1. The distance between two points on a map is 5 cm correct to the nearest centimetre. (a) Write down the (i) least upper bound of the measurement (ii) greatest lower bound of the measurement. (b) The scale of the map is 1 to 20 000. Work out the actual distance in real life (in kilometres) between the upper and lower bounds.

4 marks

 2. Triangle ABC is isosceles. AB = AC = 12cm . Angle ABC is 55 degrees. Calculate the area of the triangle correct to 3 significant figures.

 6 marks

 3. Solve the equations: (i) 4y² - 81 = 0 (ii)     1     +  1  =  -1      (x + 2)      3 6 marks

 4. There are 8 eggs. Two of the eggs have passed their sell by date and are 'bad'. 3 eggs are selected at random. (a) Complete the probability tree diagram.

 (b) Work out the probability that 3 'good' eggs will be selected. (c) Work out the probability that at least one 'bad' egg will be selected. 9 marks

 5. (a) Solve the inequality 7x + 3 > 17 + 5x (b) Simplify the following. (i) 2x³ × 6x² (ii) (3y³)² (c) Multiply out and simplify (2x - 1)(x - 3) 6 marks

 6. (a) Write down the nth term of the sequence 2, 5, 8, 11, ... . (b) Write down the nth term of the sequence 2, 5, 10, 17, ... . 4 marks

 7. Twenty five people took a test. The points scored are grouped in the frequency table below. (a) Work out an estimate for the mean number of points scored.

 Points Scored

 Number of people

 1 to 5

 1

 6 to 10

 2

 11 to 15

 5

 16 to 20

 7

 21 to 25

 8

 26 to 30

 2

 (b) Complete the table below to show the cumulative frequency for this data. (c) Draw a cumulative frequency graph for this data. (d) Use your graph to find an estimate for the median of this data.

 Points Scored

 Cumulative frequency

 1 to 5

 1 to 10

 1 to 15

 1 to 20

 1 to 25

 1 to 30

 9 marks

 8

 AB : AC = 1 : 3 (i) Work out the length of CD. (ii) Work out the length of BC. 4 marks

 9. Matthew and Nicola divide £94.50 in the ratio 11 : 4. How much does each of them receive? 3 marks

 10. (a) Ö12 can be written in the form aÖb where a and b are prime numbers. Calculate the values of a and b. (b) B = Ö12 + Ö3 . Without using your calculator show that B² = 27. 4 marks

 11. The temperature from a factory furnace varies inversely as the square of the distance from the furnace. The temperature 2 metres from the furnace is 50 degrees Celsius. Calculate the temperature 3.5 metres from the furnace. Give your answer to 2 decimal places. 5 marks

 12. A planet is 81 900 000 000 000 km from the Earth. (a) Write 81 900 000 000 000 in standard form. Light travels 3 × 10^5 km in 1 second. (b) Calculate the number of seconds that light takes to travel from the planet to the Earth. Give your answer in standard form correct to 2 significant figures. (c) Convert your answer to part (b) to days. Give your answer as an ordinary number. 7 marks

 13. Triangle ABC and vectors a and b are shown on the grid.

 (a) Draw the position of the triangle ABC after translation by the vector b - 2a. (b) (i) Write the vector AB in terms of a and b. (ii) Write the vector BC in terms of a and b. (c) D is an unmarked point on the grid.  BD = 2/3 BC and AD = xa + yb . Use your answers to (b) to calculate the values of x and y. You must show all your working. 7 marks

 14. A company makes compact discs (CDs). The total cost, P pounds, of making n compact discs is given by the formula P = a + bn , where a and b are constants. The cost of making 1000 compact discs is £58 000. The cost of making 2000 compact discs is £64 000. Calculate the values of a and b. 4 marks

 (c) Matthew Pinkney