Cambridge IGCSE Mathematics 0580: Graphs in practical situations – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover subtopic 2.9, Graphs in practical situations, in the Cambridge IGCSE Mathematics 0580 syllabus for examination in 2025, 2026 and 2027. Questions 1 to 6 use Core content (C2.9) and suit every candidate. Questions 7 to 11 are labelled (Extended): they use E2.9 content (tangents, speed–time graphs, acceleration and area under a graph) that is examined only on Papers 2 and 4. Each question is also labelled (non-calculator) or (calculator).

Graphs are described by the points where their straight sections meet, so you can sketch them. For explanations, read the graphs in practical situations study guide.

Questions

1. (non-calculator) A conversion graph for kilograms (horizontal axis) and pounds (vertical axis) is a straight line through (0, 0) and (10, 22).

(a) Use the graph to convert 5 kg to pounds. [1] (b) The graph only goes up to 10 kg. Convert 154 pounds to kilograms. [2]

2. (non-calculator) The total cost, $C, of gym membership for m months is shown by a straight line through (0, 40) and (12, 160).

(a) State the joining fee. [1] (b) Calculate the gradient of the line and explain what it represents. [2]

3. (non-calculator) Tariq walks from home to a shop and back. His distance–time graph joins these points with straight lines: (0 min, 0 km), (40 min, 3 km), (55 min, 3 km), (85 min, 0 km).

(a) Calculate his walking speed to the shop, in km/h. [2] (b) How long did he spend at the shop? [1] (c) Calculate his speed on the way home, in km/h. [1]

4. (calculator) A bus leaves a station at 08 00. It travels 30 km at a constant 45 km/h, stops for 10 minutes, then travels a further 20 km at a constant 40 km/h.

(a) Find the times at which the bus arrives at the stop, leaves the stop and reaches the end of the route. [3] (b) Write down the four points you would plot to draw the distance–time graph. [1] (c) Calculate the average speed for the whole route. [2]

5. (non-calculator) Towns A and B are 36 km apart. Ben leaves A at 10 00 and cycles towards B at 18 km/h. Cara leaves B at 10 15 and cycles towards A at 24 km/h. Both travel at constant speed. On a distance–time graph showing distance from A, their lines cross. Find the time at which they meet and their distance from A. [4]

6. (calculator) Water is pumped into a cuboid tank and later drained. The depth of water joins these points with straight lines: (0 min, 20 cm), (5 min, 50 cm), (8 min, 50 cm), (14 min, 20 cm).

(a) Find the rate at which the depth rises during the first 5 minutes. [2] (b) Find the rate at which the depth falls while the tank is draining. [1] (c) The base of the tank measures 40 cm by 25 cm. Find the rate at which water is pumped in during the first 5 minutes, in litres per minute. (1 litre = 1000 cm³.) [2]

7. (Extended) (non-calculator) A speed–time graph joins these points with straight lines: (0 s, 4 m/s), (10 s, 16 m/s), (40 s, 16 m/s), (48 s, 0 m/s).

(a) Find the acceleration during the first 10 seconds. [1] (b) Find the deceleration during the last 8 seconds. [1] (c) Calculate the total distance travelled. [3]

8. (Extended) (calculator) A train starts from rest and accelerates steadily to a speed of V m/s in 25 s. It travels at V m/s for 90 s, then decelerates steadily to rest in 35 s. The total distance is 3 km.

(a) Find V. [3] (b) Write V in km/h. [1] (c) Find the acceleration in the first 25 s. [1]

9. (Extended) (calculator) A trolley rolls from rest. Its distance d metres after t seconds is shown in the table.

t (s)	0	1	2	3	4	5	6
d (m)	0	0.5	2	4.5	8	12.5	18

(a) Draw the distance–time graph for 0 ≤ t ≤ 6. [2] (b) By drawing a tangent, estimate the speed of the trolley when t = 4. [3] (c) Explain how the graph shows that the trolley is speeding up. [1]

10. (Extended) (calculator) A cyclist’s speed–time graph joins these points with straight lines: (0 s, 0 m/s), (6 s, 9 m/s), (20 s, 9 m/s), (26 s, 3 m/s).

(a) Find the distance travelled in the first 4 seconds. [2] (b) Find the total distance travelled in the 26 seconds. [3] (c) Find the average speed over the 26 seconds. [1] (d) Find the deceleration between 20 s and 26 s. [1]

11. (Extended) (calculator) A tram starts from rest and accelerates steadily to 36 km/h in 20 seconds. It then travels at this constant speed for t seconds. Finally it decelerates steadily at 0.4 m/s² until it stops. The tram travels 1 km in total.

(a) Write 36 km/h in m/s. [1] (b) Find the acceleration. [1] (c) Find the time taken to stop. [1] (d) Find t. [3] (e) Find the total time for the journey. [1]

Answers

1. (a) Up from 5 to the line and across: 11 pounds [1] (b) The line goes through the origin, so scale: 22 pounds = 10 kg [1]; 154 ÷ 22 = 7, so 154 pounds = 7 × 10 = 70 kg [1] Examiner insight: scaling is valid only because the line passes through (0, 0); show the scale factor so the method mark can still be given.

2. (a) Value at m = 0: $40 [1] (b) Gradient = (160 − 40) ÷ 12 = 10 [1]; it represents the monthly charge of $10 per month [1] Examiner insight: “explain what it represents” needs the rate in context with units (dollars per month); “the slope of the line” earns nothing for the second mark.

