# 2010 Nov UNIT 1F 43601F tsddcs

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2010 November UNIT 1F 43601F

Question 1 complete tally chart; fraction of days; simplify fraction; interpret percentage;
use probability words
Question 2 * complete pictogram; interpret key; read bar chart; compare results
Question 3 given small data set, find mode, median & mean; criticise a claim; discuss
sampling method
Question 4 * calculate percentage of an amount; compare ways of working it out
Question 5 read a scatter diagram; comment on a hypothesis; draw a scatter diagram to
support a hypothesis
Question 6 given a bag of counters, find probability; find number of counters
Question 7 * design observation sheet; find evidence to decide hypothesis
Question 8 share amount in given ratio
Question 9 find winnings for probability game

* The quality of written communication is specifically assessed in questions 2, 4 and 7

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2010 November UNIT 1F 43601F

1 The table shows the weather in London each day for 40 days

10
18
4
8

1(a) Complete the table                                               2 marks

1(b) What fraction of the 40 days are sunny?         10

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2010 November UNIT 1F 43601F

1(c) In Manchester for the 40 days

• 16 days are sunny
• 50% of the days have rain
• there is no snow

1(c) (i) Complete the table for Manchester

16
50% of 40 days is 20                                          20
0
20 + 16 + 0 = 36                                                   4
40 – 36 = 4

3 marks
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2010 November UNIT 1F 43601F

16
20
0
4

1 (c) (ii) One of the 40 days in Manchester is chosen at random.
Use a suitable probability word to complete the sentences.

impossible
The chance of choosing a day with snow is ……………………………………………

evens
The chance of choosing a day with rain is ………………………………………………

2 marks

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2010 November UNIT 1F 43601F

2* Nick takes four tests. The pictogram shows his scores.

2(a) Nick scores 60% in English.   Complete the key.

20                 1 mark

2(b) In which subject is his highest score?

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2010 November UNIT 1F 43601F

2 (c) Jen takes the same four tests.
The bar chart shows her scores.

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2010 November UNIT 1F 43601F

2(c) (i) Nick wants to compare his scores with Jen’s scores.
Draw a suitable diagram that he can use.

Jen
Nick

4 marks

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2 (c) (ii) Write down three facts comparing     2010 November UNIT 1F 43601F
their scores
Jen
Nick

Fact: Jen scored higher than Nick in English, Geography and Science
Fact: Nick scored higher than Jen in Mathematics
Fact: both scored 40% or more in every test; they both had a highest
score of 90%
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3 marks
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2010 November UNIT 1F 43601F

3 A company makes bags of toffees

The company checks that the bags contain
50 toffees.

3(a) The number of toffees in a sample of 11 bags is

51    50   51    51    52     43    50     50       51       51     50

3(a) (i) Write down the mode
the mode is the data that occurs the most
3(a)(ii) Work out the median.        You must show your working
the median is halfway along the ordered list of data

43    50    50    50    50     51   51     51     51        51    52

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2010 November UNIT 1F 43601F

3(a) The number of toffees in a sample of 11 bags is

51     50   51   51    52    43    50    50       51      51     50

3(a) (iii) Work out the mean
the mean is calculated by adding all the data together, then
dividing the total by the number of items

51 + 50 + 51 + 51 + 52 + 43 + 50 + 50 + 51 + 51 + 50 = 550

550 ÷ 11 = 50                                    answer       50         3 marks

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2010 November UNIT 1F 43601F

3(b) The company claims there are 50 toffees in a bag

3(b) (i) Give a reason why this claim seems fair.

All the averages are 50 or bigger than 50                         1 mark

3(b) (ii) Give a reason why this claim seems unfair

one of the sample bags only had 43 sweets in it                   1 mark

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2010 November UNIT 1F 43601F

3(c) The company uses the first 11 bags produced each
Monday to check the contents.

State two ways this method of sampling can be improved

Take several samples during the week

Take bigger samples

Take samples at different times and on different days

Take every hundredth bag during production to be part of the sample

3 marks

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2010 November UNIT 1F 43601F

4(a) * Work out 70% of £986

70% is the same as 0.7

70% of 986 = 0.7 × 986 =      answer   £690.20            2 marks
690.2

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2010 November UNIT 1F 43601F

4(b) Circle the calculations that have the same answer as

57% of 372       0.57 × 372 = 212.04
A 58% of 371         No !

