level 6
KS3 Revision work Level 6 1.
Thinking fractions Write the missing numbers in these fraction sums.
1 +
=
1
8
4
1 mark
8
1 +
=
1
3
1 mark
2.
Pi The value of correct to 7 decimal places is: 3.1415927
(a)
Write the value of correct to 4 decimal places.
1 mark
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1
(b)
Which value below is closest to the value of π? Put a ring round the correct one.
179 57
1 3 7
16 9
2
355 113 1 mark
3.
Cube Look at the cube. The area of a face of the cube is 9x2 Area = 9x 2
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2
Write an expression for the total surface area of the cube. Write your answer as simply as possible.
.................... 1 mark
4.
Walk I went for a walk. The distance-time graph shows information about my walk.
Distance travelled
Time taken
Tick () the statement below that describes my walk.
I was walking faster and faster.
I was walking slower and slower.
I was walking north-east.
I was walking at a steady speed.
I was walking uphill. 1 mark
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3
5.
Tomatoes The graph shows information about the diameters and heights of a sample of three types of tomato.
height, h
diameter, d
The dotted lines on the graph can be used to decide which type of tomato each point is likely to represent. type A
12 × ×
11
type B ×
10
type C
9
Height (cm)
×
8
×
7
×
× ××
× ××××× ×
6 5
×
×
4 3 2 1 0 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Diameter (cm)
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4
(a)
The diameter of a tomato of type C is 11 cm. What would you expect its height to be?
......................... cm 1 mark
(b)
The diameter of a different tomato is 3.2 cm. Its height is 5.8 cm. Which of the three types of tomato is it most likely to be? A
B
C
Explain your answer.
1 mark
(c)
Which type of tomato is most nearly spherical in shape? A
B
C
Explain your answer.
1 mark
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5
6.
Same area The triangle and the rectangle below have the same area. Not drawn accurately
w cm
6 cm
4 cm
4 cm
Work out the value of w Show your working.
w ......................... cm 2 marks
7.
Newspaper In a survey, 60 people were asked: What kind of newspaper did you buy today?
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6
Here are the results. Type of newspaper
Number of people
Morning newspaper
35
Evening newspaper
10
No newspaper
15
Complete the pie chart to show this information.
Morning newspaper
2 marks
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7
8.
Vowels A computer is going to choose a letter at random from an English book. The table shows the probabilities of the computer choosing each vowel. Vowel
A
E
I
O
U
Probability
0.08
0.13
0.07
0.08
0.03
What is the probability that it will not choose a vowel?
2 marks
9.
Travelling by car A pupil investigated how the teachers at his school travel to work. The table shows the results.
(a)
Number of teachers who travel by car
Number of teachers who do not travel by car
18
7
What percentage of these teachers travel by car?
............................% 1 mark
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8
(b)
18 teachers travel by car. Some of these teachers travel together. Write the missing frequency in the table below.
Number of teachers in one car
Number of cars
1 2
4
3
2 1 mark
10.
Points and rules (a)
The grid shows six points labelled A, B, C, D, E and F
y 4 3
B
A
2 1
C –4
–3
–2
–1
x
0 0
1
–1
2
3
4 F
–2
D
–3
E
–4
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9
Complete the table to show which points have coordinates that match the rules below. The first one is done for you. Rule
A
B
C
D
E
F
x3 y –3 xy 2 marks
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10
(b)
This grid shows six different points. One rule matches the coordinates of each of the six points. y 6 5 4 3 2 1 x
0 –1
0
1
2
3
4
5
6
–1
Write a rule, using x and y, that matches all six points.
1 mark
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11
11.
Drawing Four cubes join to make an L-shape. The diagram shows the L-shape after quarter turns in one direction. On the paper below, draw the L-shape after the next quarter turn in the same direction.
2 marks
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12
12.
Dice The diagrams show nets for dice. Each dice has six faces, numbered 1 to 6 Write the missing numbers so that the numbers on opposite faces add to 7
6
2
4
1 mark
4
1
5
1 mark
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13
13.
Isosceles A teacher said: Use compasses to construct an isosceles triangle. One side must be 5 cm Another side must be 7 cm.
