level 7
Ks3 Revision material Level 7 1.
Powers Work out the values of m and n 58 × 54 = 5m
m = .................... 1 mark
58 n 4 = 5 5
n = .................... 1 mark
2.
Multiplication grids Write the missing numbers in these multiplication grids.
×
8
9
72
–6
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30
1
× 3
0.2 1.2 6 3 marks
3.
Quiz In a quiz game two people each answer 100 questions. They score one point for each correct answer. The quiz game has not yet finished. Each person has answered 90 questions. The table shows the results so far. Person A
Person B
60% of the first 90 questions correct
50% of the first 90 questions correct
Can person B win the quiz game? Explain your answer.
Hertfordshire La Schools
2
Tick (
) your answer.
B can win.
B cannot win but can draw.
B cannot win or draw. 2 marks
4.
Random numbers Chris read the first 55 numbers from a book of random numbers. As he read each number he recorded it in the diagram below.
0
5
9
9
8
3
1
6
3
1
0
3
2
8
2
3
1
1
6
9
3
4
6
9
9
4
7
0
5
5
7
7
6
6
0
2
8
4
8
0
7
6
8
0
1
5
4
8
6
6
9
2
8
5
9
6
7
8
0
0
(a)
4
1 Key 1
3
3
represents 13
5
7
What was the largest number he recorded?
.................... 1 mark
Hertfordshire La Schools
3
(b)
Explain how Chris could change the diagram to make it easier for him to find the median of his data set.
1 mark
5.
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
4
(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
(c)
What is the mean number of teachers in each car?
................ 2 marks
Hertfordshire La Schools
5
6.
Sweets Altogether, I have 10 bags of sweets. The mean number of sweets in the bags is 41 The table shows how many sweets there are in 9 of the bags. Number of sweets in a bag
Frequency
39
3
40
2
41
1
42
1
43
0
44
2
Calculate how many sweets there are in the 10th bag. You must show your working.
............................... 2 marks
Hertfordshire La Schools
6
.................... 1 mark
(b)
Explain how Chris could change the diagram to make it easier for him to fid the median of his data set.
7. 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.
(a)
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
7
No
............ people 40%
Yes
126 people 60% 1 mark
(b)
The error could be in the percentages. Complete the table with the correct percentages.
No
80 people ............ %
Yes
126 people ............ % 2 marks
Hertfordshire La Schools
8
8.
Which pupil? The table shows the number of boys and girls in two different classes. Class 9A
Class 9B
Boys
13
12
Girls
15
14
A teacher is going to choose a pupil at random from each of these classes. In which class is she more likely to choose a boy? You must show your working.
Tick ( ) your answer. Class 9A
Class 9B 2 marks
Hertfordshire La Schools
9
9.
Pitch A groundsman marks out a football pitch. 93 metres
50 metres
(a)
He makes the pitch 93 metres long, to the nearest metre. What is the shortest possible length of the pitch?
........................... m 1 mark
(b)
He makes the pitch 50 metres wide, to the nearest metre. What is the shortest possible width of the pitch?
........................... m 1 mark
Hertfordshire La Schools
10
(c)
Des wants to know how many times he should run around the outside of this pitch to be sure of running at least 3km. Use your answer to parts (a) and (b) to find how many times Des should run around the pitch. You must show your working.
2 marks
10.
Counters A bag contains counters that are red, black, or green.
1 of the counters are red 3
1 of the counters are black 6
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11
There are 15 green counters in the bag. How many black counters are in the bag?
................ 2 marks
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12
11.
x and y Solve these simultaneous equations using an algebraic method. 3x + 7y 18
x + 2y 5 You must show your working.
x = .........................
y = ......................... 3 marks
12.
Triangles ABC and ACD are both right-angled triangles.
D 6 cm Not drawn accurately
C 6 cm
B
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8 cm
A
13
(a)
Explain why the length of AC is 10 cm.
1 mark
(b)
Calculate the length of AD Show your working.
......................... cm 2 marks
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14
13.
Area The diagram shows two circles and a square, ABCD. A and B are the centres of the circles. The radius of each circle is 5 cm.
A
B
5 cm
5 cm
D
C Not drawn accurately
Calculate the area of the shaded part of the square.
............................... 3 marks
Hertfordshire La Schools
15
14.
