Year 8 Subject Math

Cairo British college

semester 2 – MID TERM
Math
Revision pack
Year 7

Name ……………..
Class: 8( )

1
1 Work out 23

(Total for Question 1 is 1 mark)

2 Work out the cube root of 64

(Total for Question 2 is 1 mark)

3 Write down the value of 49

(Total for Question 3 is 1 mark)

4 Write down the value of 32

(Total for Question 4 is 1 mark)

5 Write down a square number that is also an even number.

(Total for Question 5 is 1 mark)

6 Write down the value of 52

(Total for Question 6 is 1 mark)

7 Work out 104

(Total for Question 7 is 1 mark)

8 Write down the value of 36

(Total for Question 8 is 1 mark)

9 Work out 24

(Total for Question 9 is 1 mark)

10 Work out the cube root of 27

(Total for Question 10 is 1 mark)

11 Write down the value of 81

(Total for Question 11 is 1 mark)

12 Write down the value of 42

(Total for Question 12 is 1 mark)

13 Write down a square number that is also an odd number.

(Total for Question 13 is 1 mark)

14 Work out 53

(Total for Question 14 is 1 mark)

15 Write down the value of 82

(Total for Question 15 is 1 mark)

16 Work out the value of 5 × 103

(Total for Question 16 is 1 mark)

17 Here is a list of numbers

4 6 8 11 12 15 16 25

From the list, write down all the numbers that are powers of 2.

(Total for Question 17 is 1 mark)

18 Write 5 × 5 × 5 × 5 as a power of 5

(Total for Question 18 is 1 mark)

19 Here is a list of numbers

5 9 11 16 20 25 32 38

From the list, write down all the square numbers.

(Total for Question 19 is 1 mark)

20 Here is a list of numbers

6 12 15 21 27 36 64 80

From the list, write down all the cube numbers.

(Total for Question 20 is 1 mark)

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Practice Substitution
If a = 4 and b = 5

1. a + 8 = 2. 3b = 3. 2a + 9 = 4. a2 + a2 =

5. 30 ÷ b = 6. 2b + 3 = 7. a2 + b = 8. 24 – 4b =

9. a + b = 10. 5a – 2b = 11. 2b – a = 12. 2(a + b) =

13. a + b2 = 14. 10a – 2b2 = 15. b2 – a2 = 16. 3(2a + 2b) =

17. 5a2 + 2b2 = 18. 8b2(a – 2) = 19. 2.5(a2 -2b) = 20. 2b(1.5a + 2b) =

NCEA Level 1 - Algebra Worksheet 1

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Substitution Word Problems

Ordering Takeaways Fish is $5.50 per piece
Chips are $3 per scoop

1. What is the cost of 2 pieces of fish?

2. What is the cost of one scoop of chips and 1 piece of fish?

3. What is the cost of 2 fish and 2 scoops of chips?

4. What is the cost of 4 fish and 3 scoops of chips?

5. What did I buy if I spent $14?

6. What did I buy if I spent $28?

7. If I spent $11.50 what could I buy?

8. 14 people order hamburgers. The very hungry ones order 2 each while the rest order 1 each.
They purchase a total of 20 hamburgers. How many people were very hungry?

NCEA Level 1 - Algebra Worksheet 2

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Collecting Like Terms

Simplify:
1. 5x + 3y – 2x + 9y = 2. 5m2 + 3n + 2m2 – 2n =

3. 3p3 – 5q2 + 9p3 – 8q2 = 4. -3x2 + 4x + 12x2 – 12x =

5. Find the total length of all the edges of this cuboid.

4y
2x

3x

Simplify:
6. 14a2 – 10b – a2 + 5b = 7. 22xyz + 12xy – 5xyz + 4x =

8. 8pq + 7p + q + 10pq – q – p = 9. 13x2 + 4x2 – 5y2 + y2 – 12x2 =

10. 11ab + 2cd – ab + 3dc + ba = 11. 4x – 5x + 3x – x + 2x – 7y =

12. Which is larger and by how much? -13 + 8 – 4 + 6 – 3 + 9

or -31 + 27 – 3 – 6 + 18
NCEA Level 1 - Algebra Worksheet 4
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Multiplying Algebraic Terms

1. 2x × 6 = 2. -4x × 3y = 3. -3x × -2y =

4. 4y × y = 5. 4 × t × t × t = 6. x5 × x5 =

7. 3m2 × 5m3 = 8. 2q2 × 3q4 × 2q = 9. (6x2) 2 =

10. –(3c)2 = 11. (2a2)3 = 12. (7y12)0 =

Dividing Algebraic Terms

25 x 4 12 6
9y6
1. 15 x = 2. 16x ÷ 12x = 3. 6 y10 =

x3 y 4 10x 2 y 4 30 x 2 y 3
4. x 5 y 5 = 5. 5xy 2 = 6. 15 xy 3 =

27x 4 y 2 y4  y4 4x 2 y 3
7. 9 x 3 y = 8. y 3  y 2 = 9. 4 xy 3 =

NCEA Level 1 - Algebra Worksheet 5

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Simplifying Fractions
Simplify:

