Untitled - Go Teach Maths

AQA Foundation: June 2017 Paper 2, Q20

A code has 4 digits.Each digit is a number from 0 to 9Digits may be repeated.

The code starts 9 8 5

1

[1 mark]

×1, 3, 5, 7, 9

Answer

9 8 5

Alice chooses a number at random for the last digit.Write down the probability that she chooses the correct number.

Answer

1 (a)

1 (b) Trevor knows the last digit is odd but not 1 or 9.

He chooses a different odd number at random.

What is the probability that he chooses the correct number?.

[1 mark]

×

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 = 10

AQA Foundation: November 2017 Paper 1, Q9In a game, three stars are hidden at random.Each star is behind a different square on this board.

1

[1 mark]

Answer

A B C D E

1

2

3

4

5

A square is chosen at random.What is the probability that there is a star behind it?

1 (a)

In one game, the stars are behind three consecutive squares.The squares are in one row or one column.One of the squares is E2Write down all the possible pairs for the other two squares.

1 (b)

[2 marks]

Answer

E1, E3C2, D2E3, E4


There are 660 boys and 840 girls in a school.

The probability that a boy chosen at random studies Drama is

The probability that a girl chosen at random studies Drama is

1

[3 marks]

Work out the number of students in the school who study Drama.1 (a)

Work out the probability that a student chosen at random from the whole school does not study Drama.

1 (b)

[2 marks]

Answer

Answer

Boys: 660 × = 264

Girls: 840 × = 360

Total = 240 + 360 = 624

Total students = 660 + 840 = 1500

NOT drama = 1500 – 624 = 876

OR

624

AQA Foundation: November 2017 Paper 2, Q21

1

[2 marks]

Answer

Outcome A B C

Frequency 66 74 60Relative

Frequency0.33 0.37 0.3

An experiment is carried out 200 times.The possible outcomes are A, B and C.Complete the table.

1 (a) Altogether, the experiment is carried out 500 times.How many times would you expect the outcome to be K?

[2 marks]

200 – 66 – 74 = 60

500 × 0.33 = 165

165

1 – 0.33 – 0.37 = 0.3


1

[2 marks]

Answer

Number of throws

Number of hits

Number of misses

Monday 20 15 5

Tuesday 30 22 8

Wednesday 40 17 23

Total 90 54 36

On three days, Ali throws darts at a target.Here are his results.

1 (a) Work out two different estimates for the probability of Ali hitting the target.

Answer and

1 (a) Which of your two answers is the better estimate for the probability of Ali hitting the target?Give a reason for your answer.

Reason

[1 [mark]

More throws = more accurate probability

AQA Foundation: May 2017 Paper 1, Q14

A number is picked at random from the first four prime numbers.A number is picked at random from the first four square numbers.The two numbers are added to get a score.

1

[4 marks]1(a)Complete the table

1 4 9 16

2 3 6 11 18

3 4 7 12 19

5 6 9 14 21

7 8 11 16 23

Square numbers

Prime numbers

1(b)

What is the probability that the score is a prime number?

Answer

[1 mark]

+


[2 marks]

Answer

2 2 3 5

1 2 2 3 52 2 0 3 54 4 4 4 56 6 6 6 6

In a game, two fair spinners are spun.

1

4 6

2Spinner A

2

2 5

3Spinner B

If the numbers the arrows land on are different, the score is the higher number.

If the numbers the arrows land on are the same, the score is 0

1 (a) Complete the table to show the possible scores.

Spinner B

Sp

inn

er A

1 (a) Write down the probability that the score is an odd number.[1 mark]

1 (a) The same game is played using spinners C and D.The numbers on C are shown.

1

6 7

4Spinner C

Spinner D

4 4 7 81 4

4 0

6

7 0 8

Spinner B

Sp

inn

er C

Write the missing numbers on spinner D.

[2 marks]

4 47 8


600 students were asked if they drink soda.

600 × = 180

1

[4 marks]

say Yes.

40% of the students who say Yes drink 2 or more sodas a day.

1(a) Complete the frequency tree.

2 or more sodas a day

Drink soda

600

1(b) What fraction of the 600 students drink 2 or more sodas a day?

Give your answer in its simplest form. [2 marks]

Answer

180

420

40% of 1804 × 18 = 72

72

108


1

[4 marks]

34 men and 56 women visit a restaurant.30 of these people have a voucher.Four times as many women as men do not have a voucher.

1 (a) Complete the frequency tree.

Voucher

Gender

Men

Women

Women

Men

Yes

No

= 90

90

60

30

4

4 : 14 :

5 = 30= 6

6

24

32

2834 − 6

56 − 24

1 (b) A voucher takes 35% off the bill.After using the voucher, the bill for a meal is £28.60How much was the bill before using the voucher?

Answer £

Old price × 0.65 = 28.60Old price = 28.60 ÷ 0.65

44


[2 marks]

A takeaway sells 10-inch pizzas and 12-inch pizzas.Here is some information about the numbers sold in two weeks.

10-inch 51212-inch 231

Total 743

Answer

Week 2 Size

Price

396

362

164

143

307

758

1065

1 (a) In each week a proportion of the pizzas sold were 10-inch.In which week was this proportion greater?Show working to support your answer.

1 (b) The table shows the profit or loss the takeaway makes on each pizza.

Week 1

10-inch

12-inch

Normal

Offer

Normal

Offer

Normal Price Offer Price10-inch £3.74 profit 51p loss12-inch £5.29 profit 4p loss

In week 1 the total profit was £1895.55At the end of week 1 the takeaway spent £175 on adverts.Was the increase in profit in week 2 more than the cost of the adverts?You must show your working.

Answer

Week 2 profit: 10-inch, normal = 3.74 × 396 = 1481.04

Week 2

10-inch, offer = 0.51 × 362 = 184.6212-inch, normal = 5.29 × 164 = 867.56

12-inch, offer = 0.04 × 143 = 5.72

Total profit = 2158.26

(minus adverts) 2158.26 – 175 = £1983.26

Week 2 loss:

= 2348.60

= 190.34

Yes

[4 marks]


1

[1 mark]

Answer

Two ordinary fair dice are rolled.

1 (a) Complete the tree diagram.

2

3

2

3

More than 2

2 or less

More than 2

2 or less

More than 2

2 or less

1st dice 2nd dice

1 (b) Work out the probability that both dice land on a number more than 2

[1 mark]

×


1

[4 marks]

Answer

ξ

In a squash tournament,

106 players took part in the singles only33 players took part in the doubles onlytwice as many players took part in the singles

as took part in the doubles.

How many players took part in both the singles and the doubles?You may use the Venn diagram to help you.

Singles Doubles

106 33

(106 + ) = 2 × (33 + )106 + = 66 + 2

106 = 66 + 40 =

40

Untitled - Go Teach Maths

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