Gill drew two different triangles. The first had sides 5 cm, 7 cm and 7 cm and looked like this:
7 cm
7 cm
5 cm
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14
The second had sides 5 cm, 5 cm and 7 cm. Complete the drawing of the triangle with sides 5 cm, 5 cm and 7 cm. One side of 5 cm has been drawn for you.
5 cm 2 marks
14.
Same volume The drawing shows 2 cuboids that have the same volume.
Cuboid A Cuboid B 4 cm 2 cm
5 cm
3 cm
5 cm
x cm Not drawn accurately
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15
(a)
What is the volume of cuboid A? Remember to state your units.
............................... 2 marks
(b)
Work out the value of the length marked x
......................... cm 1 mark
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16
15.
Three straight lines The diagram shows three straight lines.
Not drawn accurately
b
c a
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17
Work out the sizes of angles a, b and c Give reasons for your answers.
a = ................° because .......................................................................................... .......................................................................................... .......................................................................................... 1 mark
b = ................° because .......................................................................................... .......................................................................................... .......................................................................................... 1 mark
c = ................° because .......................................................................................... .......................................................................................... .......................................................................................... 1 mark
16.
Sizing (a)
Put these values in order of size with the smallest first.
52
32
33
24
.............. smallest
..............
..............
.............. largest 2 marks
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18
(b)
Look at this information. 55 is 3125 What is 57?
............................... 2 marks
17.
Doubles I have two fair dice. Each of the dice is numbered 1 to 6.
(a)
The probability that I will throw double 6 (both dice showing number 6) is
1 36 What is the probability that I will not throw double 6?
1 mark
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19
(b)
I throw both dice and get double 6. Then I throw the dice again. Tick the box that describes the probability that I will throw double 6 this time. less than
1 36 1 36
more than
1 36
Explain your answer.
1 mark
I start again and throw both dice. (c)
What is the probability that I will throw double 3 (both dice showing 3)?
1 mark
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20
(d)
What is the probability that I will throw a double? (It could be double 1 or double 2 or any other double.)
1 mark
Hertfordshire La Schools
21
18.
Enlarging Enlarge the shape by a scale factor of 2, using P as the centre of enlargement.
P
Isometric grid 2 marks
Hertfordshire La Schools
22
19.
Circle working Kevin is working out the area of a circle with radius 4 He writes:
4
Area = π × 8
Explain why Kevin’s working is wrong.
1 mark
Hertfordshire La Schools
23
20.
Values (a)
Here are two equations.
k=a+b a + b + k = 30 What is the value of k?
k = ......................... 1 mark
(b)
Look at this information. 10 = c + d
c is one more than d What is the value of c?
c = ......................... 1 mark
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24
21.
Speed The line on the graph below represents a speed of 60km/hour.
60km/hour 60
50
40 Distance (km)
30
20
10
0 0
10
20
30
40
50
60
Time (minutes)
(a)
Draw a line on the graph to represent a speed of 30 km/hour. Label the line by writing 30km/hour. 1 mark
(b)
Now draw a line on the graph to represent a speed of 120 km/hour. Label the line by writing 120km/hour. 1 mark
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25
22.
Tiles This is a series of patterns with grey and white tiles.
pattern number 1
pattern number 2
The series of patterns continues by adding
(a)
pattern number 3
each time.
Complete this table:
pattern number
number of grey tiles
number of white tiles
5 16 2 marks
(b)
Complete this table by writing expressions:
pattern number
expression for the number of grey tiles
expression for the number of white tiles
n 2 marks
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26
(c)
Write an expression to show the total number of tiles in pattern number n. Simplify your expression.
1 mark
23.
Error Kate asked people if they read a daily newspaper. Then she wrote this table to show her results.
No
80 people 40%
Yes
126 people 60%
The values in the table cannot all be correct.
The error could be in the number of people. Complete each table to show what the correct numbers could be.
No
80 people 40%
Yes
............ people 60% 1 mark
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27
No
............ people 40%
Yes
126 people 60% 1 mark
24.
Solving Solve these equations. Show your working.
8k 1 15
k ............................ 1 mark
2m + 5 10
m ............................ 1 mark
3t + 4 t + 13
t ............................ 2 marks
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28
2(3n + 7) 8
n ............................ 1 mark
25.
