year 9 classwork booklet all questions to be answered …€¦ · 11 exercise 5 – define a prime...

Year 9 Mathematics – NUMBER CLASSWORK BOOK

1

Year 9 Classwork Booklet

All questions to be answered in exercise book

SECTION 1 – The Calculator - Pages 2 - 7

SECTION 2 – Number Review – Pages 8 - 26

SECTION 3 – Percentages will have its own separate booklet


2

Exercise 1 – No calculator requires

Round a number to a given number of calculations

Nearest whole number

a) 6.0 b) 9.9 c) 4.9 d) 8.5 e) 3.1 f) 8.9

g) 1.7 h) 9.0 i) 4.7 j) 7.9 k) 6.7 l) 3.3

m) 6.3 n) 2.2 o) 9.6 p) 8.8 q) 3.4 r) 6.4

s) 7.9 t) 1.2 u) 7.2 v) 8.7 w) 7.3 x) 5.1

1 Decimal Place (extension)

a) 56.5 b) 75.6 c) 34.7 d) 78.9 e) 31.7 f) 95.9

g) 45.4 h) 59.6 i) 35.2 j) 99.1 k) 70.8 l) 42.8

m) 64.8 n) 81.7 o) 51.8 p) 72.9 q) 29.5 r) 31.0

s) 36.6 t) 97.7 u) 48.8 v) 64.7 w) 77.3 x) 43.5

2 Decimal Places

a) 7.66 b) 5.97 c) 2.45 d) 1.22 e) 6.24 f) 8.59

g) 9.39 h) 5.90 i) 2.21 j) 7.16 k) 3.81 l) 4.52

m) 5.33 n) 1.72 o) 8.96 p) 8.95 q) 4.78 r) 5.48

s) 8.97 t) 1.46 u) 8.75 v) 2.82 w) 1.94 x) 8.42

2 Decimal Places (extension)

a) 73.30 b) 74.34 c) 23.06 d) 92.19 e) 45.77 f) 98.05

g) 22.35 h) 30.27 i) 49.34 j) 47.38 k) 52.07 l) 60.47

m) 21.36 n) 87.08 o) 51.95 p) 20.74 q) 62.42 r) 24.91

s) 12.01 t) 54.42 u) 39.35 v) 57.24 w) 57.87 x) 41.05

3 Decimal Places

a) 3.4250 b) 4.8630 c) 8.9620 d) 1.1250 e) 2.3430 f) 7.2370

g) 5.6920 h) 5.7870 i) 7.7490 j) 4.3450 k) 8.1770 l) 3.5440

m) 2.1430 n) 2.8120 o) 8.2040 p) 2.7290 q) 5.6060 r) 1.3710

s) 6.5400 t) 5.5160 u) 9.1300 v) 7.2790 w) 8.8710 x) 1.5010


3

Exercise 2

Use your calculator to answer the following. GIVE YOUR ANSWER TO 1 decimal place

Exercise 3

Use your calculator to answer the following. GIVE YOUR ANSWER TO 2 decimal places

