# Year 9 Revision - Level 3

This is a level 3 revision exercise to help prepare for Year 9/end of Key Stage 3 tests.

Key stage:  KS 3

Curriculum topic:  Revision

Curriculum subtopic:  Year 9 Revision

Difficulty level:

### QUESTION 1 of 10

In this worksheet, you will find 40 questions that include many of the level 3 topics that you have learned this year.

Work through the questions carefully.

Calculators may not be used unless the question says that you may use one.

Good luck!

Work out:

8403 - 8.403 × 3

Work out:

78.39 × 8.7 ÷ 0.3

Is
 1 9
closer to
 1 8
or to
 1 10
?
1/8

1/10

both the same

By which of the given numbers is the following number divisible?

1 663 893

2

3

4

5

6

8

9

10

11

Select all the number types which could describe the number:

-√25

natural number

whole number

rational

irrational

integer

The number 37 999 is rounded to 38 000.

To how many significant figures could it have been rounded?

1 sig. fig.

2 sig. figs.

3 sig. figs.

4 sig. figs.

5 sig. figs.

¼ × 3.7 × 2.5 + ½ (5.22 + 3.42)

Write the answer to 1 decimal place.

Subtract these numbers, written in standard form

3.1 × 10-  3.1 × 10-2

Work out:

 8 - 4 + 5 15 18 21

(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)

Work out:

 8 ÷ 4 × 5 15 18 21

(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)

Change this fraction to a decimal:

 3 7

Work out:

 ( 6 )3 8

Simplify:

53 × 54

534

512

57

257

Round each of these numbers to 1 sig. fig. to work out an approximate answer to:

 29.12 × 31.9 √857.8

You may use a calculator for this question.

At this year's annual fete, Jack sold 476 hotdogs, which is a 12% increase compared to last year.

How many hotdogs did he sell in total in the two years, i.e this year and last year?

A book costs £24.56 but the price is increased by 12.5%.

This new price is then decreased by 12.5%.

Is the final price... ?

less than £24.56

£24.56

more than £24.56

Find the first 5 terms in the sequence given by the formula:

Tn = 100 - 2n2

where n is the position of the term in the sequence.

Also find the 20th term and the 100th term.

 value T1 T2 T3 T4 T5 T20 T100

Simplify:

a(-3a + 1) - 2a(a - 3)

-5a2 + 7a

-5a2 - 5a

-a2 - 5a

Select the correct HCF (Highest Common Factor) of these two algebraic expressions:

7p5q4r  and  21pq6r6

7pq4r

14pq4r

21pq4r

Simplify:

 15x4y3 35y4

 1. 3x4 2. 5x4 3. 3x3 7y 7y4 7y2
1.

2.

3.

Multiply out and simplify:

(4n - 1)2

16n2 + 1

16n2 - 8n - 1

16n2 - 8n + 1

16n2 - 1

Simplify:

(2p3q4)7

128p10q11

128p21q11

128p21q28

Solve for a:

3(5 - 2a) = 2 - 5(4 - a)

(Just write the value of a as a number.)

Solve simultaneously:

6x + 5y = 32

3x + y = 10

You may use a calculator for this question.

Solve the following equation:

 2a + 3a = 57 3 5

(Just write the value of a.)

State the gradient of a line which is perpendicular to the line with equation:

y = 4 - 7x

(If it is not a whole number, write it as a fraction in the form a/b.)

Use the graph shown below to solve the quadratic equation:

2x2 - x - 5 = 0

Select all the values of x that satisfy the quadratic equation.

x = -1.4

x = -2.6

x = 1.9

x = 2.1

The speed of light is approximately 300 000 000 m/s.

The average distance from the sun to the earth is 150 000 000 km.

Find the time taken for light to travel from the sun to the earth to the nearest minute.

(Just write the number.)

Convert the following area into one measured in cm2.

12.6 m2

(Just write the number.)

You may use a calculator for this question.

Find the area in cm2 of a circle of circumference 16 cm.

(Just write the number to 1 decimal place.)

You may use a calculator for this question.

Calculate the diameter, d cm, of a circle which has an area of 201 cm2

(Just write the number.)

You may use a calculator for this question.

The formula for the volume of a sphere, V, in terms of its radius, r, is:

V = 4/3πr3

A sphere has a volume of 1000 cm3

Calculate its radius in cm and its surface area in cm2.

(Just write the number.)

You may use a calculator for this question.

A regular polygon has an interior angle of 168¾º.

How many sides does it have?

You may NOT use a calculator for this question.

Look at these right-angled triangles, which are not drawn to scale.

Which side is longer, a or c?

a

c

both the same

You may use a calculator for this question.

