2.9 Manipulation of rational expressions: Use of + – × ÷ for algebraic fractions with denominators being numeric, linear or quadratic Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Work out 1/2 + 1/3.

   • 1/5
   • 2/6
   • 5/6
   • 2/5

2. Simplify x^2 ÷ x.

   • x
   • x^2
   • 1/x
   • 2x

3. Simplify 6x/(9x^2).

   • 2x/3
   • 6/(9x)
   • 2/(3x)
   • 3/(2x)

4. What is the definition of an algebraic rational expression?

   • Sum of polynomials
   • Power of polynomials
   • Product of polynomials
   • Ratio of polynomials

5. Work out 2/5 × 3/7.

   • 6/12
   • 6/10
   • 6/35
   • 5/21

6. Work out (3/4) ÷ (9/8).

   • 2/3
   • 4/3
   • 27/32
   • 1/6

7. Simplify (x + 1)/2 + (x − 1)/3.

   • (5x + 1)/5
   • (4x + 2)/6
   • (5x + 1)/6
   • (5x − 1)/6

8. Simplify (x^2 − 4)/(x + 2).

   • (x − 2)/(x + 2)
   • x + 2
   • x^2 − 2
   • x − 2

9. Simplify (2x)/(x + 3) × (x + 3)/(4x^2).

   • 2x
   • 1/(2x)
   • 1/(2x^2)
   • 1/(4x)

10. Simplify (x^2 − 9)/(x^2 + x − 6).

    • (x − 3)/(x − 2)
    • (x + 3)/(x − 2)
    • (x − 2)/(x − 3)
    • (x − 3)/(x + 2)

11. Express 3/(x + 1) + 2/(x − 1) as a single fraction.

    • 5x/(x^2 − 1)
    • (5x − 1)/(x^2 − 1)
    • (5x + 1)/(x^2 − 1)
    • (3x + 2)/(x^2 − 1)

12. Simplify (x^2 + x)/(x^2 − 1).

    • (x + 1)/(x − 1)
    • x/(x − 1)
    • x^2/(x − 1)
    • x/(x + 1)

13. Simplify (2x^2 − 8)/(x + 2) ÷ (x − 2)/(x + 2).

    • 2(x + 2)
    • (2x + 4)/(x − 2)
    • 2(x − 2)
    • 2(x + 2)(x − 2)

14. Simplify x/(x − 2) − 2/(x − 2).

    • 1
    • x + 2
    • (x − 4)/(x − 2)
    • x − 2

15. Simplify (3x − 6)/(2x) ÷ (x − 2)/(4x^2).

    • 12x
    • 6x^2
    • 6x
    • 3x

16. Simplify (2x + 3)/(x^2 − x − 6) − (x − 1)/(x^2 − x − 6).

    • (x + 4)/(x^2 − x − 6)
    • (x + 4)/(x^2 − 6)
    • (x + 2)/(x^2 − x − 6)
    • (3x + 2)/(x^2 − x − 6)

17. Simplify (x^2 − 1)/(x^2 + 2x + 1) ÷ (x − 1)/(x + 1).

    • (x + 1)/(x − 1)
    • 0
    • (x − 1)/(x + 1)
    • 1

18. Express 1/x − 1/(x + 1) as a single fraction.

    • 1/(x(x + 1))
    • 1/(x^2 + 1)
    • 1/(x + 1)
    • (2x + 1)/(x(x + 1))

19. Simplify (x/(x + 2)) ÷ (x^2/(x^2 − 4)).

    • (x + 2)/x
    • x/(x − 2)
    • (x − 2)x
    • (x − 2)/x

20. Simplify 4/(x^2 − 9) − 2/(x − 3).

    • −2(x + 1)/(x^2 − 9)
    • −2/(x^2 − 9)
    • −2(x − 1)/(x^2 − 9)
    • 2(x + 1)/(x^2 − 9)

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