1. Work out 5% of $25.
2. Factorise 5 p+ pt .
3. Share 518 in the ratio 2 : 5.
4. Simplify 5 d−d−3 d−2 c
5. Calculate the area of a circle with radius 12cm.
6. Paula invests $600 at a rate of r% per year simple interest. At the end of 10 years, the total interest earned
is $90. Find the value of r.
x−2
7. Solve. (a) 8(w+11)=120 b ¿ 5( y−3)=3( y−2) c) =3
3
8. Solve the simultaneous equations. You must show all your working.
5 x+ 4 y =10
7 x−6 y =43
9.
The diagram shows a cuboid measuring 15cm by 12 cm by 4 cm.
Calculate a) Volume of cuboid b) surface area of the cuboid.
10. Javier invests $750 for 3 years at a rate of 1.8% per year compound interest. Calculate the value of his
investment at the end of the 3 years.
11. Factorise 12 x+15.
12. The price of a television is $560. This price is reduced by 18% in a sale. Work out the sale price.
13. Calculate the circumference of a circle with radius 4.5cm.
15. Expand and simplify a) 2(x +3) b) 3( y+ 2)−2 ( y−5) c) (x−3)(x +5)
16. The sides of a square are 15.1cm, correct to 1 decimal place. Find the upper bound of the area of the
square.
x 2 x+ 4
17. write − as a single fraction, in its simplest form.
2 x +1
18. Expand. x (x 3+ 3)
x+2 x−4
19. simplify a) −
3 2
19.
The diagram shows two sectors of circles with the same centre. Calculate the shaded area.
20. Factorise. a ¿ 18 y−3 ay+12 x−2 ax b) x 2−64
c) p2−9 q2 d) x 2−8 x +15 e) 2 x 2−5 x −12
21. A container is made from a cylinder and a cone, each of radius 5cm. The height of the cylinder is 12cm
and the height of the cone is 4.8cm.
Find the volume of the shape
[The volume, V, of a cone with radius r
1 2
and height h is V = π r ]
3
22. 540 tickets out of 630 are sold for this match. Calculate the percentage of tickets sold.
23. A cuboid measures 5cm by 4 cm by 2cm. (i) Calculate the volume of this cuboid. Give the units of your
answer.
24. Ella invests $4000 for 3 years at a rate of 1.2% per year compound interest. Calculate the value of her
investment at the end of the 3 years.
25. 7 (a) Soraya makes rectangular flags.
(ii) Each flag measures 1.2m by 1.8m. Calculate the area of one flag
(b) Each flag costs $15 to make. Soraya sells one flag for $21. Calculate the percentage profit.
26. 8 (a) The interior angle of a regular polygon with n sides is 150°. Calculate the value of n.
The diagram shows the floor of the room. (i) Calculate the area of the floor.
The height of the room is 3.6m (i) Calculate the volume
27.
28. Another glass is in the shape of a cylinder.
The cylinder has height 15cm and diameter 7cm.
Calculate the volume of the glass.
29. ) The amount of water, w litres, in a jug is 1.5 litres, correct to the nearest 0.1 litre. Complete this
statement about the value of w.
................... ≤ w ¿.................... [2]
30. 2 (a) Ali and Mo share a sum of money in the ratio Ali : Mo = 9 : 7. Ali receives $600 more than Mo.
Calculate how much each receives.
(b) In a sale, Ali buys a television for $195.80 . The original price was $220. Calculate the percentage
reduction on the original price.
(c) In the sale, Mo buys a jacket for $63. The original price was reduced by 25%. Calculate the original price
of the jacket.
31. (a) Dina invests $600 for 5 years at a rate of 2% per year compound interest. Calculate the value of this
investment at the end of the 5 years.
(b) The value of a gold ring increases exponentially at a rate of 5% per year. The value is now $882. (i)
Calculate the value of the ring 2 years ago.
32. Calculate the external curved surface area of a cylinder with radius 8m and height 19m.
33. ) The apples cost Mohsin $0.85 per kilogram to produce. He sells them at a profit of 60%. Work out the
selling price per kilogram of the apples.
34. Mohsin’s earnings increase exponentially at a rate of 8.7% each year. During 2018 he earned $195600.
During 2027, how much more does he earn than during 2018?
35. The diagram shows a hemisphere with radius 6cm.
Calculate the volume. Give the units of your answer.
4 3
[The volume, V, of a sphere with radius r isV = π r .]
3
36.
The diagram shows a prism ABCDEF. The cross-section is a right-angled triangle BCD. DC = 10 cm, BC =
5.2cm and ED = 18cm.find (a) volume of the cross –section
(a) Work out the volume of the prism.
37. (a) In a cycling club, the number of members are in the ratio males : females = 8 : 3. The club has 342
females. (i) Find the total number of members.
(ii) Find the percentage of the total number of members that are female.
(b) The price of a bicycle is $1020. Club members receive a 15% discount on this price. Find how much a
club member pays for this bicycle.
(c) In 2019, the membership fee of the cycling club is $79.50 . This is 6% more than last year. Find the
increase in the cost of the membership.
38.
(i) For the triangle, show that 3a+ 5 b = 170. (ii) For the quadrilateral, show that 9a+ 7 b = 310.
39. The price of another watch increases from $18 to $19.17 . Find the percentage increase in the price of this
watch.
40. Ella’s height is 75 cm, correct to the nearest cm.
Write down the upper bound of Ella’s height.
41.Find an expression for the perimeter of this triangle.
Give your answer in its simplest form.
42. The diagram shows an isosceles triangle.
Find the value of x.
43. The diagram shows two pairs of parallel lines.
Find the value of a, the value of b and the value of c.
44. Roberto buys a toy for $5.00 .
He then sells it for $4.60 .
Calculate his percentage loss.
45. (a) Find the value of x.
Give a geometrical reason for your answer.
(b) Work out the value of y.
Give a geometrical reason for your answer.
48. The interior angle of a regular polygon with n sides is 120°. Calculate the value of n.
49. find the value if x=2 w=−1
2x
a) Y =x −2 w b) Y =x 2−w c) Y = +3 w
w
50. make x the subject of the following
x+2 y
a) y=x −2 w b) A(x −3)=P c) =P d) x 2+ b2=C
W
