PAKISTAN INTERNATIONAL SCHOOL JEDDAH-

ENGLISH SECTION

ACADEMIC SESSION 2023-2024

Y8 MID YEAR REVIEW PACK 1*

NAME : ____________________

CLASS:_________

HARDWORK IS THE KEY TO SUCCESS

*Calculator is not allowed

 7 5
1. Work out −1 8 + 3 8 .
Give your answer as a fraction in mixed fraction. You
must show each step of your working.

1 1
2. Without using a calculator, work out × 303 − 6 × 3
6
You must show all your working and give your answer.

3. The penguin nursery is opened two times a day.

2 5
hour at noon and 12 hour in the afternoon.
3
Calculate for how much time is the penguin nursery opened every day?
Give your answer in hours and minutes.

2|Page
4. Work out the shaded area.

5. Ahmed buys a pack of 20 drinks to sell at the school shop.

The pack costs $5.
He wants to make a 40% profit.
How much should he sell each drink for?

6. Three students took a test. The test was out of 50 marks.

David scored 38 marks.

John scored half marks
Susan scored 72%

Who scored the highest? Show your working.

______________________

3|Page
7. Write the correct fraction in the box.

8. There are two cycle routes.

a) David is cycling the red route.

2
He has cycled 8 3 km.
How much further does he have to cycle?

b) Sam is cycling the blue route.

He takes a break exactly half way.
How many kilometres has he cycled at this point?

1 1
9. A boy spends 4 of his money on sweets and 3
on computer games.
What fraction of his money he does not spend?

__________________
4|Page
10. Look at the following equation.
45.6 ÷ 1.2 = 38
Use this information to write down the answers to the following.

(a) 456 ÷ 12 = _________

(b) 38 × 1.2 = __________

(c) 3.8 × 1.2 = __________

11. Work out 7.2 ÷ 0.15

_________________[2]

12. Work out the temperature when

(a) The temperature is 6°𝐶 and it falls by 13°𝐶, _______________________[1]

(b) The temperature is −2°𝐶 and it falls by 8°𝐶. _______________________[1]

13. Determine if each number is a rational number or an irrational number.

a) _______________________

b) ________________________

c) 4𝜋 ________________________

1
d) _________________________
3

e) √42 + 32 ________________________

f) ________________________

5|Page
14. Give the answer to each calculation as a single power.

a. 12−3 × 122 ________________________

b. 35 ÷ 3−3 ________________________

15. Show that is between 8 and 9.

16. Find the value of a in the following cases.

a. 5𝑎 × 5−3 = 54

________________________

b. 3𝑎 ÷ 35 = 1

________________________
𝑎 −5
c. 3 ×3 =3

________________________
3
17. Estimate √26 to the nearest integer.

________________________

6|Page
18. Solve these. Write the answer in standard form.
Show full working.

a) 9.5 × 103 + 6.5 × 103

________________________

b) 9.5 × 10−7 − 9.2 × 10−7

________________________

19. Write these numbers as powers of 2.

a) 32 __________________

b) 1 __________________

20. Work out the value of each expression when 𝑥 = 5, 𝑦 = 3 𝑎𝑛𝑑 𝑧 = −3 .

a. (2𝑥)3 + 𝑦 2

________________________
b. 𝑦(3𝑥 + 15𝑧)

________________________

4𝑥
c. 10𝑦 − 𝑥

________________________

7|Page
21. Simplify each expression.

a. 5𝑔2+ 10𝑔2 _______________________

b. (3𝑛5)2 _______________________

c. 13𝑥 − 4𝑥 + 6𝑥 _______________________

22. Expand the brackets and simplify.

a. (3𝑥 − 5)(𝑥 + 2)

