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GCSE Mathematics Assignment 2
Due Date: Friday 29th
November 2013
NAME………………………….
GCSE GROUP: C/D/E/F
Instructions to Students
All questions must be attempted. You should present your solutions on file paper and submit them
with this cover sheet.
(Work submitted without a cover sheet complete with name will not be
marked). All work is to be submitted either to your subject teacher or the Faculty Office by
4.15pm on the due date above.
SUBJECT SPECIFIC SKILLS
1. Presentation : written work presented legibly using standard mathematical notation
Grade
1 2 3 4 5
Evidence/Comment :
2. Communication: written solutions presented in a logical and coherent manner ( showing workings
clearly)
Grade
1 2 3 4 5
Evidence/Comment :
3. Problem solving: identifying and using appropriate mathematical techniques
Grade
1 2 3 4 5
Evidence/Comment :
MathsWatch DVD References
Q1,2 – Clip 55,56 Q12, 18 – Clip 133 Students Feedback: Q3 – Clip 135 Q13 – Clip 87
Please comment on how you performed on this assignment and state the questions that
you found difficult.
Q3 – Clip 87 Q14 – Clip 132 Q4 – Clip 137 Q16 – Clip 151 Q5 – Clip 138 Q17 – Clip 89 Q6 – Clip 52 Q19 – Clip 152 Q7,8 – Clip 61,62 Q20 – Clip 183 Q9,10,11 – Clip 95,96
Q21 – Clip 153
1. (a) Work out
……………………… (2)
(b) Work out 5 – 2
……………………… (3)
(Total 5 marks)
2. (a) Work out 1 –
.................................... (3)
(b) Work out 12
.................................... (3)
(Total 6 marks)
3. (a) (i) Write 40 000 000 in standard form.
...................................
(ii) Write 3 10–5
as an ordinary number.
................................... (2)
(b) Work out the value of
3 10–5
40 000 000
Give your answer in standard form.
................................... (2)
(Total 4 marks)
8
3
5
2
3
2
4
3
6
1
2
1
2
1
8
5
4. Ben bought a car for £12 000.
Each year the value of the car depreciated by 10%.
Work out the value of the car two years after he bought it.
£ …………………. (Total 3 marks)
5. Loft insulation reduces annual heating costs by 20%.
After he insulated his loft, Curtley’s annual heating cost was £520.
Work out Curtley’s annual heating cost would have been, if he had not insulated his loft.
£ ……………………… (Total 3 marks)
6. A hotel has 56 guests.
35 of the guests are male.
(a) Work out 35 out of 56 as a percentage.
.................................. % (2)
40% of the 35 male guests wear glasses.
(b) Write the number of male guests who wear glasses as a fraction of the 56 guests.
Give your answer in its simplest form.
.................................... (4)
(Total 6 marks)
7. Brass is made up of copper and zinc.
Every 100 grams of brass contains 20 grams of zinc.
(a) Work out the weight of zinc in 60 grams of brass.
……………………… g (2)
Brass contains 4 parts by weight of copper to 1 part by weight of zinc.
(b) Work out the weight of copper in 350 grams of brass.
……………………… g (2)
(Total 4 marks)
8. Here are the ingredients needed to make 8 pancakes.
Pancakes
Ingredients to make 8 pancakes
300 ml milk
1 egg
120 g flour
5 g butter
Jacob makes 24 pancakes.
(a) Work out how much milk he needs.
................................................. ml (2)
Cathie makes 12 pancakes.
(b) Work out how much flour she needs.
.................................................... g (2)
(Total 4 marks)
9. Write 140 as the product of its prime factors.
.............................................................................. (Total 2 marks)
10. Find the Highest Common Factor (HCF) of 84 and 180
...................................... (Total 2 marks)
11. Find the Lowest Common Multiple (LCM) of 20 and 36
.................................... (Total 2 marks)
12. 20 students scored goals for the school hockey team last month.
The table gives information about the number of goals they scored.
Goals scored Number of students
1 9
2 3
3 5
4 3
Work out the mean number of goals scored.
.......................... (Total 3 marks)
13. The scatter graph shows some information about six new-born baby apes.
For each baby ape, it shows the mother’s leg length and the baby ape’s birth weight.
The table shows the mother’s leg length and the birth weight of two more baby apes.