Using trigonometry, calculate the side length x to 3 sig. figs.

You may use a calculator for this question.

Using trigonometry, find the height of this isosceles triangle in metres to 3 sig. figs.

(Just write the number.)

These two fair spinners are spun and the two scores are added together.

Use a sample-space diagram to answer the question.

What is the probability of getting a total score of 5?

(Write your answer with the / symbol, e.g. 2/3 and remember to reduce your fraction to its lowest terms.)

There are 7 red balls and 5 yellow balls in Bag 1.

There are 6 red balls and 4 yellow balls in Bag 2.

I take one ball from Bag 1 and then one ball from Bag 2.

What is the probability that I select a ball of each colour?

A tree diagram has been started for you below.

You may use a calculator for this question.

This table shows the masses of children in a Year 9 class at school.

Estimate the total mass in kg of all the children in the class.

Mass (m kg) Frequency
40 ≤ m < 45 2
45 ≤ m < 50 5
50 ≤ m < 55 9
55 ≤ m < 60 3
60 ≤ m < 65 1

You may use a calculator for this question.

This chart shows the heights of children in a Year 9 class at school.

Estimate the mean height of all the children in cm to 1 decimal place.

(Just write the number.)

• Question 1

Work out:

8403 - 8.403 × 3

8377.791
EDDIE SAYS
Work out 8.403 × 3 first. This equals 25.209.
Then subtract 8403.000 - 25.209.
• Question 2

Work out:

78.39 × 8.7 ÷ 0.3

2273.31
EDDIE SAYS
Use long multiplication to work out 7839 × 87.
Then divide the answer by 1000 to get 681.993.
Then multiply both numbers by 10 to give 6819.93 ÷ 3.
• Question 3
Is
 1 9
closer to
 1 8
or to
 1 10
?
1/10
EDDIE SAYS
1/9 = 1 ÷ 9 = 0.11111...
1/8 = 1 ÷ 8 = 0.125
1/10 = 1 ÷ 10 = 0.1
• Question 4

By which of the given numbers is the following number divisible?

1 663 893

3
9
11
EDDIE SAYS
2: ends in odd digit.
3: digit sum is 36, which is divisible by 3.
4: last two-digit number is not divisible by 4.
5: does not end in 0 or 5.
6: not divisible by 2.
8: last three-digit number is not divisible by 8.
9: digit sum is 36, which is divisible by 9.
10: does not end in 0.
11: compare alternate digit sums which are both 18.
• Question 5

Select all the number types which could describe the number:

-√25

rational
integer
EDDIE SAYS
This is -5, which can be written as a fraction so is rational.
It is not a whole number as it is negative, but it is an integer.
• Question 6

The number 37 999 is rounded to 38 000.

To how many significant figures could it have been rounded?

2 sig. figs.
3 sig. figs.
4 sig. figs.
EDDIE SAYS
37 999 is 40 000 to 1 sig. fig.
37 999 is 38 000 to 2 sig. figs.
37 999 is 38 000 to 3 sig. figs.
37 999 is 38 000 to 4 sig. figs.
37 999 is 37 999 to 5 sig. figs.
• Question 7

¼ × 3.7 × 2.5 + ½ (5.22 + 3.42)

Write the answer to 1 decimal place.

21.6
EDDIE SAYS
This comes to 21.6125.
• Question 8

Subtract these numbers, written in standard form

3.1 × 10-  3.1 × 10-2

309.969
EDDIE SAYS
3.1 × 102 = 310
3.1 × 10-2 = 0.031
310 - 0.031 = 309.969
• Question 9

Work out:

 8 - 4 + 5 15 18 21

(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)

173/315
EDDIE SAYS
LCM of 15, 18 and 21 is 630.
336/630 - 140/630 + 150/630 = 346/630 = 173/315
• Question 10

Work out:

 8 ÷ 4 × 5 15 18 21

(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)

4/7
EDDIE SAYS
8/15 × 18/4 × 5/21
Reduce within the calculation to get:
2/15 × 18/1 × 5/21
2/3 × 18/1 × 1/21
2/3 × 6/1 × 1/7 etc.
• Question 11

Change this fraction to a decimal:

 3 7

0.4286
EDDIE SAYS
3.00000000 ÷ 7 = 0.42857...
• Question 12

Work out:

 ( 6 )3 8

27/64
EDDIE SAYS
Reduce 6/8 to 3/4 first.
33 = 27
43 = 64
• Question 13

Simplify:

53 × 54

57
EDDIE SAYS
5×5×5 × 5×5×5×5 = 57
• Question 14

Round each of these numbers to 1 sig. fig. to work out an approximate answer to:

 29.12 × 31.9 √857.8
900
EDDIE SAYS
302 = 900
900 × 30 = 27000
√900 = 30
27000 ÷ 30 = 2700 ÷ 3 = 900
• Question 15

You may use a calculator for this question.