3. (a) 40 min = 2/3 h [1]; speed = 3 ÷ (2/3) = 4.5 km/h [1] (b) 55 − 40 = 15 minutes [1] (c) 3 km in 30 min = 6 km/h [1] Examiner insight: dividing 3 by 40 gives a speed in km per minute; the units asked for are km/h, so convert the time before dividing or the accuracy mark is lost.

4. (a) 30 ÷ 45 = 2/3 h = 40 min, so arrives at the stop at 08 40 [1]; leaves at 08 50 [1]; 20 ÷ 40 = 0.5 h = 30 min, so ends at 09 20 [1] (b) (08 00, 0), (08 40, 30), (08 50, 30), (09 20, 50) with distance in km [1] (c) Total time 08 00 to 09 20 = 80 min = 4/3 h [1]; average speed = 50 ÷ (4/3) = 37.5 km/h [1] Examiner insight: the 10-minute stop counts in the total time; using 70 minutes loses the accuracy mark but can keep the method mark.

5. Ben: distance from A = 18T, where T is hours after 10 00 [1] Cara starts 0.25 h late: distance from A = 36 − 24(T − 0.25) = 42 − 24T [1] 18T = 42 − 24T, so 42T = 42 and T = 1 [1] They meet at 11 00, 18 km from A [1] Examiner insight: reading the crossing point from an accurate graph is also a valid method; whichever you use, both the time and the distance are needed for the final mark.

6. (a) Rise = 50 − 20 = 30 cm in 5 min [1]; rate = 6 cm per minute [1] (b) 30 cm in 6 min = 5 cm per minute [1] (c) Volume per minute = 40 × 25 × 6 = 6000 cm³ [1] = 6 litres per minute [1] Examiner insight: the depth rate and the volume rate are different quantities; give the unit with each answer, since “6” alone is ambiguous between cm/min and litres/min.

7. (a) (16 − 4) ÷ 10 = 1.2 m/s² [1] (b) 16 ÷ 8 = 2 m/s² [1] (c) Trapezium ½ × (4 + 16) × 10 = 100 m and rectangle 30 × 16 = 480 m [1]; triangle ½ × 8 × 16 = 64 m [1]; total = 644 m [1] Examiner insight: the first section starts at 4 m/s, so it is a trapezium; a triangle (80 m) loses the accuracy mark but the other areas still earn credit.

8. (a) Area = V × 90 + ½ × 25 × V + ½ × 35 × V = 120V [1]; 120V = 3000 (using 3 km = 3000 m) [1]; V = 25 [1] (b) 25 × 3.6 = 90 km/h [1] (c) 25 ÷ 25 = 1 m/s² [1] Examiner insight: leaving the distance as 3 instead of 3000 m gives V = 0.025; check that units match before setting area equal to distance.

9. (a) Points plotted correctly [1]; joined with a smooth curve through the origin [1] (b) Tangent drawn touching the curve at (4, 8) [1]; for example, it passes through about (2, 0) and (6, 16), so gradient = 16 ÷ 4 [1]; speed ≈ 4 m/s [1] (c) The curve gets steeper as t increases, so the gradient (speed) increases [1] Examiner insight: the gradient must come from two points on your drawn tangent, read from the grid; a line joining two table values is a chord, not a tangent, so it is not the method the question asks for.

10. (a) Speed at 4 s = 9 ÷ 6 × 4 = 6 m/s [1]; distance = ½ × 4 × 6 = 12 m [1] (b) ½ × 6 × 9 = 27 m and 14 × 9 = 126 m [1]; trapezium ½ × (9 + 3) × 6 = 36 m [1]; total = 189 m [1] (c) 189 ÷ 26 = 7.27 m/s (3 s.f.) [1] (d) (9 − 3) ÷ 6 = 1 m/s² [1] Examiner insight: in (a) the height of the triangle is the speed at 4 s, not 9 m/s; using 9 gives 18 m and scores no accuracy mark.

11. (a) 36 ÷ 3.6 = 10 m/s [1] (b) 10 ÷ 20 = 0.5 m/s² [1] (c) 10 ÷ 0.4 = 25 s [1] (d) Areas: ½ × 20 × 10 = 100 m and ½ × 25 × 10 = 125 m [1]; 100 + 10t + 125 = 1000 [1]; t = 77.5 [1] (e) 20 + 77.5 + 25 = 122.5 s [1] Examiner insight: convert the speed to m/s before finding areas; mixing km/h with seconds makes every later area wrong.

Where marks are usually lost

• Misreading a scale where each square is worth 2, 5 or 10 units.
• Using minutes with km/h, or km with m/s, without converting.
• Leaving out stopped time when finding an average speed.
• Scaling from a graph that does not pass through the origin.
• Giving a gradient with no units or no meaning when asked to interpret it.
• Calling the gradient of a distance–time graph an acceleration.
• (Extended) Measuring a tangent gradient from points on the curve.
• (Extended) Treating a trapezium section of a speed–time graph as a triangle.
• (Extended) Writing a deceleration as a negative value.

Next steps

• Review the explanations in the graphs in practical situations study guide.
• Recap the whole topic with the Algebra and graphs revision notes and the Algebra and graphs study guide.
• More Topic 2 questions: Algebra and graphs practice questions and Algebra and graphs (Extended) practice.
• Take the free Core diagnostic or Extended diagnostic.
• Browse other resources for syllabus 0580 on the Cambridge IGCSE Mathematics hub and use the printable checklist.
• Book a free trial class.

Official syllabus

Cambridge IGCSE Mathematics 0580 syllabus for examination in 2025, 2026 and 2027 (Version 3), Cambridge University Press & Assessment. Subtopic C2.9 / E2.9 Graphs in practical situations.