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O Level Elementary Mathematics Numbers Ratio Proportion Quiz

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Questions

O-Level Elementary Mathematics Quiz - Numbers Ratio Proportion

Name: _________________________ Class: _________________________ Date: _________________________ Score: ______ / 50

Duration: 1 hour 15 minutes Total Marks: 50

Instructions:

Answer ALL questions.
Show all working clearly. Marks are awarded for method, not just final answers.
Give answers to 3 significant figures unless otherwise stated.
Approved calculators may be used.
The number of marks is given in brackets [ ] at the end of each question or part question.

Section A: Short Answer Questions (10 marks)

Answer all questions in this section.

1. Express 45 seconds as a percentage of 3 minutes. [1 mark]

Answer: _________________________

2. Simplify the ratio 0.75 : 1.25 : 2, giving your answer in its simplest integer form. [1 mark]

Answer: _________________________

3. A map has a scale of 1 : 25 000. Two villages are 8.4 cm apart on the map. Find the actual distance between the villages in kilometres. [1 mark]

Answer: _________________________ km

4. Given that $y$ is directly proportional to $x^2$ , and $y = 48$ when $x = 4$ , find the value of $y$ when $x = 7$ . [2 marks]

Answer: _________________________

5. A machine produces 240 components in 5 hours. At the same rate, how many components will it produce in 3 hours 45 minutes? [2 marks]

Answer: _________________________

Section B: Structured Questions (24 marks)

Answer all questions in this section. Show all working clearly.

6. The price of a laptop is increased by 15% to $1840. Find the original price of the laptop. [2 marks]

Answer: $_________________________

7. Write down the value of $\left(\frac{27}{8}\right)^{-\frac{2}{3}}$ as a fraction in its simplest form. [1 mark]

Answer: _________________________

8. A school has 480 students. 55% of the students are boys. Of the boys, 40% wear spectacles. Of the girls, 35% wear spectacles.

(a) Find the number of boys in the school. [1 mark]

(b) Find the number of girls who wear spectacles. [2 marks]

(c) What percentage of the total number of students wear spectacles? [2 marks]

9. The variables $p$ , $q$ , and $r$ are related such that $p$ is directly proportional to the square of $q$ , and $q$ is inversely proportional to the cube root of $r$ .

(a) Write down an equation connecting $p$ , $q$ , and $r$ . [1 mark]

(b) Given that $p = 36$ when $q = 3$ and $r = 8$ , find the value of the constant of proportionality. [2 marks]

(c) Hence, find the value of $p$ when $q = 6$ and $r = 27$ . [2 marks]

10. A container in the shape of a cuboid measures 30 cm by 20 cm by 15 cm. A smaller container is geometrically similar to the larger container. The volume of the smaller container is $\frac{8}{27}$ of the volume of the larger container.

(a) Find the linear scale factor from the larger container to the smaller container. [2 marks]

(b) Calculate the height of the smaller container. [1 mark]

(c) Find the ratio of the total surface area of the smaller container to the total surface area of the larger container. [2 marks]

Section C: Problem-Solving and Reasoning Questions (16 marks)

Answer all questions in this section. You must show all working and reasoning clearly.

11. In a class of 40 students, 25 study Mathematics (M), 20 study Physics (P), and 12 study both subjects.

(a) Draw a clearly labelled Venn diagram to represent this information, showing the number of students in each region. [3 marks]

(b) Find the number of students who study neither Mathematics nor Physics. [1 mark]

(c) A student is chosen at random from the class. Find the probability that the student studies exactly one of these two subjects. [2 marks]

12. The table below shows the distribution of marks obtained by 200 students in a Mathematics test.

Marks ( $x$ )	Frequency
$0 \leq x < 20$	10
$20 \leq x < 40$	30
$40 \leq x < 60$	65
$60 \leq x < 80$	60
$80 \leq x \leq 100$	35

(a) Calculate an estimate of the mean mark. [2 marks]

(b) The passing mark for the test is 40. Two students are chosen at random from those who took the test. Find the probability that both students passed the test. [3 marks]

13. A tank contains 120 litres of water. Water leaks out at a constant rate. After 25 minutes, the tank contains 95 litres of water.

