level 5
KS3 Revision work Level 5 1.
Frog spawn The graph shows the date each year that frogs’ eggs were first seen.
28th Feb
21st Feb
14th Feb Date eggs first seen 7th Feb
31st Jan
24th Jan 87
88
89
90
91
92
93
94
95
96
97
98
99
Year
(a)
On what date in 1997 were frogs’ eggs first seen?
............................... 1 mark
Hertfordshire La Schools
1
(b)
At the beginning of each year, the warmer the weather, the earlier frogs’ eggs are first seen. What can you say about the weather at the beginning of 1991?
1 mark
2.
1976 v 2002 Look at this information. In 1976, a man earned £16 each week.
The pie chart shows how he spent his money.
Other Clothes
Entertainment
Rent
Food
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2
(a)
How much did the man spend on food each week? £ 1 mark
(b)
Now look at this information. In 2002, a man earned £400 each week.
The table shows how he spent his money.
Hertfordshire La Schools
Rent
£200
Food
£100
Entertainment
£50
Other
£50
3
Complete the pie chart below to show how the man spent his money. Remember to label each sector of the pie chart.
2 marks
Hertfordshire La Schools
4
3.
Mean and median (a)
Look at these three numbers.
9
11
10
Show that the mean of the three numbers is 10
1 mark
Explain why the median of the three numbers is 10
1 mark
(b)
Four numbers have a mean of 10 and a median of 10, but none of the numbers is 10 What could the four numbers be? Give an example.
1 mark
Hertfordshire La Schools
5
4.
Percentages (a)
Write the missing numbers.
50% of 80 = .................
5% of 80 = .................
1% of 80 = .................
2 marks
(b)
Work out 56% of 80 You can use part (a) to help you.
................. 1 mark
Hertfordshire La Schools
6
5.
Completing calculations Write a number in each box to make the calculations correct.
+
=
–8
–
=
–8
2 marks
6.
Numbers Here is a list of numbers:
–7
–5
–3
–1
0
2
4
6
You can choose some of the numbers from the list and add them to find their total.
For example,
...6... (a)
+
..–..1..
=
5
Choose two of the numbers from the list which have a total of 3
......
+
......
=
3 1 mark
Hertfordshire La Schools
7
(b)
Choose two of the numbers from the list which have a total of –1
......
+
–1
...... =
1 mark
Choose two other numbers from the list which have a total of –1
......
+
–1
...... =
1 mark
–7 (c)
–5
–3
–1
0
2
4
6
What is the total of all eight of the numbers on the list?
1 mark
Hertfordshire La Schools
8
(d)
Choose the three numbers from the list which have the lowest possible total. Write the three numbers and their total. You must not use the same number more than once.
......
+
...... =
...... 2 marks
7.
Odd or even? (a)
I am thinking of a number. My number is a multiple of 4 Tick (
) the true statement below. My number must be even
My number must be odd
My number could be odd or even
Explain how you know.
1 mark
Hertfordshire La Schools
9
(b)
I am thinking of a different number. My number is a factor of 20 Tick (
) the true statement below. My number must be even
My number must be odd
My number could be odd or even
Explain how you know.
1 mark
8.
Fir trees The graph shows the average heights of fir trees of different ages.
2.5
2
1.5 Height (metres) 1
0.5
0 2
Hertfordshire La Schools
3
4 Age (years)
5
6
10
The table shows the cost of fir trees of different heights.
Cost
(a)
120 cm to 159 cm
160 cm to 199 cm
200 cm to 239 cm
£ 20.00
£ 25.00
£ 30.00
One of these fir trees is 5
1 years old. 2
How much is it likely to cost? £ ...................... 1 mark
(b)
One of these fir trees costs £ 25.00 How old is the tree likely to be?
Between ...................... and ...................... years old 1 mark
Hertfordshire La Schools
11
9.
Teachers A newspaper predicts what the ages of secondary school teachers will be in six years’ time. They print this chart. 100%
Key:
Age in years 50+ 40 to 49 30 to 39 20 to 29
50%
0% Male
(a)
Female
The chart shows 24% of male teachers will be aged 40 to 49 About what percentage of female teachers will be aged 40 to 49?
........................... % 1 mark
(b)
About what percentage of female teachers will be aged 50+?
........................... % 1 mark
Hertfordshire La Schools
12
(c)
The newspaper predicts there will be about 20 000 male teachers aged 40 to 49 Estimate the number of male teachers that will be aged 50+
............................... 1 mark
(d)
Assume the total number of male teachers will be about the same as the total number of female teachers. Use the chart to decide which statement is correct. Tick () your answer.
Generally, male teachers will tend to be younger than female teachers. Generally, female teachers will tend to be younger than male teachers.
Explain how you used the chart to decide.
1 mark
Hertfordshire La Schools
13
10.