a. 8 . 5 6 X 6 . 2 m. 7 . 5 4 ÷ 2 . 1

b. 9 . 7 2 X 1 . 1 n. 8 . 5 2 ÷ 2 . 1

c. 1 . 6 1 X 2 . 7 o. 8 . 4 6 ÷ 3 . 2

d. 4 . 4 6 X 7 . 9 p. 8 . 2 6 ÷ 1 . 4

e. 2 . 4 2 X 6 . 5 q. 8 . 1 3 ÷ 1 . 5

f. 2 . 8 1 X 8 . 5 r. 8 . 1 1 ÷ 2 . 9

g. 8 . 6 1 X 1 . 1 s. 9 . 3 8 ÷ 3 . 4

h. 9 . 6 4 X 9 . 1 t. 7 . 2 1 ÷ 3 . 7

i. 7 . 6 2 X 9 . 4 u. 9 . 3 1 ÷ 3 . 9

j. 6 . 9 7 X 6 . 3 v. 9 . 8 1 ÷ 1 . 7

k. 2 . 4 5 X 7 . 4 w. 9 . 4 3 ÷ 2 . 1

l. 7 . 5 9 X 5 . 5 x 7 . 5 6 ÷ 2 . 7

a. 7 . 1 7 X 4 . 8 7 m. 9 . 4 8 ÷ 3 . 7 2

b. 8 . 7 1 X 8 . 5 1 n. 6 . 7 7 ÷ 3 . 8 4

c. 6 . 3 6 X 1 . 6 5 o. 6 . 1 7 ÷ 3 . 5 9

d. 6 . 2 2 X 4 . 2 5 p. 7 . 4 6 ÷ 3 . 8 8

e. 7 . 3 5 X 9 . 6 6 q. 7 . 7 1 ÷ 2 . 5 1

f. 5 . 8 6 X 7 . 9 7 r. 7 . 7 2 ÷ 3 . 2 2

g. 5 . 3 5 X 3 . 5 4 s. 7 . 3 4 ÷ 3 . 6 3

h. 4 . 3 6 X 9 . 5 2 t. 6 . 7 7 ÷ 2 . 8 3

i. 4 . 5 7 X 4 . 9 9 u. 8 . 4 1 ÷ 1 . 1 3

j. 1 . 2 3 X 4 . 2 9 v. 8 . 4 6 ÷ 1 . 1 3

k. 3 . 3 8 X 6 . 1 9 w. 8 . 8 8 ÷ 2 . 8 5

l. 6 . 3 8 X 5 . 1 9 x 9 . 8 8 ÷ 1 . 7 9


4

Exercise 4

BRACKETS - Use your calculator to answer the following

Exercise 5

POWERS – Use your calculator to answer the following

a. ( 0.28 + 0.16 ) x 7 l. 29 - ( 0.25 + 0.12 )b. ( 0.24 + 0.21 ) x 19 m. 23 - ( 0.18 + 0.26 )c. ( 0.30 + 0.11 ) x 4 n. 25 - ( 0.21 + 0.27 )d. ( 0.20 + 0.13 ) x 15 o. 29 - ( 0.12 + 0.12 )e. ( 0.18 + 0.26 ) x 6 p. 21 - ( 0.15 + 0.28 )f. ( 0.16 + 0.13 ) x 2 q. 27 - ( 0.22 + 0.24 )g. ( 0.25 + 0.28 ) x 9 r. 24 - ( 0.16 + 0.21 )h. ( 0.19 + 0.18 ) x 9 s. 25 - ( 0.25 + 0.29 )i. ( 0.15 + 0.18 ) x 11 t. 22 - ( 0.23 + 0.18 )j. ( 0.23 + 0.19 ) x 18 u. 26 - ( 0.18 + 0.27 )k. ( 0.11 + 0.22 ) x 15 v. 21 - ( 0.14 + 0.26 )

a. 13 3 i. 3 2 q. 0.68 3

b. 13 2 j. 11 3 r. 0.24 2

c. 9 2 k. 12 2 s. 0.61 2

d. 7 3 l. 11 3 t. 0.38 3

e. 12 3 m. 4 3 u. 0.31 3

f. 2 2 n. 10 3 v. 0.2 3

g. 13 2 o. 11 3 w. 0.83 2

h 3 2 p. 4 2 x. 0.61 3

Extension

a. 10 2 x 6 2

b. 4 2 x 12 2

c. 9 2 x 12 2

d. 7 2 x 12 2

e. 3 2 x 12 2

f. 6 2 x 7 2

g. 11 2 x 13 2

h 13 2 x 11 2


5

Exercise 6 – Roots – Use your calculator to answer the following:

Give answers to one decimal place where necessary

a. √ 64 h. √ 62

b. √ 81 i. √ 124

c. √ 144 j. √ 54

d. √ 121 k. √ 621

e. √ 49 l. √ 234

f. √ 12 m. √ 34

g. √ 45 n. √ 555

Exercise 7 – Negatives

a. -1 + -1 a. -4 - -2

b. -6 + -2 b. 2 - -3

c. 0 + -3 c. -3 - -3

d. -5 + -3 d. -6 - -2

e. -5 + -3 e. -4 - -3

f. 3 + -2 f. -3 - -2

g. -6 + -3 g. 1 - -1

h. -3 + -1 h. -2 - -2

i. 0 + -2 i. 3 - -2

j. -5 + -3 j. 4 - -1

k. 1 + -3 k. 0 - -1

l. -4 + -3 l. 1 - -1

m. -5 + -2 m. -3 - -1

n. -4 + -2 n. 3 - -1

o. -4 + -3 o. -4 - -2

SECTION 1 SECTION 2


6

Exercise 8 – Fractions

Exercise 9 – Extension 1

Extension 2

1 3 6 2 3 4

13 10 13 12 14 7

1 3 6 3 4 6

9 15 12 11 16 13

3 5 4 4 4 1

9 12 15 8 14 9

1 3 4 4 1 4

13 9 7 16 8 13

6 5 4 5 6 4

8 11 10 8 8 8

1 3 3 4 4 6

16 11 7 10 11 11

p. x

q. x

r. x

m. x

n. x

o. x

j. +

k. +

l. +

g. +

h. +

i. +

d. +

e. +

f. +

+a.