24 x 15 y 16
1. 3 2. 2 3. 12 x 2

y9 8 x10  6x5 y8
4. y3 5. x 8 6. xy 10

25 z 8 8x6  9 x10 y 5
7. 5 z 4 8. 4 x 10 9. 6 x 8 y10

4 x 3 2
2 xy 
2 3
4x3 y3
10. 2x3 11. 4 xy 2 12. ( 2 xy ) 2

NCEA Level 1 - Algebra Worksheet 8

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Expanding (1)
Expand these expressions:

1. 4(2x + y) 2. 5(5x – 2) 3. y(y + 2)

4. x(2x + 5) 5. 2y(3y – 8) 6. -3(x – 2)

Expand and simplify these expressions:

7. 3(x + 1) + 2(x + 3) 8. 4x + 3(x + 5) 9. 6(x – 2) + 2(2x – 1)

10. -2(y + 3) + 5(2y – 1) 11. 5(x + 8) – 4(x – 5) 12. 5(z – 1) – 2(z + 4)

NCEA Level 1 - Algebra Worksheet 10

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Expanding (2)
Expand these expressions:

1. 4(2x + y) 2. 5(5x – 2) 3. y(y + 2)

4. x(2x + 5) 5. 2y(3y – 8) 6. -3(x – 2)

Expand and simplify these expressions:

7. 3(x + 1) + 2(x + 3) 8. 4x + 3(x + 5) 9. 6(x – 2) + 2(2x – 1)

10. 2(y + 3) - 5(2y – 1) 11. -5(x + 8) + 4(x + 5) 12. 5(z + 1) – 2(z + 4)

NCEA Level 1 - Algebra Worksheet 11

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Factorising (1)
Factorise:

1. 5x + 5y 2. 12x + 3y 3. 20g – 10h

4. 12s – 16t 5. 30 – 16x 6. 4xy2 + 8xy

7. 5g + gh 8. xy + 10y 9. 3xy + 5y

10. 3pq – q2 11. 8xy + 24x 12. 3x2y – x3

13. 2xy2 + 4x2y 14. 6a2b2 + 3ab 15. 12ab + 14

NCEA Level 1 - Algebra Worksheet 13

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Solving Equations (1)

Solve for x:

1. 4x + 2 = 34 2. 3x + 4 = 25 3. 8y – 5 = 35

x x x2
4. 7 = 5 5. 4 + 9 = 16 6. 3 =7

2x  4
7. 2 =8 8. 2(x + 10) + 6 = 50 9. 3x + 25 = 8x – 10

4x  6
10. 2 + 5 = 18 11. 8x – 16 = 6x + 2 12. 12 – x = 9x

NCEA Level 1 - Algebra Worksheet 16

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Solving Equations (2)

Solve these equations:

1. x – 10 = 3(x + 2) 2. -4(x + 5) = 16

3. 5(x + 5) = 3(x – 4) 4. 3(x – 3) – (x – 2) = 5

x2
5. 10(x + 3) – 4(x – 2) = 7(x + 5) 6. 3
= 48

120 x2
7. x = 16 8. 30 – 2 = 28

NCEA Level 1 - Algebra Worksheet 17

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Inequalities
Solve:
1. 8x < 24 2. y + 6 ≥ 15 3. 3x + 5 ≤ 39

4. 22 + x > 30 5. x – 5 ≥ 24 6. 4y + 2 ≤ 2y + 11

7. -10x < 30 8. -5y ≥ -25 9. 32 – 4x ≤ 40

Mark the values on the number lines:

10. -4 < x ≤ 2 xR 11. -2 ≤ x ≤ 2 x R

-4 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3

12 -3 < x < 2 xI 13. -2 < x ≤ 3 x I

-4 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3

NCEA Level 1 - Algebra Worksheet 25

1 Work out 10% of £95

£.......................................................
(Total for question 1 is 1 mark)

2 Work out 50% of 1200 grams

....................................................... grams
(Total for question 2 is 1 mark)

3 Work out 1% of 200 litres

.......................................................litres
(Total for question 3 is 1 mark)

4 Find 21% of £160

£.......................................................
(Total for question 4 is 2 marks)

5 Find 45% of 820

.......................................................
(Total for question 5 is 2 marks)

6 Find 36% of 2500

.......................................................
(Total for question 6 is 2 marks)
7 Work out 252% of 120.

.......................................................
(Total for question 7 is 2 marks)

8 Which is greater
25% of 90 or 28% of 82

You must show your working.

….............…..........................….........................
(Total for question 8 is 3 marks)

9 Which is greater
30% of 105 or 32% of 98

You must show your working.