________________________
b. (𝑚 + 6)2

________________________
c. (2𝑎 − 7)(𝑎 − 3)

________________________

23. Simplify these expressions.

55𝑚 3
a. 5𝑚

________________________
12𝑥 13𝑥
b. −
6 3

______________________
7𝑔 5ℎ
c. +
10 2

_______________________

8|Page
 5𝑥 2 +15𝑥
d.
10

________________________
9𝑎+27
e.
3

_________________________

24.
(a) Use the formula 3𝑥 = 𝑦3 + 2𝑧 to work out the value of x when y = 2 and z = 6.

x = ________

(b) Make z the subject of the formula. Work out the value of z when x = 6 and y = 2.

z = ______________

25. Write an algebraic expression for the sentence below (use the letter n to represent the missing number):

a) Subtract 5 from a number and then double it, ________________________

b) Double a number and add 4, ________________________

c) Square a number and add 5, ________________________

d) Subtract the number from 8 and then halve it. ________________________

9|Page
26. Make the subject, the letter mentioned in the given bracket.
a) 8 = 3𝑥 + 10𝑦 (𝑦)

ℎ
b) 𝑠 = (𝑚)
4𝑚

c) 𝑎 = √𝑔 (𝑔)

d) 𝑡 = 3𝑞2 − 1 (𝑞)

27. Complete these calculations

0.64 × __________ = 640

6400 ÷_______________= 64

_________ × 100 = 6.4

- 10 - | P a g e
28. Work out.

a) 13 × 10−5 ____________

b) 3.5 × 103 ____________

c) 6 ÷ 100 ____________

d) 0.05 ÷ 10−5 ____________

e) 36 ÷ 0.06 ____________

f) −36 ÷ −0.6 ____________

g) −36 × −0.06 ____________

29. Work out.

a) 5𝑥 + 5 = 30 − 2𝑥

x = ________
b) −3 = 15 − 2𝑦

y = ________
5
c) 𝑥−1 = 15

x = _________
36
d) =9
𝑑+3

d = ________

- 11 - | P a g e
 e) 18 + 3𝑦 = 33 − 2𝑦

y = ________

f) 12(𝑥 + 5) − 5(3𝑥 − 8) = 112

x = _________

g) 10(𝑥 − 4) = 5𝑥 + 11

x = _________

h) 9𝑥 2 + 50 = 3𝑥 2 + 536

x = _________

- 12 - | P a g e
30. Fanny is x years old.
Jane is 6 years elder than Fanny.

The sum of their ages is 30.

Work out the age of Fanny.

x = ________

31. Solve these inequalities.

Show each of these on a number line.
a. 4𝑥 − 3 ≥ 13

b. 6𝑦 + 8 < 8𝑦 − 2

c. 10 < 𝑦 + 3 < 15

- 13 - | P a g e
32. Work out

a. P is a prime number, write the smallest possible value of P when P ≥ 4

b. Q is an integer, write the largest possible value of Q when Q< −5

c. W is a whole number, write the possible values of W when −3 ≤ W < 5

33. Solve the simultaneous equations.

a) 𝑥 + 2𝑦 = 25
𝑥 − 2𝑦 = 15 (Elimination)

x = ________ y = ________
b) 𝑥 + 3𝑦 = 7
3𝑥 + 3𝑦 = 3 (Elimination)

x = ________ y = ________
c) 2𝑥 + 𝑦 = 20
𝑦 = 3𝑥 + 5 (Substitution)

x = ________ y = ________

- 14 - | P a g e
d) 𝑥 = 8 − 2𝑦
3𝑥 − 𝑦 = 10 (Substitution)

x = ________ y = ________

34. In this question use a ruler and compasses only. Show your construction lines.
Complete this construction to construct an angle of 30°.

35. Construct perpendicular bisector of the line 4 cm.

- 15 - | P a g e
36. Construct a regular hexagon inside a circle of radius 5cm.

37. Make an angle of 100 °.

Bisect it to get an angle of 50°. Show the working for bisection.

- 16 - | P a g e
38. Construct a triangle ABC with AB = 7cm, angle A = 90o, angle B = 30o.
At the end, measure the sides BC and AC.

