Chapter 3 Practice Paper: Quadratic Expressions and Equations — question paper

Section A: Multiple-choice questions[10 marks]

Answer all questions. For each question, write the letter (A, B, C or D) of the correct answer in the brackets provided.

1. 1

   Expand (x + 6)(x + 2).

   1. Ax² + 12x + 8
   2. Bx² + 8x + 8
   3. Cx² + 8x + 12
   4. Dx² + 12
   ( )
2. 2

   Expand (x − 3)².

   1. Ax² − 6x + 9
   2. Bx² − 9
   3. Cx² − 6x − 9
   4. Dx² + 6x + 9
   ( )
3. 3

   Factorise x² − 36.

   1. A(x − 6)²
   2. B(x + 6)²
   3. C(x − 36)(x + 1)
   4. D(x + 6)(x − 6)
   ( )
4. 4

   Factorise x² − 2x − 15.

   1. A(x + 5)(x − 3)
   2. B(x − 5)(x + 3)
   3. C(x − 15)(x + 1)
   4. D(x − 5)(x − 3)
   ( )
5. 5

   Factorise 3x² − 12x fully.

   1. A3(x² − 4x)
   2. B3x(x − 12)
   3. C3x(x − 4)
   4. Dx(3x − 4)
   ( )
6. 6

   Solve (x − 2)(x + 7) = 0.

   1. Ax = 2 or −7
   2. Bx = −2 or 7
   3. Cx = 2 or 7
   4. Dx = −2 or −7
   ( )
7. 7

   Solve x² = 100.

   1. Ax = 10
   2. Bx = 50
   3. Cx = −10
   4. Dx = 10 or −10
   ( )
8. 8

   The graph of y = (x + 1)(x − 9) crosses the x-axis at

   1. Ax = 1 and −9
   2. Bx = −1 and 9
   3. Cx = 1 and 9
   4. Dx = −1 and −9
   ( )
9. 9

   Expand (3x − 2)(x + 4).

   1. A3x² − 10x − 8
   2. B3x² + 14x − 8
   3. C3x² + 10x − 8
   4. D3x² + 10x + 8
   ( )
10. 10

    A ball’s height in metres after t seconds is h = t(20 − t). The ball is on the ground when

    1. At = 0 or 20
    2. Bt = 20 only
    3. Ct = 0 or −20
    4. Dt = 10
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show your working clearly.

1. 1

   This question is about expanding (x + 4)(x − 9).

   1. (a)

      Write down the four partial products.

      [2]
   2. (b)

      Collect the terms to write the expansion in its simplest form.

      expansion =[1]
   3. (c)

      Check your expansion by substituting x = 2 into both sides.

      [2]
2. 2

   Factorise each expression fully.

   1. (a)

      6x² − 15x

      factors =[1]
   2. (b)

      x² + 11x + 24

      [2]
   3. (c)

      x² − 81, naming the identity you used.

      [2]
3. 3

   This question uses factorisation to solve x² + x − 12 = 0.

   1. (a)

      Factorise the left-hand side.

      [2]
   2. (b)

      Write down both solutions of the equation.

      [2]
   3. (c)

      Verify one solution by substitution.

      [1]
4. 4

   A photo frame is (x + 6) cm long and (x − 2) cm wide, and its area is 20 cm².

   1. (a)

      Show that x satisfies the equation x² + 4x − 32 = 0.

      [2]
   2. (b)

      Find both values of x.

      [2]
   3. (c)

      State which solution fits the frame, and give its actual dimensions.

      [1]