GCSE Mathematics
Year 10 Topic Test – Higher (December 2015)
Question
Topic
Marks
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Linear Sequences
Linear Sequences
Linear Sequences
Quadratic Sequences
Quadratic Sequences
Quadratic Sequences
Stem & Leaf
Frequency Polygons
Line Graphs
Cumulative Frequency
Cumulative Frequency
Box & Whiskers
Histograms
Histograms
Bounds
Bounds
Bounds with Fractions
Basic Percentages
Percentage of an Amount
Depreciation
Percentage of an Amount
Percentages in context
5
2
2
3
2
4
3
5
5
7
6
4
3
2
2
2
4
4
2
3
2
3
Name _______________________________________
Class Teacher _________________________________
Achieved
Q1.
Here are the first four terms of a number sequence.
6
10
14
18
(a) Write down the next term in this sequence.
..............................................................................................................................................
(1)
(b) Find the 10th term in this sequence.
..............................................................................................................................................
(1)
(c) The number 101 is not a term in this sequence.
Explain why.
..............................................................................................................................................
..............................................................................................................................................
(1)
(d) Write an expression, in terms of n, for the nth term of this sequence.
..............................................................................................................................................
(2)
(Total for Question is 5 marks)
Q2.
Here are the first four terms of a number sequence.
6
14
22
30
Write an expression, in terms of n, for the nth term of this sequence.
..............................................................................................................................................
(Total for Question is 2 marks)
Q3.
Here are the first five terms of an arithmetic sequence.
–3
1
5
9
13
Find an expression, in terms of n, for the nth term of this sequence.
...........................................................
(Total for question = 2 marks)
Q4.
Here are the first 5 terms of a quadratic sequence.
1
3
7
13
21
Find an expression, in terms of n, for the nth term of this quadratic sequence.
...........................................................
(Total for question is 3 marks)
Q5.
Here are the first five terms of a sequence.
2
8
18
32
50
(a) Find the next term of this sequence.
...........................................................
(1)
The nth term of a different sequence is
2
3n – 10
(b) Work out the 5th term of this sequence.
...........................................................
(1)
(Total for question = 2 marks)
Q6.
Here are the first five terms of an arithmetic sequence.
(a) Write down an expression, in terms of n, for the nth term of this sequence.
..............................................................................................................................................
(2)
The nth term of a different number sequence is 3n2 + 7
(b) Find the 10th term of this sequence.
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q7.
The list below shows the weight, in grams, of 15 baskets of strawberries.
193
189
223
200
218
190
207
195
207
211
206
205
198
189
212
Show this information in an ordered stem and leaf diagram.
You must include a key.
(Total for Question is 3 marks)
Q8.
The frequency table gives information about the times it took some office workers to get to the office one
day.
Time (t minutes)
Frequency
0 < t ≤10
10 < t ≤20
20 < t ≤30
30 < t ≤40
40 < t ≤50
50 < t ≤60
4
8
14
16
6
2
(a) Draw a frequency polygon for this information.
(2)
(b) Write down the modal class interval.
..............................................................................................................................................
(1)
One of the office workers is chosen at random.
(c) Work out the probability that this office worker took more than 40 minutes to get to the office.
..............................................................................................................................................
(2)
(Total for Question is 5 marks)
Q9.
The diagram shows the average midday temperature in Tenerife and in London during 6 months.
(a) During which two months is the average midday temperature in Tenerife the same?
..............................................................................................................................................
(1)
(b) During which month is there the greatest difference between the average midday temperatures in
London and in Tenerife?
..............................................................................................................................................
(1)
(c) Write down the average midday temperature in May for London.
. . . . . . . . . . . . . . . . . . . . . . °C
(1)
(d) In September, what is the difference between the average midday temperatures in London and in
Tenerife?
. . . . . . . . . . . . . . . . . . . . . . °C
(2)
(Total for Question is 5 marks)
Q10.
The grouped frequency table shows information about the weekly wages of 80 factory workers.