Sequences (a)
Draw lines to match each nth term rule to its number sequence.
nth term
Number sequence
4n
4, 7, 12, 19, …
(n + 1)2
4, 8, 12, 16, …
n2 + 3
4, 9, 16, 25, …
n (n + 3)
4, 10, 18, 28, …
2 marks
(b)
Write the first four terms of the number sequence using the nth term rule below.
n3 + 3
,
,
, 2 marks
Hertfordshire La Schools
16
15.
Fence plan Here is a plan of some land. There will be a fence that is always the same distance from tree A as from tree B, going all the way from one road to the other road. Use compasses and a straight edge to show accurately on the plan where the fence will go. You must leave in your construction lines.
Road
Tree A
Tree B
Road 2 marks
Hertfordshire La Schools
17
16.
Running machine Kali uses a running machine to keep fit. The simplified distance-time graph shows how she used the machine during one run.
4
3
Distance (km)
2
1
0930
0940
0950
1000 Time
Use the graph to answer these questions. (a)
Between 0930 and 0940, what was her speed in kilometres per hour? ....................... km/h 1 mark
Hertfordshire La Schools
18
(b)
Throughout the run, for how many minutes did she travel at this speed? .................. minutes 1 mark
(c)
At 0940, she increased her speed. By how many kilometres per hour did she increase her speed? ....................... km/h 1 mark
17.
Sixty (a)
Each of these calculations has the same answer, 60 Fill in each gap with a number.
2.4 × 25
0.24 × ..........
= 60 60 ÷ 1
6 ÷ .......... 2 marks
Hertfordshire La Schools
19
(b)
Solve these equations to find the values of a, b and c.
5a – 40
= 60
4b + 80
c 2 + 24
a ....................
b ....................
c .................... 3 marks
18.
Graphing Here are six different equations, labelled A to F
A
y = 3x – 4
B
y=4
C
x=–5
D
x + y = 10
E
y = 2x + 1
F
y=x2
Think about the graphs of these equations.
(a)
Which graph goes through the point (0, 0)?
............................... 1 mark
Hertfordshire La Schools
20
(b)
Which graph is parallel to the y-axis?
............................... 1 mark
(c)
Which graph is not a straight line?
............................... 1 mark
(d)
Which two graphs pass through the point ( 3 , 7 )?
..................... and ..................... 2 marks
Hertfordshire La Schools
21
(e)
The diagram shows the graph of the equation y
4 x2
What are the coordinates of the points where the graph of this equation meets the graph of equation E? y 5
4
3
2
1
–3
–2
–1
0
x 0
1
2
3
–1
–2
–3
–4
–5 y = 4 – x2
(
,
) and (
,
) 3 marks
Hertfordshire La Schools
22
19.
Bracket multiplication Multiply out the brackets in these expressions.
y (y – 6) .......................................................... 1 mark
(k + 2)(k + 3) .................................................. 1 mark
20.
Evens or Odds (a)
m is an odd number. Which of the numbers below must be even, and which must be odd? Write ‘odd’ or ‘even’ under each one.
2m
m2
3m
–1
(m – 1)(m + 1)
2 marks
Hertfordshire La Schools
23
(b)
m is an odd number. Is the number
m 1 2
odd, or even, or is it not possible to tell?
Tick () the correct box.
odd
even
not possible to tell
Explain your answer.
1 mark
21.
Triangle Look at the triangle. Not drawn accurately
a° 2b°
a°
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b°
24
Work out the value of a
a = ......................... 3 marks
Hertfordshire La Schools
25
22.
Two semicircles This shaded shape is made using two semicircles. One semicircle has a diameter of 20cm. The other has a diameter of 30cm.
20cm 30cm Not drawn accurately
Calculate the perimeter of the shaded shape.
......................... cm 2 marks
Hertfordshire La Schools
26
23.
Thinking diagonally The diagram shows a square with side length 5 cm.
Not drawn accurately
y cm
The length of the diagonal is y cm. Show that the value of y is
50
1 mark
24.
Brackets (a)
Jenny wants to multiply out the brackets in the expression 3(2a+ 1) She writes: 3 (2a + 1) = 6a + 1
Show why Jenny is wrong.
1 mark
Hertfordshire La Schools
27
(b)
Sandeep wants to multiply out the brackets in the expression (k + 4) (k + 7) He writes (k + 4) (k + 7)= K2 + 28
Show why Sandeep is wrong.
1 mark
Hertfordshire La Schools
28
Powers Work out the values of m and n 58 × 54 = 5m
m = .................... 1 mark
58 n 4 = 5 5
n = .................... 1 mark
2.
