Paper 2 style practice paper: Extended (non-calculator) — question paper

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

1. 1

   Evaluate (2³)².

   1. A64
   2. B256
   3. C12
   4. D512
   ( )
2. 2

   Simplify (x³)⁴ ÷ x⁵.

   1. Ax⁷
   2. Bx¹²
   3. Cx²
   4. Dx⁶⁰
   ( )
3. 3

   Work out 45% of 80.

   1. A36
   2. B40
   3. C45
   4. D32
   ( )
4. 4

   Written as an ordinary number, 6.3 × 10⁻² is

   1. A0.0063
   2. B0.63
   3. C630
   4. D0.063
   ( )
5. 5

   The nth term of 3, 7, 11, 15, … is 4n − 1. The 20th term is

   1. A79
   2. B80
   3. C81
   4. D76
   ( )
6. 6

   The solutions of x² − 5x + 6 = 0 are

   1. Ax = 1 and x = 6
   2. Bx = −2 and x = −3
   3. Cx = 2 and x = 3
   4. Dx = 3 only
   ( )
7. 7

   sin 30° + cos 60° equals

   1. A½
   2. B1
   3. C√3
   4. D0
   ( )
8. 8

   The gradient of the line through (1, 2) and (3, 8) is

   1. A⅓
   2. B2
   3. C6
   4. D3
   ( )
9. 9

   A translation maps (2, 3) to (−1, 7). The translation vector is

   1. A(−3, 4)
   2. B(3, −4)
   3. C(−1, 4)
   4. D(1, −4)
   ( )
10. 10

    A coin lands heads with probability 0.3. Flipped twice, P(two heads) is

    1. A0.6
    2. B0.09
    3. C0.3
    4. D0.21
    ( )

Section B: Structured questions[60 marks]

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

1. 11

   Indices, surds and standard form.

   1. (a)

      Evaluate 27^(2⁄3).

      [2]
   2. (b)

      Simplify √50.

      [2]
   3. (c)

      Work out (3 × 10⁴) × (4 × 10³), giving your answer in standard form.

      [1]
2. 12

   Fractions and percentages.

   1. (a)

      Work out (2½)².

      [2]
   2. (b)

      A price falls from $80 to $68. Find the percentage decrease.

      [2]
3. 13

   Ratio and proportion.

   1. (a)

      x : y = 3 : 4 and x + y = 84. Find x and y.

      [2]
   2. (b)

      A map has scale 1 : 50 000. Two towns are 3 cm apart on the map. Find the real distance in kilometres.

      [2]
   3. (c)

      Four workers take 9 days to dig a trench. How long would six workers take, working at the same rate?

      [1]
4. 14

   x = 8.4 correct to 1 decimal place and y = 3.2 correct to 1 decimal place.

   1. (a)

      Write down the upper and lower bounds of x.

      [2]
   2. (b)

      Calculate the upper bound of x + y.

      [2]
5. 15

   Factorise and simplify.

   1. (a)

      Factorise x² − 9.

      [1]
   2. (b)

      Factorise x² + 7x + 12.

      [2]
   3. (c)

      Simplify (x² − 4) ÷ (x + 2).

      [2]
6. 16

   Equations.

   1. (a)

      Make r the subject of V = ⅓πr²h.

      [2]
   2. (b)

      Solve the simultaneous equations 2x + y = 11 and x − y = 1.

      [3]
7. 17

   Quadratics.

   1. (a)

      Solve x² − 5x + 6 = 0 by factorising.

      [3]
   2. (b)

      Solve x² + 2x − 4 = 0 by completing the square, giving your answers in the form −1 ± √5.

      [2]
8. 18

   A sequence begins 4, 10, 18, 28, 40, …

   1. (a)

      Write down the next term.

      [1]
   2. (b)

      Show that the nth term is n² + 3n.

      [2]
   3. (c)

      Find the 10th term.

      [2]
9. 19

   f(x) = 2x − 3 and g(x) = x².

   1. (a)

      Find fg(2).

      [2]
   2. (b)

      Find f⁻¹(x).

      [2]
   3. (c)

      Find gf(1).

      [2]
10. 20

    The graph of y = x² − 4x + 3 is drawn.

    1. (a)

       Factorise x² − 4x + 3.

       [1]
    2. (b)

       Write down the coordinates of the x-intercepts.

       [1]
    3. (c)

       Find the coordinates of the turning point.

       [2]
    4. (d)

       Write down the y-intercept.

       [1]
11. 21

    A(1, 2) and B(5, 10).

    1. (a)

       Find the midpoint of AB.

       [1]
    2. (b)

       Find the gradient of AB.

       [1]
    3. (c)

       Find the exact length AB, giving your answer as a surd in its simplest form.

       [2]
    4. (d)

       Find the equation of the perpendicular bisector of AB.

       [2]
12. 22

    a = (4, −2) and b = (−1, 3).

    1. (a)

       Find a + b as a column vector.

       [1]
    2. (b)

       Find 2a − b as a column vector.

       [2]
    3. (c)

       Find |a|, giving your answer as a simplified surd.

       [2]