Mathematics questions, unit 4

Nama / NameKelas / ClassTarikh / Date

Time

46 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 of these years is a leap year?

2018
2022
2024
2026

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A leap year can be divided by 4 with no remainder. 2024 ÷ 4 = 506, so February 2024 has 29 days. The other years leave a remainder of 2.

For the teacher: Remembering, low difficulty, standard 4.1.1 (ii)

Textbook p. 124

Question 2

A school fair is held from 3 March to 6 March in the same year. What is the duration, in days?

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Count the first day as well: 3, 4, 5 and 6 March are 4 days. (6 − 3 + 1 = 4. The answer is not 3, because the first day is also counted.)

For the teacher: Remembering, low difficulty, standard 4.1.1 (ii)

Textbook p. 125

Question 3

134 hours = ______ minutes

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1 hour = 60 minutes. 74 × 60 = 7 × 15 = 105 minutes. (60 + 34 × 60 = 60 + 45 = 105.)

For the teacher: Remembering, low difficulty, standard 4.2.1 (i)

Textbook p. 127

Question 4

Convert 1.75 days to hours.

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1 day = 24 hours. 1.75 × 24 = 24 + 0.75 × 24 = 24 + 18 = 42 hours.

For the teacher: Remembering, low difficulty, standard 4.2.2 (ii)

Textbook p. 135

Question 5

What is the duration, in days, from 5 February 2020 to 3 March 2020?

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2020 is a leap year (2020 ÷ 4 has no remainder), so February has 29 days. 5 to 29 February = 29 − 5 + 1 = 25 days. 1 to 3 March = 3 days. 25 + 3 = 28 days.

For the teacher: Understanding, low difficulty, standard 4.1.1 (ii)

Textbook p. 124

Question 6

7.6 centuries = ______ decades

0.76
7.6
760
76

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1 century = 10 decades. 7.6 × 10 = 76 decades. (760 is the number of years: 7.6 × 100.)

For the teacher: Understanding, low difficulty, standard 4.2.2 (v)

Textbook p. 138

Question 7

0.6 hour + 14 hour = ______ minutes

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0.6 hour = 0.6 × 60 = 36 minutes. 14 hour = 15 minutes. 36 + 15 = 51 minutes. (Adding as decimals: 0.6 + 0.25 = 0.85 hour, and 0.85 × 60 = 51 minutes. The answer is not 85 minutes, because 1 hour is 60 minutes.)

For the teacher: Applying, medium difficulty, standard 4.3.2 (i)

Textbook p. 142

Question 8

3 days 9 hours + 34 day = ______

3 days 12 hours
4 days 3 hours
4 days 9 hours
3 days 18 hours

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34 day = 34 × 24 = 18 hours. 9 hours + 18 hours = 27 hours = 1 day 3 hours. So 3 days + 1 day = 4 days 3 hours.

For the teacher: Applying, medium difficulty, standard 4.3.1 (ii)

Textbook p. 144

Question 9

Diagram 1 shows the ages of two trees. How many decades older is the older tree?

A strip of 100 years in ten blocks with marks at 35 years (0.35 century) and 75 years (3/4 century) — Diagram 1

0.4 decade
40 decades
14 decades
4 decades

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34 century = 0.75 century. 0.75 − 0.35 = 0.4 century. 0.4 × 10 = 4 decades. (0.4 century is 40 years, which is 4 decades.)

For the teacher: Analysing, medium difficulty, standard 4.3.2 (v)

Textbook p. 163

Question 10

Diagram 2 shows the start and end of a programme. What is the duration of the programme?

Two clocks: start, Tuesday 8:15 p.m.; end, Thursday 6:15 a.m. — Diagram 2

1 day 10 hours
1 day 14 hours
2 days 2 hours
1 day 2 hours

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Tuesday 8:15 p.m. to Wednesday 8:15 p.m. is 1 day. Wednesday 8:15 p.m. to Thursday 6:15 a.m. is 3 hours 45 minutes + 6 hours 15 minutes = 10 hours. The duration is 1 day 10 hours.

For the teacher: Analysing, medium difficulty, standard 4.1.1 (i)

Textbook p. 126

Section B: structured questions

36 marks

Answer all questions. Show your working.

Question 11

Convert the units of time.

[1 mark] (a)16 day = ______ hours

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16 × 24 = 4 hours [1]1

Tick each point you got.

[1 mark] (b)2 12 years = ______ months

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2 × 12 + 12 × 12 = 24 + 6 = 30 months [1]1

Tick each point you got.

[1 mark] (c)35 decade = ______ years

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35 × 10 = 6 years [1]1

Tick each point you got.

[1 mark] (d)710 century = ______ years

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710 × 100 = 70 years [1]1

Tick each point you got.

For the teacher: Remembering, low difficulty, standard 4.2.1

Textbook p. 133

Question 12

State the number of days in each month.

[1 mark] (a)April

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30 days [1]1

Tick each point you got.

[1 mark] (b)August

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31 days [1]1

Tick each point you got.

[1 mark] (c)February 2020 (a leap year)

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29 days [1]1

Tick each point you got.

For the teacher: Remembering, low difficulty, standard 4.1.1 (ii)

Textbook p. 124

Question 13

Convert these units of time that are given in decimals.

[1 mark] (a)2.4 hours = ______ minutes

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2.4 × 60 = 144 minutes [1] (120 + 24)1

Tick each point you got.