Multiplication grids Write the missing numbers in these multiplication grids.
×
8
9
72
–6
Hertfordshire La Schools
30
1
× 3
0.2 1.2 6 3 marks
3.
Quiz In a quiz game two people each answer 100 questions. They score one point for each correct answer. The quiz game has not yet finished. Each person has answered 90 questions. The table shows the results so far. Person A
Person B
60% of the first 90 questions correct
50% of the first 90 questions correct
Can person B win the quiz game? Explain your answer.
Hertfordshire La Schools
2
Tick (
) your answer.
B can win.
B cannot win but can draw.
B cannot win or draw. 2 marks
4.
Random numbers Chris read the first 55 numbers from a book of random numbers. As he read each number he recorded it in the diagram below.
0
5
9
9
8
3
1
6
3
1
0
3
2
8
2
3
1
1
6
9
3
4
6
9
9
4
7
0
5
5
7
7
6
6
0
2
8
4
8
0
7
6
8
0
1
5
4
8
6
6
9
2
8
5
9
6
7
8
0
0
(a)
4
1 Key 1
3
3
represents 13
5
7
What was the largest number he recorded?
.................... 1 mark
Hertfordshire La Schools
3
(b)
Explain how Chris could change the diagram to make it easier for him to find the median of his data set.
1 mark
5.
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
4
(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
(c)
What is the mean number of teachers in each car?
................ 2 marks
Hertfordshire La Schools
5
6.
Sweets Altogether, I have 10 bags of sweets. The mean number of sweets in the bags is 41 The table shows how many sweets there are in 9 of the bags. Number of sweets in a bag
Frequency
39
3
40
2
41
1
42
1
43
0
44
2
Calculate how many sweets there are in the 10th bag. You must show your working.
............................... 2 marks
Hertfordshire La Schools
6
.................... 1 mark
(b)
Explain how Chris could change the diagram to make it easier for him to fid the median of his data set.
7. 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.
(a)
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
7
No
............ people 40%
Yes
126 people 60% 1 mark
(b)
The error could be in the percentages. Complete the table with the correct percentages.
No
80 people ............ %
Yes
126 people ............ % 2 marks
Hertfordshire La Schools
8
8.
Which pupil? The table shows the number of boys and girls in two different classes. Class 9A
Class 9B
Boys
13
12
Girls
15
14
A teacher is going to choose a pupil at random from each of these classes. In which class is she more likely to choose a boy? You must show your working.
Tick ( ) your answer. Class 9A
Class 9B 2 marks
Hertfordshire La Schools
9
9.
Pitch A groundsman marks out a football pitch. 93 metres
50 metres
(a)
He makes the pitch 93 metres long, to the nearest metre. What is the shortest possible length of the pitch?
........................... m 1 mark
(b)
He makes the pitch 50 metres wide, to the nearest metre. What is the shortest possible width of the pitch?
........................... m 1 mark
Hertfordshire La Schools
10
(c)
Des wants to know how many times he should run around the outside of this pitch to be sure of running at least 3km. Use your answer to parts (a) and (b) to find how many times Des should run around the pitch. You must show your working.
2 marks
10.
Counters A bag contains counters that are red, black, or green.
1 of the counters are red 3
1 of the counters are black 6
Hertfordshire La Schools
11
There are 15 green counters in the bag. How many black counters are in the bag?
................ 2 marks
Hertfordshire La Schools
12
11.
x and y Solve these simultaneous equations using an algebraic method. 3x + 7y 18
x + 2y 5 You must show your working.
x = .........................
y = ......................... 3 marks
12.
Triangles ABC and ACD are both right-angled triangles.
D 6 cm Not drawn accurately
C 6 cm
B
Hertfordshire La Schools
8 cm
A
13
(a)
Explain why the length of AC is 10 cm.
1 mark
(b)
Calculate the length of AD Show your working.
......................... cm 2 marks
Hertfordshire La Schools
14
13.
Area The diagram shows two circles and a square, ABCD. A and B are the centres of the circles. The radius of each circle is 5 cm.
A
B
5 cm
5 cm
D
C Not drawn accurately
Calculate the area of the shaded part of the square.
............................... 3 marks
Hertfordshire La Schools
15
14.
