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Edexcel GCSE

Mathematics B
Unit 1: Statistics and Probability (Calculator) Higher Tier
Friday 2 March 2012 – Afternoon Time: 1 hour 15 minutes
Paper Reference

5MB1H/01
Total Marks

You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions
Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided – there may be more space than you need. Calculators may be used. If your calculator does not have a button, take the value of to be 3.142 unless the question instructs otherwise.

Information
The total mark for this paper is 60 The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed.

Advice
Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end.

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P40619A
©2012 Pearson Education Ltd.

*P40619A0120*

6/6/6/3

GCSE Mathematics 2MB01

Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. 1 Area of trapezium = 2 (a + b)h a cross section

Volume of prism = area of cross section × length

h lengt h

b

Volume of sphere = 4 r3 3 Surface area of sphere = 4 r2 r

Volume of cone = 1 r2h 3 Curved surface area of cone = rl

l r

h

In any triangle ABC b A c

C a B

The Quadratic Equation The solutions of ax2 + bx + c = 0 where a ≠ 0, are given by

x=

−b ± (b 2 − 4ac) 2a

Sine Rule

a b c = = sin A sin B sin C

Cosine Rule a2= b2+ c2– 2bc cos A Area of triangle = 1 ab sin C 2

2

*P40619A0220*

Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working.

1 Marta asked some students how many cans of drink they each drank yesterday. The table shows her results.

Number of cans 0 1 2 3 4 5

Frequency 6 9 7 3 2 1

Work out the total number of cans these students drank yesterday.

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

(Total for Question 1 is 2 marks)

*P40619A0320*

3

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*2 Mrs Collins is organising a school trip. 120 students are going on the trip. The ratio of the number of staff to the number of students must be 1 : 15 Mrs Collins books three coaches for the trip. Each coach has 42 seats. Are there enough seats for all the students and staff? You must show all your working.

(Total for Question 2 is 4 marks)

4

*P40619A0420*

3 Here is a five-sided spinner.

1

The table shows the probabilities that the spinner will land on 1 or 2 or 3 or 4 or 5

Number Probability

1 0.15

2 0.20

2
3 0.10

Pete spins the spinner once. (a) Work out the probability that the spinner will land on a number greater than 2

Elinor is going to spin the spinner 200 times. (b) Work out an estimate for the number of times the spinner will land on 5

*P40619A0520*

3
5

4

4 0.25

5 0.30

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

(2)

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

(2) (Total for Question 3 is 4 marks)
5

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*4 Debra and Mark are planning to go on a cruise. They can travel with one of two companies, Caribbean Calypso or Royal European. The table shows the cost per person to travel with each company.

Type of cabin Inside Cost per person Caribbean Calypso Royal European £1136 £1043 Outside Balcony £1319 £1263 £1529 £1484 Suite £2329 £2147

Caribbean Calypso has a discount of 10% if you book online. Royal European has a discount of 5% if you book online. Debra and Mark are going to book a suite for their cruise. They are going to book online. Debra and Mark want to pay the lowest possible cost. Which company should they choose? You must show all your working.

(Total for Question 4 is 5 marks)
6

*P40619A0620*

5 Here are the heights, in cm, of 20 sunflower plants. 73 81 84 92 78 95 96 103 98 100 84 96 101 87 93 91 71 88 104 96

(a) Draw an ordered stem and leaf diagram for these heights.

Key: (3) (b) Find the median height.

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

cm

(1) (Total for Question 5 is 4 marks)

*P40619A0720*

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6 Water is leaking out of two containers. The water started to leak out of the containers at the same time. The straight line P shows information about the amount of water, in litres, in container P. The straight line Q shows information about the amount of water, in litres, in container Q.

16 14 12 10 Amount of water (litres) 8 6 4 2 0 0 10 20 30 Time (seconds) 40 50 60 Q P

(a) Work out the gradient of line P.

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

(2)

8

*P40619A0820*

One container will become empty first. (b) (i) Which container? You must explain your answer.
. . . . . . . . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... ............................................................................................................................... . . . . . . . . . . . . . . . . . . .

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

(ii) How much water is then left in the other container? litres

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

(2) (Total for Question 6 is 4 marks)

*P40619A0920*

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7 Each year group in a school raised money for charity. The incomplete table and pie chart show some information about this. Complete the table.

Year Group 7 8 9 10 11

Amount raised
.............................................................

£225

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

£125 £162.50 £900

Year 7 100°

(Total for Question 7 is 3 marks)
10

*P40619A01020*

8 The cumulative frequency graph shows information about the heights of some hollyhock plants.

80

60 Cumulative frequency

40

20

0

60

70

80 Height (cm)

90

100

(a) Find an estimate for the median height. cm

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

(1) (b) Work out an estimate for the interquartile range.

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

cm

(2) (c) Find an estimate for the number of hollyhock plants taller than 90 cm.

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

(2) (Total for Question 8 is 5 marks)

*P40619A01120*

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9 In a newsagent’s shop, the probability that any customer buys a newspaper is 0.6 In the same shop, the probability that any customer buys a magazine is 0.3 (a) Complete the probability tree diagram.

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

buys magazine

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

buys newspaper
...............................

does not buy magazine buys magazine

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

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

does not buy newspaper
...............................

does not buy magazine
(2)

(b) Work out the probability that a customer will buy either a newspaper or a magazine but not both.

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

(3) (Total for Question 9 is 5 marks)

12

*P40619A01220*

10 Daniela works in a shop. Daniela served 50 customers in the morning. She served 75 customers in the afternoon. The mean time to serve 50 customers in the morning was 48.7 seconds. The mean time to serve all 125 customers was 50.2 seconds. (a) Work out the mean time to serve the 75 customers in the afternoon.

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

seconds

(3) For the 75 customers served in the afternoon the least time was 18 seconds the greatest time was 96 seconds the median time was 56 seconds the lower quartile was 32 seconds the upper quartile was 72 seconds (b) On the grid, draw a box plot for this information.

0

20

40 Seconds

60

80

100

(3) (Total for Question 10 is 6 marks)

*P40619A01320*

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11 Raul is the manager of a restaurant. He wants to find out how often local people eat in a restaurant. Raul is going to carry out a survey using a questionnaire. (a) Design a suitable question for Raul to use on his questionnaire.

(2) (b) The two-way table shows information about the ages of the customers in Raul’s restaurant one evening.

Age (years) 0–16 Male Female Total 8 7 15 17–30 10 9 19 31–60 17 22 39 over 60 20 34 54

Total 55 72 127

Raul carries out his survey using only these customers. He uses a sample of 50 of these customers stratified by gender and by age. Calculate the number of males aged 17–30 in his sample.

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

(2)

14

*P40619A01420*

Raul’s survey is biased. (c) Give two possible reasons why. 1 . . . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......................................................................................................................................... . . . . . . . . . . . . . . . . . . .

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

2 . . . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......................................................................................................................................... . . . . . . . . . . . . . . . . . . .

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

(2) (Total for Question 11 is 6 marks)

*P40619A01520*

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12 The table gives some information about the distances, in miles, that some men travelled to work. Distance (d miles) 0