[1 mark] (b)3.25 days = ______ hours

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3.25 × 24 = 78 hours [1] (72 + 6)1

Tick each point you got.

[1 mark] (c)Hani says, "6.5 decades = 65 years." Is she correct?

AYesBNo

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Yes

1 decade = 10 years, so 6.5 × 10 = 65 years. Hani is correct. (650 years would be 6.5 centuries.)

For the teacher: Understanding, low difficulty, standard 4.2.2

Textbook p. 140

Question 14

A reading campaign was held from 12 May 2021 to 20 June 2021.

[2 marks] (a)What is the duration of the campaign, in days?

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12 May to 31 May = 31 − 12 + 1 = 20 days [1]1
20 + 20 (1 to 20 June) = 40 days [1]1

Tick each point you got.

[1 mark] (b)The same campaign is held from 12 May to 20 June in 2020, a leap year. Is the duration different?

AYesBNo

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The leap day is 29 February, which comes before 12 May. The dates from 12 May to 20 June are the same in a leap year, so the duration is still 40 days.

For the teacher: Applying, low difficulty, standard 4.1.1 (ii)

Textbook p. 125

Question 15

A school camp started at 9:30 a.m. on Thursday, 3 June 2021, and ended at 4:30 p.m. on Saturday, 5 June 2021. Diagram 3 shows the timeline.

Timeline: Thu 3 June 9:30 a.m., Fri 4 June 9:30 a.m., Sat 5 June 9:30 a.m., Sat 5 June 4:30 p.m. — Diagram 3

[2 marks] (a)Calculate the duration of the camp, in days and hours.

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2 days [1]1
7 hours (9:30 a.m. to 4:30 p.m.) [1]1

Tick each point you got.

[1 mark] (b)State the duration of the camp in hours.

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2 × 24 + 7 = 55 hours [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 4.1.1 (i)

Textbook p. 123

Question 16

Shafiq took 2 12 years to build a boat, and then 3 years 8 months to build a second boat.

[2 marks] (a)Find the total time to build the two boats. Give the answer in years and months.

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2 12 years = 2 years 6 months [1]1
2 years 6 months + 3 years 8 months = 5 years 14 months = 6 years 2 months [1]1

Tick each point you got.

[2 marks] (b)Shafiq repairs a boat in 1.5 years and paints it in 14 year. How many months does he take for the repair and painting?

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14 year = 3 months and 1.5 years = 18 months [1]1
18 + 3 = 21 months [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 4.3.1 (iii)

Textbook p. 145

Question 17

A tailor needs 2 34 days to sew a set of curtains and 1.5 days to sew a sofa cover.

[2 marks] (a)How much more time, in days, does he need for the curtains?

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2.75 days − 1.5 days [1]1
1.25 days (or 1 14 days) [1]1

Tick each point you got.

[1 mark] (b)Give your answer in (a) in hours.

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1.25 × 24 = 30 hours [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 4.3.2 (ii)

Textbook p. 156

Question 18

A packet of biscuits was made on 15.3.2020 and its expiry date is 4.5.2020.

[3 marks] (a)Calculate the shelf life of the biscuits, in days.

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15.3.2020 to 31.3.2020 = 31 − 15 + 1 = 17 days [1]1
April = 30 days; 1.5.2020 to 4.5.2020 = 4 days [1]1
17 + 30 + 4 = 51 days [1]1

Tick each point you got.

[1 mark] (b)The shopkeeper says the biscuits will stay good for more than 7 weeks. Is this true?

AYesBNo

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Yes

7 weeks = 7 × 7 = 49 days. The shelf life is 51 days, which is more than 49 days.

For the teacher: Analysing, high difficulty, standard 4.4.1

Textbook p. 166

Question 19

The total age of two old coins is 410 years. Coin A is 2.35 centuries old.

[1 mark] (a)Convert 2.35 centuries to years.

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2.35 × 100 = 235 years [1]1

Tick each point you got.

[2 marks] (b)How old is coin B? Give the answer in centuries and years.

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410 − 235 = 175 years [1]1
1 century 75 years [1]1

Tick each point you got.

[1 mark] (c)Which strategy is used to solve this problem?

ATrial and errorBWork backwardsCDraw a diagram

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Work backwards

We know the total and one part, so we subtract the known part from the total to find the other part.

For the teacher: Analysing, medium difficulty, standard 4.4.1

Textbook p. 170

Question 20

Siti says, "0.5 hour + 0.25 hour = 0.75 hour, so the answer is 75 minutes."

[1 mark] (a)Is Siti correct?

AYesBNo

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0.75 hour is not 75 minutes.

[2 marks] (b)Explain her mistake and give the correct answer in minutes.

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Siti took 1 hour as 100 minutes, but 1 hour = 60 minutes [1]1
0.75 × 60 = 45 minutes [1]1

Tick each point you got.

For the teacher: Evaluating, low difficulty, standard 4.2.2 (i)

Textbook p. 134

Question 21

Write one time in fractions and one time in decimals (both in hours) that add up to 1 hour 30 minutes.

[2 marks] (a)Write your two times and show that they add up to 1 hour 30 minutes.

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Two valid times in hours, one a fraction and one a decimal, for example 34 hour and 0.75 hour [1]1
Check: sum = 1.5 hours = 1 hour 30 minutes (any correct pair, such as 14 hour + 1.25 hours) [1]1

Tick each point you got.

For the teacher: Creating, medium difficulty, standard 4.3.2

Textbook p. 176

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