INTERMEDIATE LEVEL GCSE - SPECIMEN PAST QUESTIONS
1. Alan is 15cm taller than Stephanie. Their heights add up to 319cm. How tall is Stephanie?
2. Sarah is 122cm tall. Sarah’s height has been given to the nearest centimetre. What is the minimum height she could be?
3. A Sequence begins 1, 3, 7, 15 ..... what are the next two numbers in the sequence?
4. The angles of a triangle are (2x - 3)° , (x + 4)° and (x + 19)° .
a) Write an expression, in terms of x, for the sum of the angles, write your answer in its simplest form.
b) The angles of a triangle add up to 180° . Write down an equation in x.
c) Solve your equation to find the size of the smallest angle in the triangle.
5. Find the value of p when 
6. Write 72 as a product of prime factors.
7. What is the highest common factor of 48 and 72?
8. What is the lowest common factor of 48 and 72?
9. Solve the equation 2x + 5 = 17 - x.
10. Solve the equation (x + 3) (x - 4) = 0
11. Solve the simultaneous equations.
2x + y = 9
x - 2y = 7
12. Some women walked one mile. The time taken by each was recorded. The results are in the table.
| TIME | 12  t < 16 |
16 t < 20 |
20 t < 24 |
24  t < 28 |
28  t < 32 |
| Number of women |
1 | 9 | 43 | 22 | 5 |
a) What is the model class for the time taken.
b) Calculate the mean time taken.
13. You are given the formula V = U + at.
a) Work out the value of V when U = 20 a = -6 and t = 
.
b) Rearrange the formula to give t in terms of V, U and a.
14. A town has a population of 645166 people. The ratio of retired people to the rest of the population is 1:3. How many people are retired?
15. In Britain there are 5.80 x 10
people. The number of retired people is 1.04 x 10
. What percentage of people in Britain are retired?
16. Complete the table of values for y = x 
- 2x - 2.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y | 6 | -2 | 1 | 13 |
17. A cake is made from fat, flour and sugar. The cake weighs 110g. The weight of the sugar is 42g.
a) What percentage of the cake is sugar?
b) The ratio of the weight of flour to the weight of sugar is 3:2. What is the weight of the flour?
c) The weight of the cake has been given to the nearest 10g, what is the minimum weight of the cake?
18. A large can of soup weighs 454g and costs 89p. A medium sized can of soup weighs 224g and costs 43p. Which size of soup gives more grams per penny?
19. 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 ...........
20. A Travel Saver Card entitles the holder to 40% off the normal price of a journey. A journey normally costs £28.50, how much would it cost with the Travel Saver Card?
21. a) Simplify x
- 2x - 3 + x - 5
b) Factorise 3a - 6a
c) Multiply out and simplify (2x - 1) (x - 3)
22. Write 186284 in standard form.
23. A cylinder is 20cm high and holds 1000cm
of water. Find the radius of the cylinder.
24. Box P contains five discs numbered 1, 2, 3, 4 & 5. Box Q also contains five discs numbered 1, 2, 3, 4 & 5. A disc is taken from each box.
a) What is the probaility that both discs are numbered 2?
b) What is the probability that both discs have the same number?