Mathematics questions, unit 8

Nama / NameKelas / ClassTarikh / Date

Data Handling and Likelihood

43 marks. Use Practice to check each answer as you go, or Exam to answer everything first.

Section A: objective questions

10 marks

Choose the correct answer.

Question 1

Which angle in a pie chart stands for half of the whole circle?

45°
90°
180°
360°

Show answerHide answer

A whole circle is 360°. Half of 360° is 180°.

For the teacher: Remembering, low difficulty, standard 8.1.1

Textbook p. 207

Question 2

Diagram 1 shows snacks bought at a school fair. 12 pupils bought keria. How many snacks were bought altogether?

Pie chart: curry puff 180 degrees, doughnut 90, sandwich 45, keria 45 with 12 — Diagram 1

Show answerHide answer

45° is 1/8 of the circle and stands for 12. The whole circle is 8 × 12 = 96.

For the teacher: Applying, low difficulty, standard 8.1.1

Textbook p. 211

Question 3

Diagram 2 shows the athletes from four schools. School R has 9 athletes. How many athletes are from school Q?

Pie chart: P 45 degrees, Q 90, R 45 with 9 athletes, S 180 — Diagram 2

Show answerHide answer

R has 45° = 9 athletes. Q has 90°, which is twice 45°, so 2 × 9 = 18.

For the teacher: Applying, low difficulty, standard 8.1.1

Textbook p. 212

Question 4

A sea turtle climbs a tree. What is the likelihood of this event?

Impossible
Less likely
Equally likely
Certain

Show answerHide answer

A sea turtle cannot climb a tree, so it can never happen: impossible.

For the teacher: Remembering, low difficulty, standard 8.2.1

Textbook p. 213

Question 5

A dice is rolled. What is the likelihood that the number is even?

Impossible
Equally likely
Less likely
Certain

Show answerHide answer

The even numbers are 2, 4 and 6 (3 numbers) and the odd numbers are 1, 3 and 5 (3 numbers). The chances are the same: equally likely.

For the teacher: Understanding, low difficulty, standard 8.2.1

Textbook p. 219

Question 6

Diagram 3 shows the marbles in a bag. One marble is picked without looking. Which statement is correct?

A bag with 1 red, 5 blue and 2 green marbles — Diagram 3

Picking a red marble is more likely than picking a green marble.
Picking a green marble is certain.
Picking a blue marble is impossible.
Picking a blue marble is more likely than picking a green marble.

Show answerHide answer

There are 5 blue marbles and only 2 green marbles, so blue is more likely than green.

For the teacher: Applying, low difficulty, standard 8.2.2

Textbook p. 218

Question 7

Diagram 4 shows the reading materials that 40 pupils like best. Which statement is true?

Pie chart: story book 180 degrees, comic 90, magazine 45, newspaper 45 — Diagram 4

The same number of pupils like magazines and newspapers.
More pupils like comics than story books.
Twice as many pupils like newspapers as magazines.
The fewest pupils like comics.

Show answerHide answer

Magazine and newspaper both have 45°, so they have equal numbers (5 each). The story book has the largest angle, and the comic is the second largest.

For the teacher: Analysing, medium difficulty, standard 8.1.1

Textbook p. 209

Question 8

Diagram 5 shows the flowers sold in a shop. The shop sold 40 roses. How many hibiscus flowers were sold?

Pie chart: rose 180 degrees, orchid 90, hibiscus 45, jasmine 45 — Diagram 5

Show answerHide answer

Rose: 180° = 40. Then 90° = 20 and 45° = 10. Hibiscus has 45°, so 10 flowers.

For the teacher: Applying, low difficulty, standard 8.3.1

Textbook p. 221

Question 9

A box has 3 yellow cubes and 3 green cubes. What can be done to make picking a green cube more likely?

Take out 1 green cube
Add 1 yellow cube
Add 1 green cube
Take out 1 yellow cube and add 1 yellow cube

Show answerHide answer

Adding 1 green cube gives 4 green and 3 yellow, so green is more likely. Taking out a green cube or adding a yellow one makes green less likely, and swapping yellow for yellow changes nothing.

For the teacher: Analysing, medium difficulty, standard 8.2.2

Textbook p. 219

Question 10

Which set of angles cannot be the slices of one pie chart?

180°, 90°, 45°, 45°
90°, 90°, 90°, 90°
180°, 90°, 90°
180°, 90°, 90°, 45°

Show answerHide answer

The slices of a pie chart must total 360°. 180° + 90° + 90° + 45° = 405°, which is too much. The other sets each make 360°.

For the teacher: Analysing, high difficulty, standard 8.1.1

Textbook p. 208

Section B: structured questions

33 marks

Answer all questions. Show your working.

Question 11

40 pupils chose their favourite sport: football 20, badminton 10, hockey 5, table tennis 5. The data will be shown in a pie chart.

[1 mark] (a)Football has 20 pupils out of 40. What fraction of the circle is football?

Show answerHide answer

1/2 [1]1

Tick each point you got.

[1 mark] (b)What angle stands for football?

Show answerHide answer

180° [1]1

Tick each point you got.

[1 mark] (c)What angle stands for hockey?

Show answerHide answer

45° (5 is half of 10, and 10 is 90°) [1]1

Tick each point you got.

[1 mark] (d)Which sport has the most pupils?

AFootballBBadmintonCHockeyDTable tennis

Show answerHide answer

Football

The sport with the most data has the largest angle, which is football with 20 pupils.