(a) Find the rate at which water is leaking from the tank, in litres per minute. [1 mark]

(b) Write down an expression for the volume, $V$ litres, of water in the tank after $t$ minutes. [1 mark]

(c) How long will it take for the tank to be completely empty? Give your answer in minutes and seconds. [2 marks]

14. The box-and-whisker diagrams below show the distribution of scores obtained by two classes, Class A and Class B, in the same Mathematics examination.

Class A:   |----[======|======]-----------|
           40   55    65    75           95

Class B:   |------[====|====]------------|
           35      50  60  70           90

Note: The diagrams show minimum, lower quartile, median, upper quartile, and maximum values.

(a) Write down the median score for each class. [1 mark]

(b) Which class has the greater interquartile range? Justify your answer with numerical values. [2 marks]

(c) A student claims that "Class A performed better than Class B because Class A has a higher maximum score." Explain whether you agree with this statement, using appropriate statistical measures to support your answer. [2 marks]

15. The cost of printing $n$ copies of a school magazine is given by the formula $C = 250 + 1.80n$ , where $C$ is the total cost in dollars.

(a) Find the cost of printing 500 copies. [1 mark]

(b) The school has a budget of $1600 for printing. Find the maximum number of copies that can be printed. [2 marks]

(c) The school decides to sell each magazine for $3.50. Find the minimum number of magazines that must be sold to make a profit. [3 marks]

Section D: Extended Problem-Solving (10 marks)

Answer all questions in this section. You must show all working and reasoning clearly.

16. A sum of money is divided among three people, Amy, Ben, and Chloe, in the ratio 5 : 3 : 2. Ben receives $72 less than Amy.

(a) Find the total sum of money. [3 marks]

(b) Chloe decides to give 25% of her share to charity. How much money does Chloe have left? [1 mark]

17. The distance an object falls from rest is directly proportional to the square of the time it has been falling. An object falls 78.4 metres in 4 seconds.

(a) Find the constant of proportionality. [1 mark]

(b) How far will the object fall in 7 seconds? [1 mark]

(c) How long will it take to fall 122.5 metres? [2 marks]

18. A recipe for 12 biscuits requires 200 g of flour, 150 g of butter, and 100 g of sugar. A baker wants to make 30 biscuits using the same recipe.

(a) Find the amount of flour needed. [1 mark]

(b) The baker has only 320 g of butter. What is the maximum number of biscuits that can be made with this amount of butter? [2 marks]

19. The population of a town increased by 8% from 2019 to 2020, and then decreased by 5% from 2020 to 2021. The population at the end of 2021 was 51 300.

(a) Find the population at the beginning of 2019. [2 marks]

(b) Find the overall percentage change in population from the beginning of 2019 to the end of 2021. [1 mark]

20. A car travels at a constant speed of 80 km/h for the first part of a journey, and then at 60 km/h for the remaining 90 km. The total time taken for the journey is 3 hours.

(a) Find the time taken for the second part of the journey. [1 mark]

(b) Find the distance travelled in the first part of the journey. [2 marks]

(c) Calculate the average speed for the whole journey. [1 mark]

END OF QUIZ

Check your work carefully before submitting.

Answers

O-Level Elementary Mathematics Quiz - Numbers Ratio Proportion

ANSWER KEY AND MARKING SCHEME

Total Marks: 50

Section A: Short Answer Questions (10 marks)

1. Express 45 seconds as a percentage of 3 minutes. [1 mark]

Answer: 25%

Working: 3 minutes = 3 × 60 = 180 seconds Percentage = $\frac{45}{180} \times 100\% = \frac{1}{4} \times 100\% = 25\%$

Marking: 1 mark for correct answer. Accept 25% or 25.

2. Simplify the ratio 0.75 : 1.25 : 2, giving your answer in its simplest integer form. [1 mark]

Answer: 3 : 5 : 8

Working: Multiply all terms by 4: 0.75 × 4 = 3, 1.25 × 4 = 5, 2 × 4 = 8 Ratio = 3 : 5 : 8 (no common factor)

Marking: 1 mark for correct simplified integer ratio.

3. A map has a scale of 1 : 25 000. Two villages are 8.4 cm apart on the map. Find the actual distance between the villages in kilometres. [1 mark]

Answer: 2.1 km

Working: Actual distance = 8.4 × 25 000 = 210 000 cm = 210 000 ÷ 100 = 2100 m = 2100 ÷ 1000 = 2.1 km

Marking: 1 mark for correct answer with units.

