date: time: total marks available: total marks achieved: · 2015/6/6 · josh's year group...

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Questions 1-11 Non Calculator Questions 12-21 Calculator

Questions Q1.

Each day a company posts some small letters and some large letters.

The company posts all the letters by first class post.

The tables show information about the cost of sending a small letter by first class post and the cost of sending a large letter by first class post.

One day the company wants to post 200 letters.

The ratio of the number of small letters to the number of large letters is 3:2

70% of the large letters weigh 0-100 g.

The rest of the large letters weigh 101-250 g.

Work out the total cost of posting the 200 letters by first class post.

£ ...........................................................

(Total for Question is 5 marks)

Q2.

There are three different types of sandwiches on a shelf.

There are

4 egg sandwiches, 5 cheese sandwiches and 2 ham sandwiches.

Erin takes at random 2 of these sandwiches.

Work out the probability that she takes 2 different types of sandwiches.

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


Q3.

Wendy goes to a fun fair. She has one go at Hoopla. She has one go on the Coconut shy.

The probability that she wins at Hoopla is 0.4 The probability that she wins on the Coconut shy is 0.3

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.

.............................................................................................................................................. (2)


Q4. There are only red counters, blue counters, white counters and black counters in a bag.

The table shows the probability that a counter taken at random from the bag will be red or blue.

Colour red blue white black

Probability 0.2 0.5

The number of white counters in the bag is the same as the number of black counters in the bag.

Tania takes at random a counter from the bag.

(a) Work out the probability that Tania takes a white counter.

..............................................................................................................................................(2)

There are 240 counters in the bag.

(b) Work out the number of red counters in the bag.

..............................................................................................................................................(2)


Q5.

The grouped frequency table shows information about the weekly wages of 80 factory workers.

Weekly wage (£x) Frequency

100 < x ≤ 200 8

200 < x ≤ 300 15

300 < x ≤ 400 30

400 < x ≤ 500 17

500 < x ≤ 600 7

600 < x ≤ 700 3

(a) Complete the cumulative frequency table.

Weekly wage (£x) Cumulative Frequency

100 < x ≤ 200

200 < x ≤ 300

300 < x ≤ 400

400 < x ≤ 500

500 < x ≤ 600

600 < x ≤ 700

(1)

(b) On the grid opposite, draw a cumulative frequency graph for your table.

(2)

(c) Use your graph to find an estimate for the interquartile range.

.............................................................................................................................................. (2)

(d) Use your graph to find an estimate for the number of workers with a weekly wage of more than £530

.............................................................................................................................................. (2)

Q6.

Here are the speeds, in miles per hour, of 16 cars.

31 52 43 49 36 35 33 29

54 43 44 46 42 39 55 48

Draw an ordered stem and leaf diagram for these speeds.


Q7.

Alison wants to find out how much time people spend reading books. She is going to use a questionnaire.

Design a suitable question for Alison to use in her questionnaire.


Q8.

The students in a class kept a record of the amount of time, in minutes, they spent doing homework last week.

The table shows information about the amount of time the girls spent doing homework last week.

(a) On the grid, draw a box plot for the information in the table.

Amount of time (minutes) (2)

The box plot below shows information about the amount of time the boys spent doing homework last week.

Amount of time (minutes)

*(b) Compare the amount of time the girls spent doing homework with the amount of time the boys spent doing homework.

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

Q9.

Paula wants to find out how much money people spend buying CDs.

She uses this question on a questionnaire.

(a) Write down two things wrong with this question.

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

(2)

Paula asks 100 people in a CD store to do her questionnaire.

(b) Her sample is biased. Explain why.

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

(1)


Q10.

Fiza has 10 coins in a bag. There are three £1 coins and seven 50 pence coins.

Fiza takes at random, 3 coins from the bag.

Work out the probability that she takes exactly £2.50

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


Q11.

The scatter graph shows information about 10 apartments in a city.

The graph shows the distance from the city centre and the monthly rent of each apartment.

The table shows the distance from the city centre and the monthly rent for two other apartments.

Distance from the city centre (km)

2 3.1

Monthly rent (£) 250 190

(a) On the scatter graph, plot the information from the table.(1)

(b) Describe the relationship between the distance from the city centre and the monthly rent.