Straight lines The graph shows a straight line. y 7 6 5 4 3 2 1 –2
–1
0 0
1
2
3
4
5
6
7
x
–1 –2
(a)
Fill in the table for some of the points on the line. (x, y)
(
, )
(
, )
(
, )
x+y 1 mark
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29
(b)
Write an equation of the straight line.
.............................................................. 1 mark
(c)
On the graph, draw the straight line that has the equation x + y 6 1 mark
26.
Consideration (a)
Give an example to show the statement below is not correct. When you multiply a number by 2, the answer is always greater than 2
1 mark
(b)
Now give an example to show the statement below is not correct. When you subtract a number from 2, the answer is always less than 2
1 mark
Hertfordshire La Schools
30
27.
Completing rules Look at the information.
x=4
y = 13
Complete the rules below to show different ways to get y using x. The first one is done for you. To get y, multiply x by .........2......... and add ..........5......... This can be written as y =......... 2x
+ 5.........
To get y, multiply x by .............................. and add .............................. This can be written as y = .............................. 1 mark
To get y, multiply x by .............................. and subtract .............................. This can be written as y = .............................. 1 mark
To get y, divide x by ....................... and add ....................... This can be written as y = ........................... 1 mark
28.
Relationships Write the missing numbers.
so
6x
+
2
=
6x
+
1
= .............
10
1 mark
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31
so
1
–
(1
–
2y
= 10
2y)2 = ............. 1 mark
29.
Equation Solve this equation. 2(2n + 5) = 12
n = ................ 2 marks
30.
Tickets Ann, Ben, Carl, Donna and Eric are friends. They have four tickets for a concert. The order in which they sit at the concert does not matter. Ben must go to the concert. If Eric goes to the concert, Donna must go too.
Hertfordshire La Schools
32
List all the different groups of four who could go to the concert. Remember, order does not matter.
2 marks
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33
Thinking fractions Write the missing numbers in these fraction sums.
1 +
=
1
8
4
1 mark
8
1 +
=
1
3
1 mark
2.
Pi The value of correct to 7 decimal places is: 3.1415927
(a)
Write the value of correct to 4 decimal places.
1 mark
Hertfordshire La Schools
1
(b)
Which value below is closest to the value of π? Put a ring round the correct one.
179 57
1 3 7
16 9
2
355 113 1 mark
3.
Cube Look at the cube. The area of a face of the cube is 9x2 Area = 9x 2
Hertfordshire La Schools
2
Write an expression for the total surface area of the cube. Write your answer as simply as possible.
.................... 1 mark
4.
Walk I went for a walk. The distance-time graph shows information about my walk.
Distance travelled
Time taken
Tick () the statement below that describes my walk.
I was walking faster and faster.
I was walking slower and slower.
I was walking north-east.
I was walking at a steady speed.
I was walking uphill. 1 mark
Hertfordshire La Schools
3
5.
Tomatoes The graph shows information about the diameters and heights of a sample of three types of tomato.
height, h
diameter, d
The dotted lines on the graph can be used to decide which type of tomato each point is likely to represent. type A
12 × ×
11
type B ×
10
type C
9
Height (cm)
×
8
×
7
×
× ××
× ××××× ×
6 5
×
×
4 3 2 1 0 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Diameter (cm)
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4
(a)
The diameter of a tomato of type C is 11 cm. What would you expect its height to be?
......................... cm 1 mark
(b)
The diameter of a different tomato is 3.2 cm. Its height is 5.8 cm. Which of the three types of tomato is it most likely to be? A
B
C
Explain your answer.
1 mark
(c)
Which type of tomato is most nearly spherical in shape? A
B
C
Explain your answer.
1 mark
Hertfordshire La Schools
5
6.
Same area The triangle and the rectangle below have the same area. Not drawn accurately
w cm
6 cm
4 cm
4 cm
Work out the value of w Show your working.
w ......................... cm 2 marks
7.
Newspaper In a survey, 60 people were asked: What kind of newspaper did you buy today?
Hertfordshire La Schools
6
Here are the results. Type of newspaper
Number of people
Morning newspaper
35
Evening newspaper
10
No newspaper
15
Complete the pie chart to show this information.
Morning newspaper
2 marks
Hertfordshire La Schools
7
8.