b. +

c. +


7

Extension 3

Extension 4

Year 9 Classwork Book – NUMBER CLASSWORK BOOK SPK 2017

8

NUMBER REVIEW


9

Exercise 1 – List all the multiples of a given whole number

Write out the first SIX multiples of each number. The first one is done for you

2 - 2,4,6,8,10,12

3 -

4 -

5 -

6 -

7 -

8 -

9 -

10 -

12 -

20 -

50 -

100 -

Exercise 2

Look at the numbers below

22 14 36 17 6 200 40 15

Write THREE multiples of 2

Write TWO multiples of 3

Write TWO multiples of 20

Write ONE multiple of 7




10

Exercise 3 – List all the factors of a given number

Write out the ALL FACTORS of each number. The first two are done for you

12 - 1,2,3,4,6,12

24 - 1,2,3,4,6,8,12,24

15 -

25 -

20 -

100 -

8 -

18 -

36 -

24 -

42 -

17 -

5 -

What is different about the last two?

Exercise 4

Look at the numbers below

2 10 7 5 6 12 13 40

Write ONE factor of 15

Write TWO factors of 12

Write THREE factors of 120

Write THREE factors of 30

Write ONE factor of 7

Write ONE number that is a factor of BOTH 15 and 30


11

Exercise 5 – Define a prime number and list the first 10 prime numbers

You will be provided with a 1-100 grid to stick into your book

On your number grid, follow the instructions below:

- Shade in the number 1

- Shade in the MULTIPLES of 2, EXCEPT FOR 2 ITSELF – LEAVE IT BLANK




What numbers are left? Make a list under your grid.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100


12

Exercise 6

Are the numbers below prime or not prime? – If not, give a reason

Exercise 7

Calculate the HCF and LCM of two numbers from a list

HCF – Highest Common Factor

LCM – Lowest Common Multiple

Example

1. List the Factors of 12 and 30

12 – 1,2,3,4,6,12

30 – 1,2,3,5,6,15,30

THE COMMON FACTORS ARE 1,2,3 AND 6

THE HIGHEST COMMON FACTOR IS 6

Questions overleaf….


13

Exercise 7 continued:


14

Exercise 8 – Lowest common multiple

Example

The multiples of 4 are: 4,8,12,16,20,24,28,32

The multiples of 5 are: 5,10,15,20,25,30,35,40

THE LOWEST COMMON MULTIPLE of 4 and 5 is 20


15

Exercise 9 – Recall the square numbers up to 12 x 12

You will be provided with a multiplication grid, similar to the one below:

A square number is found by multiplying a number by itself, for example 4 x 4 = 16. So 16 is

a square number.

Stick the grid into your book and highlight the square numbers. Make a list of them under

your grid.

x 1 2 3 4 5 6 7 8 9 10 11 12

1 1 2 3 4 5 6 7 8 9 10 11 12

2 2 4 6 8 10 12 14 16 18 20 220 22

3 3 6 9 12 15 18 21 24 27 30 33 36

4 4 8 12 16 20 24 28 32 36 40 44 48

5 5 10 15 20 25 30 35 40 45 50 55 60

6 6 12 18 24 30 36 42 48 54 60 66 72

7 7 14 21 28 35 42 49 56 63 70 77 84

8 8 16 24 32 40 48 56 64 72 80 88 96

9 9 18 27 36 45 54 63 72 81 90 99 108

10 10 20 30 40 50 60 70 80 90 100 110 120

11 11 22 33 44 55 66 77 88 99 110 121 132

12 12 24 36 48 60 72 84 96 108 120 132 144


16

Exercise 10

Work out the square root of a given number

Without a calculator, work out the SQUARE ROOT of the following:

a. 25

b. 36

c. 121

d. 4

e. 49

f. 64

g. 100

h. 144

i. 1

j. 9

k. 81

Using your calculator, work out the square root of the following:

a. 289

b. 256

c. 400

d. 324

e. 361

Exercise 11 – Use your calculator to work out the following:

Extension


17

Exercise 11 – Recall the cube of 2, 3, 4, 5, and 10

Copy and complete into your exercise books

1 x 1 x 1 = 13 =

2 x 2 x 2 = 23 =

3 x 3 x 3 = 33 =

4 x 4 x 4 = 43 =

5 x 5 x 5 = 53 =

10 x 10 x 10 = 103 =

Exercise 12 – Work out the cube root of a number


18

Exercise 13 – Use index notation to write repeated products of numbers more concisely