….............…..........................….........................
(Total for question 9 is 3 marks)
10 Richard gets a bonus of 30% of £130
Connor gets a bonus of £40

Work out the difference between the bonus Richard gets and the bonus Connor gets

£.......................................................
(Total for question 10 is 3 mark)

11 There are adults and children in a cinema.

There are 48 adults.
25% of the people at the cinema are children.

Work out the total number of people at the cinema.

.......................................................
(Total for question 11 is 3 marks)
12 David is paid £34000 per year.
He is going to get a 3% increase in the amount of money he is paid.

Work out how much money David will be paid per year after the increase

£.......................................................
(Total for question 12 is 2 marks)

13 Abbie buys a sofa for £540

She pays a deposit of 15% and the rest of the money in monthly payments of £17.

How many monthly payments will Abbie need to pay?

.......................................................
(Total for question 13 is 3 marks)
14 Dermot bakes 420 cakes.
He bakes only vanilla cakes, banana cakes and lemon cakes.
120 of the cakes are vanilla cakes.
35% of the cakes are banana cakes.

Work out the number of lemon cakes Dermot bakes.

.......................................................

(Total for question 14 is 3 marks)

15 Amelia and Sophie did a test.

The total for the test was 75 marks.

Amelia got 56% of the 75 marks.

Sophie got 43 out of 75

Who got the highest mark?

You must show all your working.

(Total for question 15 is 2 marks)

16 Zoe wants to buy 6 tins of beans for the cheapest possible price.

Shop A and Shop B both have a special offer.

Shop A Shop B

5% off the normal price of 48p 65p each

Buy 2 get 1 free

Which shop should Zoe buy the beans from?

You must show how you get your answer.

(Total for question 16 is 3 marks)

17 Gary buys a dress in a sale.

The normal price of the dress is reduced by 20%
The normal price is £36.80

Work out the sale price of the dress.

£.......................................................
(Total for question 17 is 3 marks)
1. (a) Simplify the ratio 25 : 35

....................
(1)
(b) Simplify the ratio 18 : 45

....................
(1)
(c) Simplify the ratio 300 : 25

....................
(1)

2. Divide £700 in the ratio 5 : 3 : 2

£............... £............... £...............

(3)
3. Alex and Thomas share 30 sweets.
They divide them in the ratio 3:2.

How many sweets does Thomas have?

.........................
(2)

4. Sophie has 60 pencils.

The ratio of sharpened pencils to blunt pencils is 4:1

How many sharpened pencils does Sophie have?

.........................
(2)
5. The number of people who voted for the Green Party in an election was 1500.
The number of people who voted for the Blue Party was 9000.

Write the ratio of Green Party voters to Blue Party voters in its simplest form.

................................
(2)

6. A piece of carpet is 240cm long.

Mr Jones cuts it into three pieces in the ratio 1 : 2 : 5

Work out the length of the longest piece of carpet.

................................
(3)
7. Sarah has some chocolates.

24 are white chocolate.

16 are milk chocolate.
8 are dark chocolate.

(a) Write down the ratio of white chocolate to milk chocolate to dark chocolate.
Give your ratio in its simplest form.

............... : ............... : ...............

(2)

Rachel has some apples and bananas.

The ratio of apples to bananas is 2 : 3
She has 14 apples.

(b) Work out how many bananas Rachel has.

.........................
(2)
8. Chris and Molly win money in a competition.
They share the money in the ratio 2 : 3
Molly receives £240.

(a) How much money does Chris receive?

£.........................
(2)

(b) How much money did they win in the competition?

£.........................
(1)

9. Divide £945 in the ratio 2 : 5

£......................... £.........................
(2)
10. At a rugby match, the ratio of children to adults is 2 : 3
There are 80 children in the crowd.
Each adult ticket costs £8
Each child ticket costs a quarter of the adult ticket.

Work out the total money made from ticket sales.

£.........................
(4)

11. Charlene and Danielle share some money in ratio 2 : 3

Danielle gets £25 more than Charlene.

How much does each girl receive?

Charlene £.........................

Danielle £.........................
(3)
12. The ratio of boys to girls in a school is 4 : 5
There are 220 boys in the school.

How many students attend the school?

.........................
(3)

13. The ratio of girls to boys in a class is 2 : 3

What fraction of the class are girls?

.........................
(1)
What percentage of the class are boys?

.........................
(1)
14. The angles in a triangle are in the ratio 1 : 2 : 9

What is the size of the largest angle?

.........................
(2)

15. Three angles are in the ratio 2 : 3 : 5

The smallest angle is 50⁰

Work out the sizes of the other two angles

............... and ...............

(2)
16. 4 schools sent students to a languages course.

One of the schools sent both French and German students.

The ratio of French to German students it sent was 1 : 3
The school sent 21 German students.

The other 3 schools sent the same number of students.

Work out the total number of students sent to the languages course.

.........................
(4)