on 2x^2 + 3x - 2 = 0, the solutions are

    • x = 0.5 or x = -2
    • x = 0.5 or x = 2
    • x = -0.5 or x = 2
    • x = 1 or x = -2

14. The solutions of x^2 = 2x + 8 are

    • x = 4 or x = -2
    • x = 2 or x = -8
    • x = 8 or x = -1
    • x = -4 or x = 2

15. A rectangle has length x + 3 cm and width x cm, with area 40 cm^2. The value of x is

    • x = 5 cm
    • x = 8 cm
    • x = -8 cm
    • x = 3 cm

16. The solutions of x(x + 2) = 15 are

    • x = 15 or x = -2
    • x = 3 or x = -5
    • x = 1 or x = -15
    • x = -3 or x = 5

17. The solutions of x^2 - 4x - 1 = 0 are

    • x = 2 ± √5
    • x = 2 ± √3
    • x = -2 ± √5
    • x = 4 ± √5

18. The solutions of x^2 - 3x - 2 = 0, to 2 decimal places, are

    • x = 3.56 or x = -0.56
    • x = 3.56 or x = 0.56
    • x = 1.56 or x = -1.56
    • x = 4.12 or x = -1.12

19. The solutions of 3/x = x - 2 are

    • x = 3 only
    • x = -3 or x = 1
    • x = 3 or x = -1
    • x = 2 or x = -3

20. If x^2 + bx + c = 0 has roots -3 and 5, then

    • b = -2 and c = 15
    • b = 8 and c = -15
    • b = 2 and c = 15
    • b = -2 and c = -15

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