OCR GCSE Mathematics: Units, compound measures, maps, bearings, perimeter, circumference and arc length (J560) – 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 follow sections 10.01 and 10.02 of the OCR GCSE (9-1) Mathematics J560 specification, Version 2.1 (August 2026). Both tiers are examined on this content, and the specification marks none of it as Higher tier only. The specification says any content can appear on calculator or non-calculator papers, so practise each method by hand as well. Learn the methods first from the study guide and the revision notes. The OCR GCSE Mathematics hub, the checklist and the 10-minute diagnostics are linked for planning. For bearings and scale questions you need a ruler and a protractor.

Questions

1. Convert: (a) 2.6 m² to cm² [1]; (b) 0.8 m³ to litres [1]; (c) 3 hours 24 minutes to hours as a decimal [1].

2. The exchange rate is £1 = 1.30 US dollars. A jacket costs 84.50 US dollars in New York and £62 in Leeds. Which price is lower, and by how much in pounds? [3]

3.

(a) Priya earns £11.20 per hour. She works for 6 hours 45 minutes. Find her pay. [2] (b) A 250 g jar of coffee costs £3.40 and a 400 g jar costs £5.20. Which jar is the better value? Show your working. [3]

4. A train travels 135 km in 1 hour 30 minutes at a steady speed.

(a) Find its speed in km/h. [2] (b) Write this speed in m/s. [2]

5. A solid metal cube has edges of 5 cm and a mass of 1 kg.

(a) Find its density in g/cm³. [2] (b) Write the density in kg/m³. [1] (c) A force of 750 N acts on an area of 0.3 m². Find the pressure in N/m². [2]

6.

(a) A rope is x metres long. It is cut into pieces of 20 cm. Write an expression for the number of pieces. [2] (b) Water flows from a tap at a litres per minute. Write this rate in cm³ per second, as a single fraction. [2]

7. A walking map has a scale of 1 : 30 000.

(a) Two huts are 6.4 cm apart on the map. Find the real distance in km. [2] (b) A real path is 4.5 km long. Find its length on the map in cm. [2] (c) How many metres does 1 cm on the map represent? [1]

8. The bearing of port B from port A is 138°. Port C is such that the bearing of C from B is 228°.

(a) Find the bearing of A from B. [2] (b) Show that angle ABC is 90°. [2] (c) AB = 10 km and BC = 24 km. Find the distance AC. [2]

9. An L-shaped field is drawn with right angles only. Going round from the bottom left corner, the sides in order are 11 m, 3 m, 6 m, b, c and 8 m. The 11 m side is the full width and the 8 m side is the full height. Sketch the field, then find b and c and the perimeter. [3]

10.

(a) A circle has radius 6.5 cm. Give its circumference as a multiple of π and as a decimal to 3 significant figures. [2] (b) A wheel has circumference 2.2 m. How many complete turns must it make to travel at least 1 km? [2] (c) A sector has radius 12 cm and angle 75°. Find its arc length in terms of π. [2] (d) Find the perimeter of this sector to 3 significant figures. [1]

11. A garden bed is a rectangle 8 m by 5 m with a semicircle added on one of the 5 m sides. Edging is placed round the whole outside of the bed, except for a 1.2 m gap for a gate. Edging costs £14.50 per metre. Find the cost of the edging, to the nearest pound. [7]

12. A circular running track has radius 35 m. An athlete runs 3 laps in 9 minutes at a steady speed.

(a) Find the distance run, to 3 significant figures. [3] (b) Find the speed in m/min. [1] (c) Find the speed in km/h, to 3 significant figures. [2]

Answers

1. (a) 1 m² = 10 000 cm², so 2.6 × 10 000 = 26 000 cm² [1]. (b) 1 m³ = 1000 litres, so 800 litres [1]. (c) 24 ÷ 60 = 0.4, so 3.4 hours [1]. [3] Examiner insight: Answers to conversions need the unit, and a clear check is whether the number is bigger when the unit gets smaller.

2. Convert the dollar price to pounds: 84.50 ÷ 1.30 = £65 [1]. Compare £65 with £62 [1]. The Leeds jacket is cheaper by £3 [1]. [3] Examiner insight: Compare prices in the same currency and say which is cheaper in a sentence, not just a number.

3. (a) 6 h 45 min = 6.75 h [1]. 11.20 × 6.75 = £75.60 [1]. (b) 250 g jar: 340 ÷ 250 = 1.36 p per gram [1]. 400 g jar: 520 ÷ 400 = 1.30 p per gram [1]. The 400 g jar is better value, since it costs less per gram [1]. [5] Examiner insight: Compare costs for the same amount, and finish with a statement naming the better buy.