4. Given that $y$ is directly proportional to $x^2$ , and $y = 48$ when $x = 4$ , find the value of $y$ when $x = 7$ . [2 marks]

Answer: 147

Working: $y = kx^2$ $48 = k(4^2)$ → $48 = 16k$ → $k = 3$ When $x = 7$ : $y = 3(7^2) = 3(49) = 147$

Marking: M1 for finding $k = 3$ , A1 for correct answer 147.

5. A machine produces 240 components in 5 hours. At the same rate, how many components will it produce in 3 hours 45 minutes? [2 marks]

Answer: 180 components

Working: Rate = 240 ÷ 5 = 48 components per hour 3 hours 45 minutes = 3.75 hours Number of components = 48 × 3.75 = 180

Alternative: 3 h 45 min = 225 minutes; 5 h = 300 minutes $\frac{240}{300} \times 225 = 180$

Marking: M1 for finding rate or setting up proportion, A1 for correct answer.

Section B: Structured Questions (24 marks)

6. The price of a laptop is increased by 15% to $1840. Find the original price of the laptop. [2 marks]

Answer: $1600

Working: Let original price = $x$ $x \times 1.15 = 1840$ $x = 1840 \div 1.15 = 1600$

Marking: M1 for correct equation or method (e.g., 1840 ÷ 115 × 100), A1 for correct answer.

7. Write down the value of $\left(\frac{27}{8}\right)^{-\frac{2}{3}}$ as a fraction in its simplest form. [1 mark]

Answer: $\frac{4}{9}$

Working: $\left(\frac{27}{8}\right)^{-\frac{2}{3}} = \left(\frac{8}{27}\right)^{\frac{2}{3}} = \left(\sqrt[3]{\frac{8}{27}}\right)^2 = \left(\frac{2}{3}\right)^2 = \frac{4}{9}$

Marking: 1 mark for correct simplified fraction.

8. A school has 480 students. 55% of the students are boys. Of the boys, 40% wear spectacles. Of the girls, 35% wear spectacles.

(a) Find the number of boys in the school. [1 mark]

Answer: 264 boys

Working: 55% of 480 = 0.55 × 480 = 264

Marking: 1 mark for correct answer.

(b) Find the number of girls who wear spectacles. [2 marks]

Answer: 75 or 76 (see note)

Working: Number of girls = 480 - 264 = 216 Girls who wear spectacles = 35% of 216 = 0.35 × 216 = 75.6

Note: Since this is a real-world context, accept 75 or 76 depending on interpretation. The mathematical answer is 75.6; accept 75.6 or 76 if rounded appropriately.

Marking: M1 for finding number of girls (216), A1 for correct number of girls wearing spectacles.

(c) What percentage of the total number of students wear spectacles? [2 marks]

Answer: 37.75% or 37.8%

Working: Boys wearing spectacles = 40% of 264 = 0.40 × 264 = 105.6 Girls wearing spectacles = 75.6 Total wearing spectacles = 105.6 + 75.6 = 181.2 Percentage = $\frac{181.2}{480} \times 100\% = 37.75\%$

Marking: M1 for finding total number wearing spectacles, A1 for correct percentage.

9. The variables $p$ , $q$ , and $r$ are related such that $p$ is directly proportional to the square of $q$ , and $q$ is inversely proportional to the cube root of $r$ .

(a) Write down an equation connecting $p$ , $q$ , and $r$ . [1 mark]

Answer: $p = k \frac{q^2}{\sqrt[3]{r}}$ or $p = k q^2 r^{-\frac{1}{3}}$

Working: $p \propto q^2$ → $p = k_1 q^2$ $q \propto \frac{1}{\sqrt[3]{r}}$ → $q = \frac{k_2}{\sqrt[3]{r}}$ Combining: $p = k \frac{q^2}{\sqrt[3]{r}}$ where $k$ is a constant.

Marking: 1 mark for correct equation with constant.

(b) Given that $p = 36$ when $q = 3$ and $r = 8$ , find the value of the constant of proportionality. [2 marks]

Answer: $k = 8$

Working: $36 = k \frac{3^2}{\sqrt[3]{8}}$ $36 = k \frac{9}{2}$ $k = 36 \times \frac{2}{9} = 8$

Marking: M1 for correct substitution, A1 for $k = 8$ .