At this year's annual fete, Jack sold 476 hotdogs, which is a 12% increase compared to last year.

How many hotdogs did he sell in total in the two years, i.e this year and last year?

901
EDDIE SAYS
476 ÷ 1.12 = 425
425 + 476 = 901
• Question 16

A book costs £24.56 but the price is increased by 12.5%.

This new price is then decreased by 12.5%.

Is the final price... ?

less than £24.56
EDDIE SAYS
Try it with a starting price of £100.
This becomes £112.50, i.e. an increase of £12.50.
Then this is decreased by 12.5% of £112.50, which is a bigger decrease than £12.50.
• Question 17

Find the first 5 terms in the sequence given by the formula:

Tn = 100 - 2n2

where n is the position of the term in the sequence.

Also find the 20th term and the 100th term.

 value T1 T2 T3 T4 T5 T20 T100
EDDIE SAYS
T1 = 100 - 2 × 12 = 100 - 2 × 1 = 100 - 2 = 98
T2 = 100 - 2 × 22 = 100 - 2 × 4 = 100 - 8 = 92
T3 = 100 - 2 × 32 = 100 - 2 × 9 = 100 - 18 = 82
T4 = 100 - 2 × 42 = 100 - 2 × 16 = 100 - 32 = 68
T5 = 100 - 2 × 52 = 100 - 2 × 25 = 100 - 50 = 50
T20 = 100 - 2 × 202 = 100 - 2 × 400 = 100 - 800 = -700
T100 = 100 - 2 × 1002 = 100 - 2 × 10000 = 100 - 20000 = -19900
• Question 18

Simplify:

a(-3a + 1) - 2a(a - 3)

-5a2 + 7a
EDDIE SAYS
-3a2 + a - 2a2 + 6a
• Question 19

Select the correct HCF (Highest Common Factor) of these two algebraic expressions:

7p5q4r  and  21pq6r6

7pq4r
EDDIE SAYS
The HCF of 7 and 21 is 7.
Choose the smaller of the powers of each letter.
• Question 20

Simplify:

 15x4y3 35y4

 1. 3x4 2. 5x4 3. 3x3 7y 7y4 7y2
1.
EDDIE SAYS
Reduce the numbers first.
There is no x term on the bottom.
Reduce the y terms by subtracting their indices.
• Question 21

Multiply out and simplify:

(4n - 1)2

16n2 - 8n + 1
EDDIE SAYS
(4n - 1)(4n - 1) = 4n(4n - 1) - 1(4n - 1) =
16n2 - 4n - 4n + 1
• Question 22

Simplify:

(2p3q4)7

128p21q28
EDDIE SAYS
2p3q4 × 2p3q4 × 2p3q4 × 2p3q4 × 2p3q4 × 2p3q4 × 2p3q4 =
2 × 2 × 2 × 2 × 2 × 2 × 2 × p3 × p3 × p3 × p3 × p3 × p3 × p3 × q4 × q4 × q4 × q4 × q4 × q4 × q4
• Question 23

Solve for a:

3(5 - 2a) = 2 - 5(4 - a)

(Just write the value of a as a number.)

3
EDDIE SAYS
15 - 6a = 2 - 20 + 5a
-5a - 6a = 2 - 20 - 15
-11a = -33
a = 3
• Question 24

Solve simultaneously:

6x + 5y = 32

3x + y = 10

EDDIE SAYS
Rearrange 2nd equation to give y = 10 - 3x.
Substitute into 1st equation to get:
6x + 5(10 - 3x) = 32
6x + 50 - 15x = 32
-9x = -18
x = 2
y = 10 - 3x = 10 - 6 = 4
• Question 25

You may use a calculator for this question.

Solve the following equation:

 2a + 3a = 57 3 5

(Just write the value of a.)

45
EDDIE SAYS
Multiply both sides by the LCM of the denominators, i.e. 15.
10a + 9a = 855
19a = 855
a = 855 ÷ 19 = 45
• Question 26

State the gradient of a line which is perpendicular to the line with equation:

y = 4 - 7x

(If it is not a whole number, write it as a fraction in the form a/b.)

1/7
EDDIE SAYS
The gradient of the given line is -7.
A perpendicular line will have gradient 1/7, so that the gradients of the two lines multiply to give -1.
• Question 27

Use the graph shown below to solve the quadratic equation:

2x2 - x - 5 = 0

Select all the values of x that satisfy the quadratic equation.

x = -1.4
x = 1.9
EDDIE SAYS

• Question 28

The speed of light is approximately 300 000 000 m/s.