42 means 4 x 4

63 means 6 x 6 x 6

105 means 10 x 10 x 10 x 10 x 10

Write the meaning of the following:

a. 122 i. 22 x 32

b. 43 j. 32 x 44

c. 143 k. 52 x 23

d. 54 l. 102 x 112

e. 73 m. 23 x 22 x 42

f. 92

g. 131

h. 203

Exercise 14

Re-write the following in index form – the first one is done for you

3 x 3 x 3 x 4 x 4 = 32 x 42

2 x 2 x 2 =

3 x 3 x 3 x 3 =

5 x 5 x 5 x 5 x 5 x 5 =

2 x 2 x 3 x 3 =

4 x 4 x 5 x 5 =

2 x 2 x 3 x 3 x 4 x 4 =

2 x 3 x 3 x 5 x 5 =

10 x 10 x 2 x 2 =


19

Exercise 15 – Extra Exercise


20

Exercise 16 – Multiply and divide positive and negative numbers


21

Exercise 17 – Perform addition and subtraction calculations involving negative numbers,

including directed numbers.

Exercise 18 – Use order of operation in numerical calculations

a. -4 + -2 a. 3 - -3

b. 1 + -1 b. -2 - -3

c. 2 + -2 c. 4 - -3

d. -1 + -1 d. -2 - -2

e. -5 + -1 e. -1 - -2

f. -6 + -1 f. -3 - -2

g. 2 + -1 g. -2 - -1

h. -6 + -1 h. -5 - -1

i. -4 + -1 i. 2 - -1

j. -2 + -2 j. 4 - -3

k. -2 + -2 k. -2 - -1

l. -6 + -1 l. 4 - -3

m. -6 + -2 m. -6 - -3

n. 3 + -3 n. -4 - -1

o. 1 + -2 o. 2 - -2

SECTION 1 SECTION 2


22

Exercise 19 – Express a number as a product of its Prime Factors

24 as a product of primes is 2 x 2 x 2 x 3 or 23 x 3 in index form

45 as a product of primes is 3 x 3 x 5 or 32 x 5 in index form.

Using the method shown in class, write the following numbers as a product of its primes:

Give your answer in index form

a. 12

b. 24

c. 20

d. 40

e. 56

f. 18

g. 72

h. 120

i. 46

j. 300

k. 100

l. 27

m. 81

n. 150

o. 200

p. 40

q. 26

r. 34

Extension

a. 9000

b. 235

c. 392

d. 715

e. 444

f. 792

g. 5625


23

Exercise 20 – Calculate the HCF and LCM of two numbers using their prime factor

decomposition.

Using the method shown in class, find the HCF of the following:

Find the LCM of the following:

Extension

Find the LCM of 15, 20 and 25


24

Extension Exercises

1. (a) Write 28 as the product of its prime factors.

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

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

Answer...............................................................................

(2)

(b) Find the least common multiple (LCM) of 28 and 42.

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Answer...............................................................................

(2)

(Total 4 marks)

2. (a) Write 18 as the product of its prime factors.

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

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

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

Answer ………………………………

(2)

(b) What is the least common multiple (LCM) of 12 and 18?

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

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

Answer ……………………………….

(1)

(Total 3 marks)

3. (a) Express 36 as a product of its prime factors.

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

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

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

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

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

Answer ................................................


25

(3)

(b) Find the Highest Common Factor (HCF) of 36 and 60.

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

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

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

Answer ................................................

(2)

(Total 5 marks)

4. (a) Express 144 as the product of its prime factors.

Write your answer in index form.

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

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

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

Answer ..................................................................

(3)

(b) Find the Highest Common Factor (HCF) of 60 and 144.

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

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

Answer ..................................................................

(2)

(Total 5 marks)

5. Express 120 as the product of its prime factors.

Give your answer in index form.

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

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

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

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Answer ............................................................

(Total 3 marks)

6. When written as the product of prime factors 22 53225


26

(a) Write 150 as the product of prime factors.


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

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

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

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

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

Answer ……………………………………………………

(3)

(b) Work out the highest common factor (HCF) of 225 and 150.

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

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

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

Answer ……………………………………………………

(2)

(Total 5 marks)

7. Express 360 as a product of its prime factors.


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

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

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

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

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

Answer .....................................................

(Total 3 marks)

year 9 classwork booklet all questions to be answered …€¦ · 11 exercise 5 – define a prime...

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