(c) Hence, find the value of $p$ when $q = 6$ and $r = 27$ . [2 marks]

Answer: $p = 96$

Working: $p = 8 \times \frac{6^2}{\sqrt[3]{27}} = 8 \times \frac{36}{3} = 8 \times 12 = 96$

Marking: M1 for correct substitution, A1 for correct answer.

10. A container in the shape of a cuboid measures 30 cm by 20 cm by 15 cm. A smaller container is geometrically similar to the larger container. The volume of the smaller container is $\frac{8}{27}$ of the volume of the larger container.

(a) Find the linear scale factor from the larger container to the smaller container. [2 marks]

Answer: $\frac{2}{3}$

Working: Volume scale factor = $\frac{8}{27}$ Linear scale factor = $\sqrt[3]{\frac{8}{27}} = \frac{2}{3}$

Marking: M1 for recognising volume scale factor = (linear scale factor)³, A1 for correct linear scale factor.

(b) Calculate the height of the smaller container. [1 mark]

Answer: 10 cm

Working: Height of smaller = $\frac{2}{3} \times 15 = 10$ cm

Marking: 1 mark for correct height.

(c) Find the ratio of the total surface area of the smaller container to the total surface area of the larger container. [2 marks]

Answer: 4 : 9

Working: Area scale factor = (linear scale factor)² = $\left(\frac{2}{3}\right)^2 = \frac{4}{9}$ Ratio = 4 : 9

Marking: M1 for squaring the linear scale factor, A1 for correct ratio.

Section C: Problem-Solving and Reasoning Questions (16 marks)

11. In a class of 40 students, 25 study Mathematics (M), 20 study Physics (P), and 12 study both subjects.

(a) Draw a clearly labelled Venn diagram to represent this information, showing the number of students in each region. [3 marks]

Answer:

Intersection (M ∩ P): 12
Mathematics only: 25 - 12 = 13
Physics only: 20 - 12 = 8
Outside both: 40 - 13 - 12 - 8 = 7

Marking: B1 for correct intersection (12), B1 for correct "only" regions (13 and 8), B1 for correct outside region (7) and clear labels.

(b) Find the number of students who study neither Mathematics nor Physics. [1 mark]

Answer: 7

Marking: 1 mark for correct answer.

(c) A student is chosen at random from the class. Find the probability that the student studies exactly one of these two subjects. [2 marks]

Answer: $\frac{21}{40}$

Working: Number studying exactly one subject = 13 + 8 = 21 Probability = $\frac{21}{40}$

Marking: M1 for identifying 21 students, A1 for correct probability.

12. The table below shows the distribution of marks obtained by 200 students in a Mathematics test.

Marks ( $x$ )	Frequency
$0 \leq x < 20$	10
$20 \leq x < 40$	30
$40 \leq x < 60$	65
$60 \leq x < 80$	60
$80 \leq x \leq 100$	35

(a) Calculate an estimate of the mean mark. [2 marks]

Answer: 58

Working: Midpoints: 10, 30, 50, 70, 90 Σfx = 10(10) + 30(30) + 65(50) + 60(70) + 35(90) = 100 + 900 + 3250 + 4200 + 3150 = 11 600 Mean = $\frac{11 600}{200} = 58$

Marking: M1 for using midpoints and finding Σfx, A1 for correct mean.

(b) The passing mark for the test is 40. Two students are chosen at random from those who took the test. Find the probability that both students passed the test. [3 marks]

Answer: $\frac{10176}{19900}$ or $\frac{2544}{4975}$ (approximately 0.511)

Working: Number of students who passed (≥40) = 65 + 60 + 35 = 160 Total students = 200 P(both passed) = $\frac{160}{200} \times \frac{159}{199} = \frac{4}{5} \times \frac{159}{199} = \frac{636}{995} = \frac{2544}{3980}$ ? Let's recalculate: $\frac{160}{200} \times \frac{159}{199} = \frac{4}{5} \times \frac{159}{199} = \frac{636}{995}$ Wait, 160/200 = 4/5. 4/5 * 159/199 = 636/995. 636/995 simplifies? 636 = 2^2 * 3 * 53; 995 = 5 * 199. No common factors. So 636/995. Check: 636/995 ≈ 0.639. But earlier I had 0.511. Let's recompute carefully. 160/200 = 0.8. 159/199 ≈ 0.79899. Product ≈ 0.639. Yes, 636/995 ≈ 0.639. Wait, 160 * 159 = 25440. 200 * 199 = 39800. 25440/39800 = 2544/3980 = 636/995. Correct. So answer is 636/995.