Vowels A computer is going to choose a letter at random from an English book. The table shows the probabilities of the computer choosing each vowel. Vowel
A
E
I
O
U
Probability
0.08
0.13
0.07
0.08
0.03
What is the probability that it will not choose a vowel?
2 marks
9.
Travelling by car A pupil investigated how the teachers at his school travel to work. The table shows the results.
(a)
Number of teachers who travel by car
Number of teachers who do not travel by car
18
7
What percentage of these teachers travel by car?
............................% 1 mark
Hertfordshire La Schools
8
(b)
18 teachers travel by car. Some of these teachers travel together. Write the missing frequency in the table below.
Number of teachers in one car
Number of cars
1 2
4
3
2 1 mark
10.
Points and rules (a)
The grid shows six points labelled A, B, C, D, E and F
y 4 3
B
A
2 1
C –4
–3
–2
–1
x
0 0
1
–1
2
3
4 F
–2
D
–3
E
–4
Hertfordshire La Schools
9
Complete the table to show which points have coordinates that match the rules below. The first one is done for you. Rule
A
B
C
D
E
F
x3 y –3 xy 2 marks
Hertfordshire La Schools
10
(b)
This grid shows six different points. One rule matches the coordinates of each of the six points. y 6 5 4 3 2 1 x
0 –1
0
1
2
3
4
5
6
–1
Write a rule, using x and y, that matches all six points.
1 mark
Hertfordshire La Schools
11
11.
Drawing Four cubes join to make an L-shape. The diagram shows the L-shape after quarter turns in one direction. On the paper below, draw the L-shape after the next quarter turn in the same direction.
2 marks
Hertfordshire La Schools
12
12.
Dice The diagrams show nets for dice. Each dice has six faces, numbered 1 to 6 Write the missing numbers so that the numbers on opposite faces add to 7
6
2
4
1 mark
4
1
5
1 mark
Hertfordshire La Schools
13
13.
Isosceles A teacher said: Use compasses to construct an isosceles triangle. One side must be 5 cm Another side must be 7 cm.
Gill drew two different triangles. The first had sides 5 cm, 7 cm and 7 cm and looked like this:
7 cm
7 cm
5 cm
Hertfordshire La Schools
14
The second had sides 5 cm, 5 cm and 7 cm. Complete the drawing of the triangle with sides 5 cm, 5 cm and 7 cm. One side of 5 cm has been drawn for you.
5 cm 2 marks
14.
Same volume The drawing shows 2 cuboids that have the same volume.
Cuboid A Cuboid B 4 cm 2 cm
5 cm
3 cm
5 cm
x cm Not drawn accurately
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15
(a)
What is the volume of cuboid A? Remember to state your units.
............................... 2 marks
(b)
Work out the value of the length marked x
......................... cm 1 mark
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16
15.
Three straight lines The diagram shows three straight lines.
Not drawn accurately
b
c a
Hertfordshire La Schools
17
Work out the sizes of angles a, b and c Give reasons for your answers.
a = ................° because .......................................................................................... .......................................................................................... .......................................................................................... 1 mark
b = ................° because .......................................................................................... .......................................................................................... .......................................................................................... 1 mark
c = ................° because .......................................................................................... .......................................................................................... .......................................................................................... 1 mark
16.
Sizing (a)
Put these values in order of size with the smallest first.
52
32
33
24
.............. smallest
..............
..............
.............. largest 2 marks
Hertfordshire La Schools
18
(b)
Look at this information. 55 is 3125 What is 57?
............................... 2 marks
17.
Doubles I have two fair dice. Each of the dice is numbered 1 to 6.
(a)
The probability that I will throw double 6 (both dice showing number 6) is
1 36 What is the probability that I will not throw double 6?
1 mark
Hertfordshire La Schools
19
(b)
I throw both dice and get double 6. Then I throw the dice again. Tick the box that describes the probability that I will throw double 6 this time. less than
1 36 1 36
more than
1 36
Explain your answer.
1 mark
I start again and throw both dice. (c)
What is the probability that I will throw double 3 (both dice showing 3)?
1 mark
Hertfordshire La Schools
20
(d)
What is the probability that I will throw a double? (It could be double 1 or double 2 or any other double.)
1 mark
Hertfordshire La Schools
21
18.