39. Complete these statements.

(a) 35% of 60 = __________

(b) 25% of _______________ = 20

40. Complete the table by ticking() the correct column for each measurement.

Less than 1 gram Equal to 1 gram More than 1 gram

1000 milligram
1400 µg

10 kg

- 17 - | P a g e
41. Calculate

24×19+26×19
(a)
25

342
(b)
17

42. Here is a calculation.

109 ÷ 15 = 7 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟 4

Put a ring around the correct fraction for the answer to this calculation.

7 4 4 4 15
7 15 7 7
4 109 7 15 4

43. The population of a country is 39 634 274.

Write this number correct to the nearest million.

44. Are these terminating or recurring decimals?

a)

b)

c)

- 18 - | P a g e
45. Convert the following:
a. 6.2 𝑔 𝑡𝑜 𝑐𝑔

b. 450 𝑙 𝑡𝑜 𝑚𝑙

c. 675𝑚 𝑡𝑜 µ𝑚

46. Simplify:

a) t × t × t × t

b) 3𝑟 + 3𝑟2 − 𝑟 − 7𝑟2

c) (3𝑥2)3

2 7 1
d) +𝑥−𝑥
𝑥

1 𝑡
e) 2 + 𝑚

47. Here is a relationship involving powers of 5

5𝑚 ÷ 5𝑛 = 54

m and n are positive whole numbers each greater than 1.

Write down one possible pair of values for m and n.

m = _____, n = ______
- 19 - | P a g e
48. Work out
1 1 2
a. 6 2 − (5 3 × 3) ÷ 2 3

3 1 2 10
b. + (7 × 3) ÷ 21
5

3
c. (0.25 + ) + 3
4

49. Work out the formula for the nth term of these sequences.

a. 5 11 17 23 _________________________

b. 2 10 18 26 _________________________

c. 19, 16, 13, 10, _________________________

- 20 - | P a g e
50. The nth term of the sequence is 2𝑛2+ 4𝑛 − 1 . Work out the 5th term of the sequence.

5th term = ________

51. Find out if the sequences are linear or non linear.

a. 7, 15, 23, 31, 39 _____________

b. 2, 5, 9, 14, 20 _____________

52. The term to term rule of a sequence is multiply by 3.

The fourth term of a sequence is 54

Work out the first term of the sequence.

53. Find the first 4 terms of these sequences.

(a) The position to term rule is multiply by 2 then add 3

…………………….. ……………………….. ……………………. ………………….

(b) The third term is 17, term to term rule is add 5

…………………….. ……………………….. ……………………. ………………….

54. Is 61 a term of a sequence with nth term 3𝑛 − 1?

Show working.

- 21 - | P a g e
55. Complete the table of values for each equation.
𝑦 = 𝑥+3

x 0 1 3
y

𝑦 = 2𝑥 + 1
x 0 1 3
y
______________[1]
On graph paper, draw a coordinate grid from 0 to 5 on the
x-axis and 0 to 10 on the y-axis.
Plot the points and find the solution of these two equations.

Please label the lines clearly.

Graph and solution: ______________[3]

- 22 - | P a g e
56.
Complete the table of values for each equation.

𝑦 = 𝑥+5
x 2 4 6
y

𝑦 = 2𝑥 − 1
x 2 4 6
y
______________[1]
On graph paper, draw a coordinate grid from 0 to 7 on the
x-axis and 0 to 12 on the y-axis.
Plot the points and find the solution of these two equations.

Please label the lines clearly.

Graph and solution: ______________[3]

- 23 - | P a g e
57. Erik makes a pattern with tiles.

He records how many tiles are used for each pattern number.

Pattern number
1 2 3 4 5
(p)
Number of tiles
1 8 15 50
(t)

(a) Complete the table.

(b) Erik finds a rule connecting the pattern number and the number of tiles. Put a ring around
the correct rule.

𝑡 = 𝑝 + 7, 𝑡 = 6𝑝 − 1, 𝑡 = 7𝑝 + 1, 𝑡 = 7𝑝 − 6

- 24 - | P a g e