Sequences (a)
Draw lines to match each nth term rule to its number sequence.
nth term
Number sequence
4n
4, 7, 12, 19, …
(n + 1)2
4, 8, 12, 16, …
n2 + 3
4, 9, 16, 25, …
n (n + 3)
4, 10, 18, 28, …
2 marks
(b)
Write the first four terms of the number sequence using the nth term rule below.
n3 + 3
,
,
, 2 marks
Hertfordshire La Schools
16
15.
Fence plan Here is a plan of some land. There will be a fence that is always the same distance from tree A as from tree B, going all the way from one road to the other road. Use compasses and a straight edge to show accurately on the plan where the fence will go. You must leave in your construction lines.
Road
Tree A
Tree B
Road 2 marks
Hertfordshire La Schools
17
16.
Running machine Kali uses a running machine to keep fit. The simplified distance-time graph shows how she used the machine during one run.
4
3
Distance (km)
2
1
0930
0940
0950
1000 Time
Use the graph to answer these questions. (a)
Between 0930 and 0940, what was her speed in kilometres per hour? ....................... km/h 1 mark
Hertfordshire La Schools
18
(b)
Throughout the run, for how many minutes did she travel at this speed? .................. minutes 1 mark
(c)
At 0940, she increased her speed. By how many kilometres per hour did she increase her speed? ....................... km/h 1 mark
17.
Sixty (a)
Each of these calculations has the same answer, 60 Fill in each gap with a number.
2.4 × 25
0.24 × ..........
= 60 60 ÷ 1
6 ÷ .......... 2 marks
Hertfordshire La Schools
19
(b)
Solve these equations to find the values of a, b and c.
5a – 40
= 60
4b + 80
c 2 + 24
a ....................
b ....................
c .................... 3 marks
18.
Graphing Here are six different equations, labelled A to F
A
y = 3x – 4
B
y=4
C
x=–5
D
x + y = 10
E
y = 2x + 1
F
y=x2
Think about the graphs of these equations.
(a)
Which graph goes through the point (0, 0)?
............................... 1 mark
Hertfordshire La Schools
20
(b)
Which graph is parallel to the y-axis?
............................... 1 mark
(c)
Which graph is not a straight line?
............................... 1 mark
(d)
Which two graphs pass through the point ( 3 , 7 )?
..................... and ..................... 2 marks
Hertfordshire La Schools
21
(e)
The diagram shows the graph of the equation y
4 x2
What are the coordinates of the points where the graph of this equation meets the graph of equation E? y 5
4
3
2
1
–3
–2
–1
0
x 0
1
2
3
–1
–2
–3
–4
–5 y = 4 – x2
(
,
) and (
,
) 3 marks
Hertfordshire La Schools
22
19.
Bracket multiplication Multiply out the brackets in these expressions.
y (y – 6) .......................................................... 1 mark
(k + 2)(k + 3) .................................................. 1 mark
20.
Evens or Odds (a)
m is an odd number. Which of the numbers below must be even, and which must be odd? Write ‘odd’ or ‘even’ under each one.
2m
m2
3m
–1
(m – 1)(m + 1)
2 marks
Hertfordshire La Schools
23
(b)
m is an odd number. Is the number
m 1 2
odd, or even, or is it not possible to tell?
Tick () the correct box.
odd
even
not possible to tell
Explain your answer.
1 mark
21.
Triangle Look at the triangle. Not drawn accurately
a° 2b°
a°
Hertfordshire La Schools
b°
24
Work out the value of a
a = ......................... 3 marks
Hertfordshire La Schools
25
22.
Two semicircles This shaded shape is made using two semicircles. One semicircle has a diameter of 20cm. The other has a diameter of 30cm.
20cm 30cm Not drawn accurately
Calculate the perimeter of the shaded shape.
......................... cm 2 marks
Hertfordshire La Schools
26
23.
Thinking diagonally The diagram shows a square with side length 5 cm.
Not drawn accurately
y cm
The length of the diagonal is y cm. Show that the value of y is
50
1 mark
24.
Brackets (a)
Jenny wants to multiply out the brackets in the expression 3(2a+ 1) She writes: 3 (2a + 1) = 6a + 1
Show why Jenny is wrong.
1 mark
Hertfordshire La Schools
27
(b)
Sandeep wants to multiply out the brackets in the expression (k + 4) (k + 7) He writes (k + 4) (k + 7)= K2 + 28
Show why Sandeep is wrong.
1 mark
Hertfordshire La Schools
28