Huts You can make ‘huts’ with matches.
1 hut needs 5 matches
2 huts need 9 matches
3 huts need 13 matches
A rule to find how many matches you need is
m = 4h + 1
m stands for the number of matches. h stands for the number of huts.
(a)
Use the rule to find how many matches you need to make 8 huts. Show your working.
................ matches 2 marks
(b)
I use 81 matches to make some huts. How many huts do I make? Show your working.
....................... huts 2 marks
Hertfordshire La Schools
14
(c)
Andy makes different ‘huts’ with matches.
1 hut needs 6 matches
2 huts need 11 matches
3 huts need 16 matches
Circle the rule below that shows how many matches he needs. Remember:
m stands for the number of matches. h stands for the number of huts.
mh+5 m 5h + 1
m 4h + 2 m 5h + 2
m 4h + 3 m h + 13 1 mark
11.
Lemonade Kate buys 24 cans of lemonade. She buys the cans in packs of 4 Each pack costs £1.20
Pack of 4 Cost £1.20
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15
Steve buys 24 cans of lemonade. He buys the cans in packs of 6 Each pack costs £1.60
Pack of 6 Cost £1.60
Kate pays more for her 24 cans than Steve pays for his 24 cans. How much more?
..................... p 2 marks
Hertfordshire La Schools
16
12.
Matching expressions A ruler costs k pence. A pen costs m pence. Match each statement with the correct expression for the amount in pence. The first one is done for you.
Statement
Expression
5k The total cost of 5 rulers 5m
5 – 5m The total cost of 5 rulers and 5 pens 500 – 5m
How much more 5 pens cost than 5 rulers
5k + m
5(k + m)
The change from £5, in pence, when you buy 5 pens
5m – 5 k
5k – 5 m 3 marks
Hertfordshire La Schools
17
13.
Yards Some people use yards to measure length. The diagram shows one way to change yards to metres.
number of yards
(a)
× 36
× 2.54
100
number of metres
Change 100 yards to metres.
................... metres 1 mark
(b)
Change 100 metres to yards. Show your working.
..................... yards 2 marks
Hertfordshire La Schools
18
14.
Thinking percentages (a)
What is 30% of 250?
............................... 1 mark
(b)
I’m thinking of a number. 10% of my number is 84 Show calculations and explain how you can work out that 15% of my number is 126
1 mark
What is 12 21 % of my number?
............................... 1 mark
Hertfordshire La Schools
19
15.
Rectangles and squares Here is a rectangle. 8cm Not drawn accurately
2cm
(a)
A square has the same area as this rectangle. What is the side length of this square?
......................... cm 1 mark
(b)
A different square has the same perimeter as this rectangle. What is the side length of this square?
......................... cm 1 mark
Hertfordshire La Schools
20
16.
Rectangles A rectangle has an area of 24 cm2 How long could the sides of the rectangle be? Give three different examples.
......................... cm
and
......................... cm
......................... cm
and
......................... cm
......................... cm
and
......................... cm 2 marks
17.
Shape rotation Look at this shape made from six cubes. Four cubes are white Two cubes are grey.
Hertfordshire La Schools
21
Part of the shape is rotated through 90° to make the shape below.
After another rotation of 90°, the shape is a cuboid. Draw this cuboid on the grid below.
Isometric grid 2 marks
Hertfordshire La Schools
22
18.
Solving Solve these equations. 2k + 3 11
k ......................... 1 mark
2t + 3 –11
t ......................... 1 mark
Hertfordshire La Schools
23
19.
Same area The square and the rectangle below have the same area. Not drawn accurately
4 cm
2 cm y cm 4 cm
Work out the value of y
y .................... cm 1 mark
Hertfordshire La Schools
24
20.
Thinking triangularly Some statements in the table are true. Some are false. Beside each statement, write true or false. For true statements you must draw an example. The first one is done for you. Statement Some triangles have one right angle and two acute angles.
Write true or false. If true, draw an example.
true
Some triangles have three right angles.
Some triangles have three acute angles.
Some triangles have one obtuse angle and two acute angles.
Some triangles have two obtuse angles and one acute angle. 3 marks
Hertfordshire La Schools
25
21.
Positive and negative Look at this equation.
y = 2x + 10 (a)
When x = 4, what is the value of y?
................. 1 mark
(b)
When x = – 4, what is the value of y?
................. 1 mark
(c)
Which equation below gives the same value of y for both x = 4 and x = – 4 ? Put a ring round the correct equation.
y = 2x
y=2+x
y = x2
y=
x 2 1 mark
Hertfordshire La Schools
26
22.
Three angles Three shapes fit together at point B.
93º A
24º B
Not drawn accurately
61º C
Will ABC make a straight line? Yes
No
Explain your answer.
