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

............

............