S3 Revision
1. Find the value of
(a) 3.12 x 60 (b) 0.456 x 200 (c) 1.25 x 400 (d) 0.0078 x 6000
(e) 12.6 ÷ 40 (f) 345 ÷ 500 (g) 2.1 – 0.63 x 3 (h) 41.2 + 61.5 ÷ 50
2. Calculate the following percentages
(a) 30% of £340 (b) 20% of $4200 (c) 70% of £12 (d) 80% of £5250
(e) 45% of £160 (f) 65% of £6000 (g) 33⅓% of £630 (h) 66⅔% of £4200
3. Find
(a)
4. (a) f(x) = . Calculate f(-5).
(b) . Evaluate P = xy – x(x + y) when x= -2 and y = -3
5. (a) Solve the inequation 3 – (x – 2) > 5 – 3x
(b) Solve 2 – 3(x – 1) > 2x
6. Expand the brackets and simplify
(a) (2x – 1)(3x + 4) (b) (3m – 2n)2 (c) (2a – 3)(a2 – a – 2)
7. Factorise
(a) 3x2 – 12x (b) x2 – 25 (c) 2c2 – 8 (d) u2 – 4u – 12 (e) 2m2 – 3m – 9
8. Simplify
9. Solve
(a) 3x2 –6x = 0 (b) 2w2 – 18 = 0 (c) d2 - 6d = 16 (d) 3n2 – 2n – 8 = 0
10. Solve 3x2 – 5x – 1 = 0 giving your answers correct to 1dp.
11. The scattergraph below shows the marks of 15 pupils in maths and physics tests.
A line of best-fit has been drawn on the diagram.
(a)Calculate the equation of the line of best-fit.
(b)Laura scored 24 in her maths test. Use your equation to estimate her physics mark.
12. A pendulum is 45 centimetres long. When the pendulum swings it travels
along the arc of a circle and covers a distance of 27.5 centimetres.
Calculate the size of the angle through which the pendulum travels.
13. The radar beam sent out by an aeroplane reaches a distance of 120
kilometres and covers an angle of 150.
Calculate the area covered by the beam.
14. Calculate the mean and standard deviation of
13 15 18 14 13 20
15. The marks of 18 pupils in a test are shown below
1 2 3 8
2 0 5 9 9
3 1 1 4 5 5 5 9
4 0 2 6 8 1 2 represents 12
(a)Write down the modal mark.
(b)Find the median mark.
(c)Find the lower and upper quartiles of the marks.
(d)Show the information in a boxplot
16. Amanda earns £32 000 per annum. She agrees to a wage package that will see
her wage rise at a rate of 4.5% p.a. for each of the next 3 years and then by
5% p.a. for 2 years.
Calculate Amanda’s wage in 5 years time.
17. A raincloud contains 2500 litres of water. The cloud is increasing in size at
a rate of 4.3% per hour. Calculate the volume of water in the cloud in 8
hours time
18. (a) Solve the equation 4tan x + 9 = 1 0 ≤ x ≤ 360
(b) Solve the equation 3cos x + 3 = 2tan 45 0 ≤ x ≤ 360
19. Calculate the volume of the prism opposite.
20. A factory building has volume 2640 m3. The cross-
section of the building consists of a rectangle and a
triangle.
Calculate the width of the building.
21. H varies as the square of L and inversely as M.
(a)Find a formula connecting H, L and M.
(b)L is doubled and M is halved. What effect does this have on H?
22. P varies directly as the square of Q and as R.
(a)Write down a formula connecting P, Q and R.
(b)If Q is multiplied by 4 and R is halved, what effect does this have on P?
23. Solve (a) 3x – 2y = 13 (b) 6a – 3b = 3
2x + y = 11 4a – 2b = 2
24. (a) Mr. Paterson and his two children go to the theatre to see a play.
The cost of their tickets is £20.50.
Let x represent the cost of an adult ticket and y the cost of a child
ticket.
Write down an equation involving x and y.
(b) Mr. And Mrs. Kaur and their three children go to see the same play.
Their tickets cost £37.
Write down another equation involving x and y.
(c)Find the cost of an adult ticket and the cost of a child ticket.
25. In Astronomy, distances can be measured using different units. For example
1 parsec = 3.08 x 1013 kilometres and 1 Astronomical Unit = 1.49599 x 108 kilometres
Calculate the number of Astronomical Units in one parsec.
Give your answer in Scientific Notation.
26. Triangle ABC has AB = 11 cm, BC = 14 cm and
AC = 17 cm.
(a)Calculate the size of angle BAC.
(b) Hence find the area of the triangle.
27. An isosceles triangle of side 7cm
is cut from a square piece of metal
as shown.
Calculate the area of metal left after 80
the triangle is removed.
28. Calculate x in the triangle opposite
29. Two identical buildings are 58 metres apart, as shown in the diagram below.
Calculate the height of the buildings.