1 mark
Hertfordshire La Schools
27
Frog spawn The graph shows the date each year that frogs’ eggs were first seen.
28th Feb
21st Feb
14th Feb Date eggs first seen 7th Feb
31st Jan
24th Jan 87
88
89
90
91
92
93
94
95
96
97
98
99
Year
(a)
On what date in 1997 were frogs’ eggs first seen?
............................... 1 mark
Hertfordshire La Schools
1
(b)
At the beginning of each year, the warmer the weather, the earlier frogs’ eggs are first seen. What can you say about the weather at the beginning of 1991?
1 mark
2.
1976 v 2002 Look at this information. In 1976, a man earned £16 each week.
The pie chart shows how he spent his money.
Other Clothes
Entertainment
Rent
Food
Hertfordshire La Schools
2
(a)
How much did the man spend on food each week? £ 1 mark
(b)
Now look at this information. In 2002, a man earned £400 each week.
The table shows how he spent his money.
Hertfordshire La Schools
Rent
£200
Food
£100
Entertainment
£50
Other
£50
3
Complete the pie chart below to show how the man spent his money. Remember to label each sector of the pie chart.
2 marks
Hertfordshire La Schools
4
3.
Mean and median (a)
Look at these three numbers.
9
11
10
Show that the mean of the three numbers is 10
1 mark
Explain why the median of the three numbers is 10
1 mark
(b)
Four numbers have a mean of 10 and a median of 10, but none of the numbers is 10 What could the four numbers be? Give an example.
1 mark
Hertfordshire La Schools
5
4.
Percentages (a)
Write the missing numbers.
50% of 80 = .................
5% of 80 = .................
1% of 80 = .................
2 marks
(b)
Work out 56% of 80 You can use part (a) to help you.
................. 1 mark
Hertfordshire La Schools
6
5.
Completing calculations Write a number in each box to make the calculations correct.
+
=
–8
–
=
–8
2 marks
6.
Numbers Here is a list of numbers:
–7
–5
–3
–1
0
2
4
6
You can choose some of the numbers from the list and add them to find their total.
For example,
...6... (a)
+
..–..1..
=
5
Choose two of the numbers from the list which have a total of 3
......
+
......
=
3 1 mark
Hertfordshire La Schools
7
(b)
Choose two of the numbers from the list which have a total of –1
......
+
–1
...... =
1 mark
Choose two other numbers from the list which have a total of –1
......
+
–1
...... =
1 mark
–7 (c)
–5
–3
–1
0
2
4
6
What is the total of all eight of the numbers on the list?
1 mark
Hertfordshire La Schools
8
(d)
Choose the three numbers from the list which have the lowest possible total. Write the three numbers and their total. You must not use the same number more than once.
......
+
...... =
...... 2 marks
7.
Odd or even? (a)
I am thinking of a number. My number is a multiple of 4 Tick (
) the true statement below. My number must be even
My number must be odd
My number could be odd or even
Explain how you know.
1 mark
Hertfordshire La Schools
9
(b)
I am thinking of a different number. My number is a factor of 20 Tick (
) the true statement below. My number must be even
My number must be odd
My number could be odd or even
Explain how you know.
1 mark
8.
Fir trees The graph shows the average heights of fir trees of different ages.
2.5
2
1.5 Height (metres) 1
0.5
0 2
Hertfordshire La Schools
3
4 Age (years)
5
6
10
The table shows the cost of fir trees of different heights.
Cost
(a)
120 cm to 159 cm
160 cm to 199 cm
200 cm to 239 cm
£ 20.00
£ 25.00
£ 30.00
One of these fir trees is 5
1 years old. 2
How much is it likely to cost? £ ...................... 1 mark
(b)
One of these fir trees costs £ 25.00 How old is the tree likely to be?
Between ...................... and ...................... years old 1 mark
Hertfordshire La Schools
11
9.
Teachers A newspaper predicts what the ages of secondary school teachers will be in six years’ time. They print this chart. 100%
Key:
Age in years 50+ 40 to 49 30 to 39 20 to 29
50%
0% Male
(a)
Female
The chart shows 24% of male teachers will be aged 40 to 49 About what percentage of female teachers will be aged 40 to 49?
........................... % 1 mark
(b)
About what percentage of female teachers will be aged 50+?
........................... % 1 mark
Hertfordshire La Schools
12
(c)
The newspaper predicts there will be about 20 000 male teachers aged 40 to 49 Estimate the number of male teachers that will be aged 50+
............................... 1 mark
(d)
Assume the total number of male teachers will be about the same as the total number of female teachers. Use the chart to decide which statement is correct. Tick () your answer.
Generally, male teachers will tend to be younger than female teachers. Generally, female teachers will tend to be younger than male teachers.
Explain how you used the chart to decide.
1 mark
Hertfordshire La Schools
13
10.