Mother’s leg length (cm) 50 65
Baby ape’s birth weight (kg) 1.6 1.75
(a) On the scatter graph, plot the information from the table. (1)
(b) Describe the correlation between a mother’s leg length and her baby ape’s birth
weight.
……………………………………………………… (1)
(c) Draw a line of best fit on the diagram. (1)
A mother’s leg length is 55 cm.
(d) Use your line of best fit to estimate the birth weight of her baby ape.
……………………kg (1)
(Total 4 marks)
Babyape’sbirthweight(kg)
1.8
1.7
1.6
1.5
1.440 50 60 70
Mother’s leg length (cm)
×
×
×
×
×
×
14. Here is a 4-sided spinner.
The sides of the spinner are labelled 1, 2, 3 and 4.
The spinner is biased.
The probability that the spinner will land on each of the numbers 2 and 3 is given in the
table.
The probability that the spinner will land on 1 is equal to the probability that it will land
on 4.
Number 1 2 3 4
Probability x 0.3 0.2 x
(a) Work out the value of x.
x = …………………. (2)
Sarah is going to spin the spinner 200 times.
(b) Work out an estimate for the number of times it will land on 2
……………………. (2)
(Total 4 marks)
15. Emma repairs bicycles.
She keeps records of the cost of the repairs.
The table gives information about the costs of all repairs which she carried
out in one week.
Cost (£C) Frequency
0 < C 10 3
10 < C 20 7
20 < C 30 6
30 < C 40 8
40 < C 50 9
Find the class interval in which the median lies.
...................................................... (Total 2 marks)
16. The cumulative frequency table gives information about the number of minutes 80
customers were in a supermarket.
Number of minutes (t)
in a supermarket
Cumulative
frequency
0 < t 10 2
0 < t 20 8
0 < t 30 18
0 < t 40 40
0 < t 50 64
0 < t 60 77
0 < t 70 80
(a) On the grid below, draw a cumulative frequency graph for the data in the table. (2)
(b) Use your cumulative frequency graph to work out an estimate for the interquartile
range of the number of minutes customers were in the supermarket.
……………………… minutes (2)
(Total 4 marks)
100
90
80
70
60
50
40
30
20
10
00 10 20 30 40 50 60 70
Cumulativefrequency
Number of minutes ( ) in a supermarkett
17. Here are the weights, in kilograms, of 15 parcels.
1.1 1.7 2.0 1.0 1.1 0.5 3.3 2.0
1.5 2.6 3.5 2.1 0.7 1.2 0.6
Draw a stem and leaf diagram to show this information.
(Total 3 marks)
18. Josh asked 30 students how many minutes they each took to get to school.
The table shows some information about his results.
Time taken (t minutes) Frequency
0 < t ≤ 10 6
10 < t ≤ 20 11
20 < t ≤ 30 8
30 < t ≤ 40 5
Work out an estimate for the mean number of minutes taken by the 30 students.
......................... minutes (Total 4 marks)
19. 40 boys each completed a puzzle.
The cumulative frequency graph below gives information about the times it took them to
complete the puzzle.
(a) Use the graph to find an estimate for the median time
............... seconds (1)
For the boys
the minimum time to complete the puzzle was 9 seconds
and the maximum time to complete the puzzle was 57 seconds.
(b) Use this information and the cumulative frequency graph to draw a box plot
showing information about the boy’s times.
(3)
The box plot below shows information about the times taken by 40 girls to
complete the same puzzle.
(c) Make two comparisons between the boys’ times and the girls’ times.
.................................................................................................................................... (2)
Cumulativefrequency
40
30
20
10
10 20 30 40 50 60
Time in seconds
O
0 10 20 30 40 50 60
Time in seconds
10 0 20 30 40 50 60
Time in seconds
20. The table shows the number of students in each year group at a school.
Year group 7 8 9 10 11
Number of students 190 145 145 140 130
Jenny is carrying out a survey for her GCSE Mathematics project.
She uses a stratified sample of 60 students according to year group.
Calculate the number of Year 11 students that should be in her sample.
............................................... (Total 3 marks)
21. There are 3 boys and 7 girls at a playgroup.
Mrs Gold selects two children at random.
(a) Complete the probability tree diagram below.
(2)
(b) Work out the probability that Mrs Gold selects two girls.
..................................... (2)
(Total 4 marks)
1st child 2nd child
boy
girl
boy
girl
boy
girl
............
............
............
3
10
............
............