.............................................................................................................................................. ..............................................................................................................................................(1)

An apartment is 2.8 km from the city centre.

(c) Find an estimate for the monthly rent for this apartment.

..............................................................................................................................................(2)


Q12.

Josh plays a game with two sets of cards.

Josh takes at random one card from each set. He adds the numbers on the two cards to get the total score.

(a) Complete the table to show all the possible total scores.

(1)

(b) What is the probability that Josh's total score will be greater than 12?

...........................................................(2)

Josh's year group are raising money for a sponsored skydive.

60 students are each going to play Josh's card game once. Each student pays 50p to play the game.

Josh pays £1.50 to any player getting a total of 8

(c) Show that Josh can expect to make a profit of £21 from his game. (4)


Q13.

60 children go to a nursery. The ratio of girls to boys is 3 : 2

The children go to the nursery either in the morning or in the afternoon.

of the children go to the nursery in the morning.

The rest of the children go to the nursery in the afternoon.

7 boys go to the nursery in the afternoon.

Work out how many girls go to the nursery in the morning.

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

(Total for question = 5 marks) Q14.

There are 10 cakes on a plate.

1 fruit slice 6 doughnuts 3 iced buns

Barry takes a cake at random and eats it. He then takes at random a second cake.

Work out the probability that Barry takes two different types of cake.

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


Q15.

Here is a four sided spinner. The spinner is biased.

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

Number 1 2 3 4

Probability 0.2 0.1

The probability that the spinner will land on 2 is the same as the probability that the spinner will land on 4

(a) Work out the probability that the spinner will land on 4

.............................................................................................................................................. (3)

Shunya is going to spin the spinner 200 times.

(b) Work out an estimate for the number of times the spinner will land on 3

.............................................................................................................................................. (2)


Q16.

23 girls have a mean height of 153 cm. 17 boys have a mean height of 165 cm.

Work out the mean height of all 40 children.

. . . . . . . . . . . . . . . . . . . . . . cm


Q17.

* Jon and Alice are planning a holiday. They are going to stay at a hotel.

The table shows information about prices at the hotel.

Jon and Alice will stay in a double room. They will eat dinner at the hotel every day.

They can stay at the hotel for 3 nights in June or 4 nights in November.

Which of these holidays is cheaper?


Q18.

Lorna carries out a survey about the number of times customers go to a shop.

She asks at random 100 customers how many times they went to the shop last month.

The table shows Lorna's results.

One of the 100 customers is chosen at random.

(a) What is the probability that this customer went to the shop 5 or more times?

........................................................... (2)

Last month the shop had a total of 1500 customers.

(b) Work out an estimate for the number of customers who went to the shop exactly 2 times last month.

........................................................... (2)

The owner of a different shop is carrying out a survey on the ages of his customers. He records the ages of the first 10 customers in his shop after 9 am one morning.

(c) This may not be a suitable sample. Give two reasons why.

1

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

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

2

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

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

(2)


Q19.

Mary plays a game of throwing a ball at a target.

The table shows information about the probability of each possible score.

Score 0 1 2 3 4 5

Probability

0.09 x 3x 0.16 0.21 0.30

Mary is 3 times as likely to score 2 points than to score 1 point.

(a) Work out the value of x.

.............................................................................................................................................. (3)

Mary plays the game twice.

(b) Work out the probability of Mary scoring a total of 8

.............................................................................................................................................. (3)


Q20.

The histogram shows some information about the weights of a sample of apples.

Work out the proportion of apples in the sample with a weight between 140 grams and 200 grams.

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


21.

There are 11 girls and 8 boys in a tennis club.

Jake is going to pick at random a team from the tennis club.

The team will have two players.

Work out the probability that Jake will pick two boys or two girls for the team.

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


Mark Scheme Q1.

Q2.

Q3.

Q5.

Q6.

Q7.

Q8.

Q9.

Q10.

Q11.

Q12.

Q13.

Q14.

Q15.

Q17.

Q18.

Q20.

Q21.

date: time: total marks available: total marks achieved: · 2015/6/6 · josh's year group...

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