Home Maths GCSE Guide English GCSE Guide Bookshop

Exam Papers

Click here to go to the answers

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) 4y - 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) 2x 6x
(ii) (3y)
(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) 12 can be written in the form ab where a and b are prime numbers. Calculate the values of a and b.
(b) B = 12 + 3 . Without using your calculator show that B = 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


Answers

 

(c) Matthew Pinkney