Marking: M1 for finding number of students who passed (160), M1 for correct probability expression (160/200 × 159/199), A1 for correct simplified probability.

13. A tank contains 120 litres of water. Water leaks out at a constant rate. After 25 minutes, the tank contains 95 litres of water.

(a) Find the rate at which water is leaking from the tank, in litres per minute. [1 mark]

Answer: 1 litre per minute

Working: Water leaked = 120 - 95 = 25 litres Time = 25 minutes Rate = 25 ÷ 25 = 1 L/min

Marking: 1 mark for correct rate.

(b) Write down an expression for the volume, $V$ litres, of water in the tank after $t$ minutes. [1 mark]

Answer: $V = 120 - t$

Working: Initial volume = 120, rate = 1 L/min, so $V = 120 - 1 \times t = 120 - t$

Marking: 1 mark for correct expression.

(c) How long will it take for the tank to be completely empty? Give your answer in minutes and seconds. [2 marks]

Answer: 120 minutes (or 2 hours 0 minutes 0 seconds)

Working: Set $V = 0$ : $0 = 120 - t$ → $t = 120$ minutes = 120 minutes 0 seconds.

Marking: M1 for setting V = 0, A1 for correct time.

14. The box-and-whisker diagrams below show the distribution of scores obtained by two classes, Class A and Class B, in the same Mathematics examination.

Class A:   |----[======|======]-----------|
           40   55    65    75           95

Class B:   |------[====|====]------------|
           35      50  60  70           90

Note: The diagrams show minimum, lower quartile, median, upper quartile, and maximum values.

(a) Write down the median score for each class. [1 mark]

Answer: Class A: 65, Class B: 60

Marking: 1 mark for both correct medians.

(b) Which class has the greater interquartile range? Justify your answer with numerical values. [2 marks]

Answer: Class A has the greater interquartile range. IQR for Class A = 75 - 55 = 20 IQR for Class B = 70 - 50 = 20 Wait, both are 20? Let's check the diagram: Class A: lower quartile 55, upper quartile 75 → IQR = 20 Class B: lower quartile 50, upper quartile 70 → IQR = 20 They are equal. So the answer should be: Both classes have the same interquartile range of 20.

Marking: M1 for calculating both IQRs, A1 for stating they are equal with correct values.

(c) A student claims that "Class A performed better than Class B because Class A has a higher maximum score." Explain whether you agree with this statement, using appropriate statistical measures to support your answer. [2 marks]

Answer: Disagree. Although Class A has a higher maximum score (95 vs 90), Class A also has a higher minimum score (40 vs 35). The median of Class A (65) is higher than that of Class B (60), which suggests Class A performed better overall. However, the interquartile ranges are equal (20), indicating similar spread of the middle 50% of scores. A better comparison would use the median or mean, not just the maximum.

Marking: M1 for disagreeing and mentioning median or other measures, A1 for clear explanation using median or IQR.

15. The cost of printing $n$ copies of a school magazine is given by the formula $C = 250 + 1.80n$ , where $C$ is the total cost in dollars.

(a) Find the cost of printing 500 copies. [1 mark]

Answer: $1150

Working: $C = 250 + 1.80 \times 500 = 250 + 900 = 1150$

Marking: 1 mark for correct answer.

(b) The school has a budget of $1600 for printing. Find the maximum number of copies that can be printed. [2 marks]

Answer: 750 copies

Working: $250 + 1.80n \leq 1600$ $1.80n \leq 1350$ $n \leq 1350 \div 1.80 = 750$

Marking: M1 for setting up inequality or equation, A1 for correct answer.

(c) The school decides to sell each magazine for $3.50. Find the minimum number of magazines that must be sold to make a profit. [3 marks]

Answer: 148 copies

Working: Revenue = $3.50n$ Profit when Revenue > Cost: $3.50n > 250 + 1.80n$ $3.50n - 1.80n > 250$ $1.70n > 250$ $n > \frac{250}{1.70} \approx 147.058...$ Minimum integer $n = 148$

Marking: M1 for setting up inequality Revenue > Cost, M1 for solving inequality, A1 for correct integer answer.

Section D: Extended Problem-Solving (10 marks)

16. A sum of money is divided among three people, Amy, Ben, and Chloe, in the ratio 5 : 3 : 2. Ben receives $72 less than Amy.