For the teacher: Remembering, low difficulty, standard 8.1.1

Textbook p. 210

Question 12

Diagram 6 shows the number of athletes from four schools. School R has 9 athletes.

[1 mark] (a)How many athletes are from school S?

Show answerHide answer

4 × 9 = 36 (180° is 4 times 45°) [1]1

Tick each point you got.

[2 marks] (b)What is the total number of athletes?

Show answerHide answer

8 × 9 [1]1
72 [1]1

Tick each point you got.

[2 marks] (c)Find the difference between the number of athletes from schools S and P.

Show answerHide answer

P has 9 athletes [1]1
36 − 9 = 27 [1]1

Tick each point you got.

For the teacher: Understanding, medium difficulty, standard 8.1.1

Textbook p. 212

Question 13

Diagram 7 shows the snacks bought at a school fair. 12 pupils bought keria.

[2 marks] (a)How many curry puffs were bought?

Show answerHide answer

45° = 12, 180° = 4 × 12 [1]1
48 [1]1

Tick each point you got.

[1 mark] (b)How many doughnuts were bought?

Show answerHide answer

2 × 12 = 24 [1]1

Tick each point you got.

[1 mark] (c)What fraction of all the snacks is doughnuts?

Show answerHide answer

1/4 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 8.3.1

Textbook p. 221

Question 14

24 pupils chose their favourite pet: cat 12, rabbit 6, fish 3, bird 3. Write the angle for each pet in a pie chart.

[1 mark] (a)Cat

Show answerHide answer

12/24 = 1/2, so 180° [1]1

Tick each point you got.

[1 mark] (b)Rabbit

Show answerHide answer

6/24 = 1/4, so 90° [1]1

Tick each point you got.

[1 mark] (c)Fish (the angle for bird is the same)

Show answerHide answer

3/24 = 1/8, so 45° [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 8.1.1

Textbook p. 209

Question 15

Diagram 8 shows the marbles in a bag. Rina picks one marble without looking.

[2 marks] (a)State the likelihood of picking a red marble. Give a reason.

Show answerHide answer

Less likely [1]1
There is only 1 red marble among 8 marbles [1]1

Tick each point you got.

[1 mark] (b)Which colour is the most likely to be picked?

ARedBBlueCGreen

Show answerHide answer

Blue

Blue has 5 marbles, more than any other colour.

[1 mark] (c)Picking a yellow marble is

AimpossibleBless likelyCmore likelyDcertain

Show answerHide answer

impossible

There is no yellow marble in the bag.

For the teacher: Applying, medium difficulty, standard 8.2.2

Textbook p. 218

Question 16

Choose the likelihood of each event.

[1 mark] (a)A heptagon has nine sides.

AimpossibleBless likelyCequally likelyDmore likelyEcertain

Show answerHide answer

impossible

A heptagon always has seven sides.

[1 mark] (b)A tossed coin shows a tail.

AimpossibleBless likelyCequally likelyDmore likelyEcertain

Show answerHide answer

equally likely

A coin has one head and one tail, so both are as likely.

[1 mark] (c)There are seven days in a week.

AimpossibleBless likelyCequally likelyDmore likelyEcertain

Show answerHide answer

certain

A week always has seven days.

For the teacher: Understanding, low difficulty, standard 8.2.1

Textbook p. 219

Question 17

Diagram 9 shows a bag of beads. Hadi picks one bead without looking.

A bag with 2 red and 2 blue beads — Diagram 9

[2 marks] (a)State the likelihood of picking a red bead. Give a reason.

Show answerHide answer

Equally likely [1]1
There are 2 red and 2 blue beads, the numbers are equal [1]1

Tick each point you got.

[1 mark] (b)Hadi adds 3 blue beads to the bag. Picking a red bead is now

AimpossibleBless likelyCequally likelyDcertain

Show answerHide answer

less likely

Now 2 red and 5 blue beads, so red is less likely.

For the teacher: Analysing, medium difficulty, standard 8.2.2

Textbook p. 219

Question 18

Farid says: "In a pie chart, 90° means there are 90 pupils."

[1 mark] (a)Is Farid correct?

AYesBNo

Show answerHide answer

An angle shows a fraction of the whole, not a count.

[2 marks] (b)Explain your answer. Use the fact that a circle is 360°.

Show answerHide answer

90° is 1/4 of the 360° circle, so it is a quarter of the pupils [1]1
The number depends on the total, e.g. with 48 pupils it is 12 pupils, not 90 [1]1

Tick each point you got.

For the teacher: Evaluating, high difficulty, standard 8.1.1

Textbook p. 207

Question 19

32 pupils each chose one favourite drink from four drinks. The pie chart for the data uses only 180°, 90°, 45° and 45°.

[2 marks] (a)Write a possible table of drinks and the number of pupils for each. The numbers must add up to 32.

Show answerHide answer

Half of 32 = 16 for the 180° drink [1]1
8 for 90° and 4 and 4 for the 45° drinks (16 + 8 + 4 + 4 = 32) [1]1

Tick each point you got.

[2 marks] (b)Write the angle for each drink in your table.

Show answerHide answer

180°, 90°, 45°, 45° matched to your numbers [1]1
Angles add to 360° [1]1

Tick each point you got.

For the teacher: Creating, high difficulty, standard 8.3.1

Textbook p. 222

Back to notes Model papers