4. (a) 1 h 30 min = 1.5 h [1]. 135 ÷ 1.5 = 90 km/h [1]. (b) 90 km = 90 000 m [1]. 90 000 ÷ 3600 = 25 m/s [1]. [4] Examiner insight: Show the conversion of both the top and the bottom of km/h, so the working is clear even if an arithmetic slip happens.

5. (a) Volume = 5 × 5 × 5 = 125 cm³ [1]. Mass = 1000 g, so density = 1000 ÷ 125 = 8 g/cm³ [1]. (b) 8 × 1000 = 8000 kg/m³ [1]. (c) Pressure = force ÷ area = 750 ÷ 0.3 [1] = 2500 N/m² [1]. [5] Examiner insight: Change the mass to grams before dividing when the answer is wanted in g/cm³.

6. (a) x metres = 100x cm [1]. Number of pieces = 100x ÷ 20 = 5x [1]. (b) a litres = 1000a cm³ and 1 minute = 60 seconds [1]. Rate = 1000a/60 = 50a/3 cm³ per second [1]. [4] Examiner insight: Write the unit conversion next to the letter, so each factor you use is visible.

7. (a) 6.4 × 30 000 = 192 000 cm [1] = 1.92 km [1]. (b) 4.5 km = 450 000 cm [1]. 450 000 ÷ 30 000 = 15 cm [1]. (c) 30 000 cm = 300 m [1]. [5] Examiner insight: Convert cm to km at the end, using 100 000 cm = 1 km, and state the unit.

8. (a) Back bearing = 138° + 180° [1] = 318° [1]. (b) At B, the bearing of A is 318° and the bearing of C is 228° [1]. The angle between them is 318° − 228° = 90°, so angle ABC is 90° [1]. (c) Pythagoras: AC² = 10² + 24² = 676 [1]. AC = 26 km [1]. [6] Examiner insight: On a “show that” question, state both bearings at B and the subtraction, not only the final angle.

9. The vertical sides on the right total the full height of 8 m, so b = 8 − 3 = 5 m [1]. The horizontal sides along the top total the full width of 11 m, so c = 11 − 6 = 5 m [1]. Perimeter = 11 + 3 + 6 + 5 + 5 + 8 = 38 m [1]. [3] Examiner insight: Mark every missing length on a sketch and then add all six sides. Counting from the sketch avoids missing a side.

10. (a) C = 2π × 6.5 = 13π cm [1] = 40.8 cm [1]. (b) 1000 ÷ 2.2 = 454.5… [1]. A whole number of turns is needed, so 455 turns [1]. (c) Arc = 75/360 × 2π × 12 [1] = 5/24 × 24π = 5π cm [1]. (d) Perimeter = 5π + 24 = 39.7 cm [1]. [7] Examiner insight: When the question asks for a number of complete turns, a rounded-down answer would not reach 1 km, so think about what the context needs.

11. The semicircle has diameter 5 m, so radius 2.5 m [1]. Arc = π × 2.5 = 7.854 m [1]. The three straight sides are 8 + 8 + 5 = 21 m [1]. The 5 m side where the semicircle is attached is inside the outline, so it is not edged [1]. Outside perimeter = 21 + 7.854 = 28.854 m [1]. Edging needed = 28.854 − 1.2 = 27.654 m [1]. Cost = 27.654 × 14.50 = 400.98, so £401 [1]. [7] Examiner insight: Keep the full unrounded value until the last step. Rounding the length early can change the final pound figure.

12. (a) Circumference = 2π × 35 = 70π m [1]. Three laps: 3 × 70π = 210π [1] = 660 m [1]. (b) 210π ÷ 9 = 73.3 m/min [1]. (c) Speed = 210π ÷ 9 × 60 = 4398 m/h [1] = 4.40 km/h [1]. [6] Examiner insight: Take the unrounded distance into the speed calculation, and convert m/min to km/h by two separate, stated steps.

Where marks are usually lost

• Using 100 or 1000 for an area or volume conversion.
• Converting time as a decimal without dividing minutes by 60.
• Using the exchange rate the wrong way round, so the answer is not sensible.
• Failing to compare unit prices for the same quantity.
• Not converting the top and bottom of a compound unit.
• Measuring a bearing from the wrong point, or forgetting the three figures.
• Using the diameter in 2πr.
• Giving the arc alone as the perimeter of a sector, or counting an inside edge.
• Rounding too early, or giving a final answer with no units.

Next steps

• Review the revision notes and the study guide.
• Go to the OCR GCSE Mathematics hub and the checklist.
• Try all free 10-minute diagnostics at /diagnostics/.
• Book a free trial class: /trial/.

Official syllabus

OCR GCSE (9-1) Mathematics J560 specification, Version 2.1 (August 2026), sections 10.01 and 10.02, published by OCR.