Weekly wage (£x)
Frequency
100 < x ≤ 200
200 < x ≤ 300
300 < x ≤ 400
400 < x ≤ 500
500 < x ≤ 600
600 < x ≤ 700
8
15
30
17
7
3
(a) Complete the cumulative frequency table.
Weekly wage (£x)
Cumulative
Frequency
100 < x ≤ 200
200 < x ≤ 300
300 < x ≤ 400
400 < x ≤ 500
500 < x ≤ 600
600 < x ≤ 700
(1)
(b) On the grid opposite, draw a cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the interquartile range.
..............................................................................................................................................
(2)
(d) Use your graph to find an estimate for the number of workers with a weekly wage of more than £530
..............................................................................................................................................
(2)
(Total for Question is 7 marks)
Q11.
The cumulative frequency table gives information about the number of minutes it took Jill to travel from
home to school each day last term.
(a) On the grid, draw a cumulative frequency graph for the information.
(2)
(b) Use your cumulative frequency graph to find the interquartile range.
..............................................................................................................................................
(2)
(c) Find an estimate for the number of times Jill took more than 45 minutes to get to school.
..............................................................................................................................................
(2)
(Total for Question is 6 marks)
Q12.
The table gives some information about the weights of 60 babies.
Lowest
Highest
Lower quartile
Upper quartile
Median
2.0 kg
6.5 kg
2.8 kg
4.2 kg
3.0 kg
(a) Draw a box plot to show this information.
(2)
There are 60 babies.
(b) Work out an estimate for the number of these babies with a weight greater than 2.8 kg.
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q13.
The table gives information about the heights, h metres, of trees in a wood.
Height (h metres)
Frequency
0<h≤2
2<h≤4
4<h≤8
8 < h ≤ 16
16 < h ≤ 20
7
14
18
24
10
Draw a histogram to show this information.
(Total for Question is 3 marks)
Q14.
Bhavna recorded the lengths of time, in hours, that some adults watched TV last week.
The table shows information about her results.
Bhavna made some mistakes when she drew a histogram for this information.
Write down two mistakes Bhavna made.
1 .............................................................................................................................................
.............................................................................................................................................
2 .............................................................................................................................................
.............................................................................................................................................
(Total for question = 2 marks)
Q15.
Chelsea's height is 168 cm to the nearest cm.
(a) What is Chelsea's minimum possible height?
........................................................... cm
(1)
(b) What is Chelsea's maximum possible height?
........................................................... cm
(1)
(Total for Question is 2 marks)
Q16.
A piece of wood has a length of 65 centimetres to the nearest centimetre.
(a) What is the least possible length of the piece of wood?
..............................................................................................................................................
(1)
(b) What is the greatest possible length of the piece of wood?
..............................................................................................................................................
(1)
(Total for Question is 2 marks)
Q17.
A solid sphere has
a mass of 1180 g measured to the nearest gram
and a radius of 6.2 cm measured to the nearest millimetre.
Given that
find the upper bound for the density of the sphere.
Give your answer to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . g/cm3
(Total for Question is 4 marks)
Q18.
(a) Write 0.7 as a percentage.
(1)
(b) Write
as a decimal.
(1)
(c) Find 15% of 120
(2)
(Total for question = 4 marks)
Q19.
Work out 65% of 300
...........................................................
(Total for question = 2 marks)
Q20.
The value of a car depreciates by 25% each year.
At the end of 2013 the value of the car was £4800
Work out the value of the car at the end of 2015
£...........................................................
(Total for Question is 3 marks)
Q21.
David is going to buy a cooker.
The cooker has a price of £320
David pays a deposit of 15% of the price of the cooker.
How much money does David pay as a deposit?
£ ...........................................................
(Total for Question is 2 marks)
Q22.
* The table gives some information about student attendance at a school on Friday.
The school has a target of 94% of students being present each day.
Did the school meet its target on Friday?
(Total for question = 3 marks)