Enlarging Enlarge the shape by a scale factor of 2, using P as the centre of enlargement.
P
Isometric grid 2 marks
Hertfordshire La Schools
22
19.
Circle working Kevin is working out the area of a circle with radius 4 He writes:
4
Area = π × 8
Explain why Kevin’s working is wrong.
1 mark
Hertfordshire La Schools
23
20.
Values (a)
Here are two equations.
k=a+b a + b + k = 30 What is the value of k?
k = ......................... 1 mark
(b)
Look at this information. 10 = c + d
c is one more than d What is the value of c?
c = ......................... 1 mark
Hertfordshire La Schools
24
21.
Speed The line on the graph below represents a speed of 60km/hour.
60km/hour 60
50
40 Distance (km)
30
20
10
0 0
10
20
30
40
50
60
Time (minutes)
(a)
Draw a line on the graph to represent a speed of 30 km/hour. Label the line by writing 30km/hour. 1 mark
(b)
Now draw a line on the graph to represent a speed of 120 km/hour. Label the line by writing 120km/hour. 1 mark
Hertfordshire La Schools
25
22.
Tiles This is a series of patterns with grey and white tiles.
pattern number 1
pattern number 2
The series of patterns continues by adding
(a)
pattern number 3
each time.
Complete this table:
pattern number
number of grey tiles
number of white tiles
5 16 2 marks
(b)
Complete this table by writing expressions:
pattern number
expression for the number of grey tiles
expression for the number of white tiles
n 2 marks
Hertfordshire La Schools
26
(c)
Write an expression to show the total number of tiles in pattern number n. Simplify your expression.
1 mark
23.
Error Kate asked people if they read a daily newspaper. Then she wrote this table to show her results.
No
80 people 40%
Yes
126 people 60%
The values in the table cannot all be correct.
The error could be in the number of people. Complete each table to show what the correct numbers could be.
No
80 people 40%
Yes
............ people 60% 1 mark
Hertfordshire La Schools
27
No
............ people 40%
Yes
126 people 60% 1 mark
24.
Solving Solve these equations. Show your working.
8k 1 15
k ............................ 1 mark
2m + 5 10
m ............................ 1 mark
3t + 4 t + 13
t ............................ 2 marks
Hertfordshire La Schools
28
2(3n + 7) 8
n ............................ 1 mark
25.
Straight lines The graph shows a straight line. y 7 6 5 4 3 2 1 –2
–1
0 0
1
2
3
4
5
6
7
x
–1 –2
(a)
Fill in the table for some of the points on the line. (x, y)
(
, )
(
, )
(
, )
x+y 1 mark
Hertfordshire La Schools
29
(b)
Write an equation of the straight line.
.............................................................. 1 mark
(c)
On the graph, draw the straight line that has the equation x + y 6 1 mark
26.
Consideration (a)
Give an example to show the statement below is not correct. When you multiply a number by 2, the answer is always greater than 2
1 mark
(b)
Now give an example to show the statement below is not correct. When you subtract a number from 2, the answer is always less than 2
1 mark
Hertfordshire La Schools
30
27.
Completing rules Look at the information.
x=4
y = 13
Complete the rules below to show different ways to get y using x. The first one is done for you. To get y, multiply x by .........2......... and add ..........5......... This can be written as y =......... 2x
+ 5.........
To get y, multiply x by .............................. and add .............................. This can be written as y = .............................. 1 mark
To get y, multiply x by .............................. and subtract .............................. This can be written as y = .............................. 1 mark
To get y, divide x by ....................... and add ....................... This can be written as y = ........................... 1 mark
28.
Relationships Write the missing numbers.
so
6x
+
2
=
6x
+
1
= .............
10
1 mark
Hertfordshire La Schools
31
so
1
–
(1
–
2y
= 10
2y)2 = ............. 1 mark
29.
Equation Solve this equation. 2(2n + 5) = 12
n = ................ 2 marks
30.
Tickets Ann, Ben, Carl, Donna and Eric are friends. They have four tickets for a concert. The order in which they sit at the concert does not matter. Ben must go to the concert. If Eric goes to the concert, Donna must go too.
Hertfordshire La Schools
32
List all the different groups of four who could go to the concert. Remember, order does not matter.
2 marks
Hertfordshire La Schools
33