Huts You can make ‘huts’ with matches.
1 hut needs 5 matches
2 huts need 9 matches
3 huts need 13 matches
A rule to find how many matches you need is
m = 4h + 1
m stands for the number of matches. h stands for the number of huts.
(a)
Use the rule to find how many matches you need to make 8 huts. Show your working.
................ matches 2 marks
(b)
I use 81 matches to make some huts. How many huts do I make? Show your working.
....................... huts 2 marks
Hertfordshire La Schools
14
(c)
Andy makes different ‘huts’ with matches.
1 hut needs 6 matches
2 huts need 11 matches
3 huts need 16 matches
Circle the rule below that shows how many matches he needs. Remember:
m stands for the number of matches. h stands for the number of huts.
mh+5 m 5h + 1
m 4h + 2 m 5h + 2
m 4h + 3 m h + 13 1 mark
11.
Lemonade Kate buys 24 cans of lemonade. She buys the cans in packs of 4 Each pack costs £1.20
Pack of 4 Cost £1.20
Hertfordshire La Schools
15
Steve buys 24 cans of lemonade. He buys the cans in packs of 6 Each pack costs £1.60
Pack of 6 Cost £1.60
Kate pays more for her 24 cans than Steve pays for his 24 cans. How much more?
..................... p 2 marks
Hertfordshire La Schools
16
12.
Matching expressions A ruler costs k pence. A pen costs m pence. Match each statement with the correct expression for the amount in pence. The first one is done for you.
Statement
Expression
5k The total cost of 5 rulers 5m
5 – 5m The total cost of 5 rulers and 5 pens 500 – 5m
How much more 5 pens cost than 5 rulers
5k + m
5(k + m)
The change from £5, in pence, when you buy 5 pens
5m – 5 k
5k – 5 m 3 marks
Hertfordshire La Schools
17
13.
Yards Some people use yards to measure length. The diagram shows one way to change yards to metres.
number of yards
(a)
× 36
× 2.54
100
number of metres
Change 100 yards to metres.
................... metres 1 mark
(b)
Change 100 metres to yards. Show your working.
..................... yards 2 marks
Hertfordshire La Schools
18
14.
Thinking percentages (a)
What is 30% of 250?
............................... 1 mark
(b)
I’m thinking of a number. 10% of my number is 84 Show calculations and explain how you can work out that 15% of my number is 126
1 mark
What is 12 21 % of my number?
............................... 1 mark
Hertfordshire La Schools
19
15.
Rectangles and squares Here is a rectangle. 8cm Not drawn accurately
2cm
(a)
A square has the same area as this rectangle. What is the side length of this square?
......................... cm 1 mark
(b)
A different square has the same perimeter as this rectangle. What is the side length of this square?
......................... cm 1 mark
Hertfordshire La Schools
20
16.
Rectangles A rectangle has an area of 24 cm2 How long could the sides of the rectangle be? Give three different examples.
......................... cm
and
......................... cm
......................... cm
and
......................... cm
......................... cm
and
......................... cm 2 marks
17.
Shape rotation Look at this shape made from six cubes. Four cubes are white Two cubes are grey.
Hertfordshire La Schools
21
Part of the shape is rotated through 90° to make the shape below.
After another rotation of 90°, the shape is a cuboid. Draw this cuboid on the grid below.
Isometric grid 2 marks
Hertfordshire La Schools
22
18.
Solving Solve these equations. 2k + 3 11
k ......................... 1 mark
2t + 3 –11
t ......................... 1 mark
Hertfordshire La Schools
23
19.
Same area The square and the rectangle below have the same area. Not drawn accurately
4 cm
2 cm y cm 4 cm
Work out the value of y
y .................... cm 1 mark
Hertfordshire La Schools
24
20.
Thinking triangularly Some statements in the table are true. Some are false. Beside each statement, write true or false. For true statements you must draw an example. The first one is done for you. Statement Some triangles have one right angle and two acute angles.
Write true or false. If true, draw an example.
true
Some triangles have three right angles.
Some triangles have three acute angles.
Some triangles have one obtuse angle and two acute angles.
Some triangles have two obtuse angles and one acute angle. 3 marks
Hertfordshire La Schools
25
21.
Positive and negative Look at this equation.
y = 2x + 10 (a)
When x = 4, what is the value of y?
................. 1 mark
(b)
When x = – 4, what is the value of y?
................. 1 mark
(c)
Which equation below gives the same value of y for both x = 4 and x = – 4 ? Put a ring round the correct equation.
y = 2x
y=2+x
y = x2
y=
x 2 1 mark
Hertfordshire La Schools
26
22.
Three angles Three shapes fit together at point B.
93º A
24º B
Not drawn accurately
61º C
Will ABC make a straight line? Yes
No
Explain your answer.
1 mark
Hertfordshire La Schools
27