The average distance from the sun to the earth is 150 000 000 km.

Find the time taken for light to travel from the sun to the earth to the nearest minute.

(Just write the number.)

8
EDDIE SAYS
Working in km, 150 000 000 ÷ 300 000 = 500 seconds.
500 ÷ 60 = 8 mins and 20 seconds
• Question 29

Convert the following area into one measured in cm2.

12.6 m2

(Just write the number.)

126000
126 000
EDDIE SAYS
There are 100 × 100 = 10 000 cm2 in 1 m2.
• Question 30

You may use a calculator for this question.

Find the area in cm2 of a circle of circumference 16 cm.

(Just write the number to 1 decimal place.)

20.4
EDDIE SAYS
Diameter = 16 ÷ π = 5.0929...
Radius = 5.0929 ÷ 2 = 2.546479...
Area = π × r2 = π × 2.5464792 = 20.3718...
Don't round off until the very end.
• Question 31

You may use a calculator for this question.

Calculate the diameter, d cm, of a circle which has an area of 201 cm2

(Just write the number.)

16.0
EDDIE SAYS
Radius = √(201 ÷ π) = √63.98 = 7.9987...
Diameter = 7.9987 × 2 = 15.9975...
• Question 32

You may use a calculator for this question.

The formula for the volume of a sphere, V, in terms of its radius, r, is:

V = 4/3πr3

A sphere has a volume of 1000 cm3

Calculate its radius in cm and its surface area in cm2.

(Just write the number.)

EDDIE SAYS
Radius = ³√ [(3 × 1000) ÷ (4 × π)]
Surface area = 4 × π × r2
Don't round off the radius to find the surface area.
• Question 33

You may use a calculator for this question.

A regular polygon has an interior angle of 168¾º.

How many sides does it have?

32
EDDIE SAYS
360 ÷ (180 - 168¾)
• Question 34

You may NOT use a calculator for this question.

Look at these right-angled triangles, which are not drawn to scale.

Which side is longer, a or c?

both the same
EDDIE SAYS
a2 = 92 - 62 = 81 - 36 = 45
c2 = 32 + 62 = 9 + 36 = 45
• Question 35

You may use a calculator for this question.

Using trigonometry, calculate the side length x to 3 sig. figs.

13.4
EDDIE SAYS
x = 12 ÷ sin64°
• Question 36

You may use a calculator for this question.

Using trigonometry, find the height of this isosceles triangle in metres to 3 sig. figs.

(Just write the number.)

13.4
EDDIE SAYS
height = 2.6/tan11º
• Question 37

These two fair spinners are spun and the two scores are added together.

Use a sample-space diagram to answer the question.

What is the probability of getting a total score of 5?

(Write your answer with the / symbol, e.g. 2/3 and remember to reduce your fraction to its lowest terms.)

1/4
EDDIE SAYS
1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8

The probability of getting a total of 5, P(5) = 4/16 = 1/4.

• Question 38

There are 7 red balls and 5 yellow balls in Bag 1.

There are 6 red balls and 4 yellow balls in Bag 2.

I take one ball from Bag 1 and then one ball from Bag 2.

What is the probability that I select a ball of each colour?

A tree diagram has been started for you below.

29/60
EDDIE SAYS
A = 7/12
B = 4/10
C = 6/10
D = 4/10
Prob (2 different colours, i.e. RY or YR) = 7/12 × 4/10 + 5/12 × 6/10
= 28/120 + 30/120 = 58/120 = 29/60
• Question 39

You may use a calculator for this question.

This table shows the masses of children in a Year 9 class at school.

Estimate the total mass in kg of all the children in the class.

Mass (m kg) Frequency
40 ≤ m < 45 2
45 ≤ m < 50 5
50 ≤ m < 55 9
55 ≤ m < 60 3
60 ≤ m < 65 1
1030
EDDIE SAYS
Total is (2 × 42.5) + (5 × 47.5) + (9 × 52.5) + (3 × 57.5) + (1 × 62.5) = 1030 kg
• Question 40

You may use a calculator for this question.

This chart shows the heights of children in a Year 9 class at school.

Estimate the mean height of all the children in cm to 1 decimal place.

(Just write the number.)

132.3
EDDIE SAYS
The total estimated height of all the children is (1 × 117.5) + (3 × 122.5) + (4 × 127.5) + (7 × 132.5) + (4 × 137.5) + (2 × 142.5) + (1 × 152.5) = 2910 cm.
There are 1 + 3 + 4 + 7 + 4 + 2 + 1 = 22 children in the class.
Mean height = 2910 ÷ 22 = 132.3 cm (1 dp)
---- OR ----

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