B 5.7% of 37.20      No !

57
C          372      0.57 × 372 = 212.04
100

D 0.57 × 0.372       No !


E 5.7% of 3720       0.057 × 3720 =                                    2 marks
212.04
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5 Freddie and Priya both like music              2010 November UNIT 1F 43601F
Freddie gives some songs a score out of 10
The scatter diagram shows his results
5(a) What fraction of the                     two scored 10 out of 10
songs is given full marks?
thirteen songs
were scored
13
1 mark

5(b) How long is the song
that is given a score of
4?
minutes and seconds.
time is 5 minutes and two sections

each section is 60 seconds ÷
5
= 12 seconds

answer = 5 minutes and 24 seconds           2 marks
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2010 November UNIT 1F 43601F

5(c) Freddie has this hypothesis
He says, “The shorter the song, the more I like it.”

Comment on his hypothesis

the line of best fit
shows weak negative
correlation which
supports his hypothesis

shorter songs scored
high marks and long
songs scored low marks

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2010 November UNIT 1F 43601F

5(d) Priya also gives some songs a score out of 10.
She has a different hypothesis.
She says, “The longer the song, the more I like it.”
Her hypothesis is strongly supported by the data she collects.

Plot points on the grid to
show how her scatter
diagram may look

• a line of best fit would show
positive correlation
• shorter songs score low marks
and long songs score high marks
• the data points would be close
to the line of best fit
1 mark

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2010 November UNIT 1F 43601F

6(a) A bag contains 3 red, 5 white and 8 blue counters.
One counter is chosen at random.

What is the probability of choosing a blue counter.

3 + 5 + 8 = 16 counters in the bag       probability =       8

8 of them are blue                                          16

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2010 November UNIT 1F 43601F

6(b) A different bag contains only black counters, pink counters
and white counters.
When one counter is chosen at random, each colour is equally likely.

Write down two possible values for the total number of counters in
this bag

three colours in the bag

probability of each colour is ⅓

number of counters in the bag must be a multiple of 3

answer 6 and 24                      2 marks

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2010 November UNIT 1F 43601F
6(c) Another bag contains only green counters and yellow
counters.
There are more than 10 counters in the bag.
When one counter is chosen at random, the probability of
choosing a green counter is ¾

Write down two possible values for the total number of
counters in this bag

probability of green = ¾  probability of yellow = ¼

number of counters in the bag must be a multiple of 4, bigger than 10

answer 16 and 24              2 marks

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2010 November UNIT 1F 43601F

7* This poster is put up in a school dinner hall

Coming soon

The headteacher thinks the number of students who eat school dinners
will increase by 25%
7(a) Design an observation sheet the headteacher can use to see if she
is right

tallies                        total
2 marks

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2010 November UNIT 1F 43601F

7(b) The number of students who eat school dinners
increases from 78 to 91.

Is the headteacher correct?       [She thinks the number of
students who eat school dinners will increase by 25%]

Show clearly how you decide.

25% of 78 = 0.25 × 78 = 19.5

a 25% increase on 78 would have to be 20 students

91 – 78 = 13   only 13 extra students ate the new lunch menu

answer: this is not enough to be 25% increase                          3 marks

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2010 November UNIT 1F 43601F

8 Peter and Alice buy a set of golf clubs for their mother.
They pay in the ratio 4 : 3
Peter pays £224

How much does Alice pay?

Peter              Alice
4                  3

224                 168

224 ÷ 4 = 56           56 × 3 =
168

answer: Alice pays £168              3 marks

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2010 November UNIT 1F 43601F

9 At the school fayre, I play a game 20 times.
Each go costs 50p.
Each time I win, I receive £1.50
The probability of winning is ⅕.

How much money do I expect to lose?

You pay 50p for each of 20 games         50p × 20 = £10

You expect to win ⅕ of the time

⅕ of 20 games = 4       Four prizes of £1.50 = £6

£10 − £6 = £4            You should expect to lose £4                 3 marks

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2010 November UNIT 1F 43601F

Total: out of 54           actual ones used

grade    G        F     E        D        C
score   10      16    22    29          36

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