HIGHER LEVEL GCSE - Specimen Past Questions
1. A solution of the equation x
+ 2x =
200 lies between 3 and 4. Use trial and improvement to find this solution correct to 1
decimal place.
2. a) You are given the formula v = u +at ; 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.
3. Solve the simultaneous equations
2x + y = 9 and x - 2y = 7
4. 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?
5. 13.8% of the world’s population live in Europe. The population of the world is
5.72 x 10
.
Calculate the population of Europe.
6. Triangle ABC has a right angle at B. Angle BAC = 50° and length BC = 8.3cm. Calculate the length AC.
7. Given that y is proportional to x
,
complete the table.
| x | 5 | 20 | ||
| y | 45 | 180 | ||
8. The sides of a rectangle have dimensions 20cm and 30cm each measured to the nearest centimetre. Calculate the smallest possible area of the rectangle.
9. Factorise 2P y
+ 4P xy
10. Sam and Anna share £94.50 in the ratio 11:4. How much does each of them receive?
11. Solve the inequality 7x + 3 > 17 + 5x.
12. Simplify : (a) 2x
x 6x
(b) (3y
)
13. Multiply out and simplify (2x - 1) (x -3)
14. Find the n
terms of the sequences :
a) 2, 5, 8, 11 ............. b) 2, 5, 10, 17 ..............
15. A runner completes a 100m sprint in 11.61 seconds. The time is recorded to the nearest hundredth of a second. What are the upper and lolwer bounds of the possible times?
16. 
can be written in the form a
where a and b are prime numbers. Calculate the
values of a and b.
17. Solve the equation x
- 19x + 84 = 0
18. Simplify the expression 2x
- 5x + 2
-------------------
x - 4
19. Calculate the values of p and q such that x
- 8x + 17 = (x - p)
+ q.