(a) Find the total sum of money. [3 marks]

Answer: $360

Working: Let shares be 5x, 3x, 2x. Amy - Ben = 5x - 3x = 2x = 72 → x = 36 Total = 5x + 3x + 2x = 10x = 10 × 36 = $360

Marking: M1 for setting up 5x - 3x = 72, M1 for finding x = 36, A1 for correct total.

(b) Chloe decides to give 25% of her share to charity. How much money does Chloe have left? [1 mark]

Answer: $54

Working: Chloe's share = 2x = 2 × 36 = $72 Amount left = 75% of$ 72 = 0.75 × 72 = $54

Marking: 1 mark for correct answer.

17. The distance an object falls from rest is directly proportional to the square of the time it has been falling. An object falls 78.4 metres in 4 seconds.

(a) Find the constant of proportionality. [1 mark]

Answer: 4.9

Working: $d = k t^2$ $78.4 = k \times 4^2 = 16k$ $k = 78.4 \div 16 = 4.9$

Marking: 1 mark for correct constant.

(b) How far will the object fall in 7 seconds? [1 mark]

Answer: 240.1 metres

Working: $d = 4.9 \times 7^2 = 4.9 \times 49 = 240.1$

Marking: 1 mark for correct distance.

(c) How long will it take to fall 122.5 metres? [2 marks]

Answer: 5 seconds

Working: $122.5 = 4.9 t^2$ $t^2 = 122.5 \div 4.9 = 25$ $t = \sqrt{25} = 5$ seconds (positive root only)

Marking: M1 for setting up equation, A1 for correct time.

18. A recipe for 12 biscuits requires 200 g of flour, 150 g of butter, and 100 g of sugar. A baker wants to make 30 biscuits using the same recipe.

(a) Find the amount of flour needed. [1 mark]

Answer: 500 g

Working: Scale factor = 30 ÷ 12 = 2.5 Flour = 200 × 2.5 = 500 g

Marking: 1 mark for correct amount.

(b) The baker has only 320 g of butter. What is the maximum number of biscuits that can be made with this amount of butter? [2 marks]

Answer: 25 biscuits

Working: Butter per biscuit = 150 ÷ 12 = 12.5 g Maximum biscuits = 320 ÷ 12.5 = 25.6 → 25 whole biscuits Alternative: 150 g for 12 biscuits → 1 g for 12/150 biscuits → 320 g for (12/150)×320 = 25.6 → 25 biscuits.

Marking: M1 for finding butter per biscuit or setting up proportion, A1 for correct integer answer.

19. The population of a town increased by 8% from 2019 to 2020, and then decreased by 5% from 2020 to 2021. The population at the end of 2021 was 51 300.

(a) Find the population at the beginning of 2019. [2 marks]

Answer: 50 000

Working: Let population at beginning of 2019 be P. End of 2020: P × 1.08 End of 2021: P × 1.08 × 0.95 = 51 300 P × 1.026 = 51 300 P = 51 300 ÷ 1.026 = 50 000

Marking: M1 for correct compound multiplier (1.08 × 0.95 = 1.026), A1 for correct population.

(b) Find the overall percentage change in population from the beginning of 2019 to the end of 2021. [1 mark]

Answer: 2.6% increase

Working: Overall multiplier = 1.08 × 0.95 = 1.026 Percentage change = (1.026 - 1) × 100% = 2.6% increase

Marking: 1 mark for correct percentage change.

20. A car travels at a constant speed of 80 km/h for the first part of a journey, and then at 60 km/h for the remaining 90 km. The total time taken for the journey is 3 hours.

(a) Find the time taken for the second part of the journey. [1 mark]

Answer: 1.5 hours

Working: Time = Distance ÷ Speed = 90 ÷ 60 = 1.5 hours

Marking: 1 mark for correct time.

(b) Find the distance travelled in the first part of the journey. [2 marks]

Answer: 120 km

Working: Time for first part = Total time - time for second part = 3 - 1.5 = 1.5 hours Distance = Speed × Time = 80 × 1.5 = 120 km

Marking: M1 for finding time for first part, A1 for correct distance.

(c) Calculate the average speed for the whole journey. [1 mark]

Answer: 70 km/h

Working: Total distance = 120 + 90 = 210 km Total time = 3 hours Average speed = 210 ÷ 3 = 70 km/h

Marking: 1 mark for correct average speed.

END OF ANSWER KEY