P6 Mathematics Practice Paper: Fractions, Percentages, Speed And Area

P6 Mathematics Practice Paper: Fractions, Percentages, Speed and Area

2026-11-05

P6 Mathematics – 12 questions – 100 marks – 50 minutes

P6 Mathematics practice paper: 12 questions, 100 marks, 50 minutes on fractions, percentages, speed, area and perimeter, with marking points and PDFs.

Download　Question paper PDF　|　Answer key PDF

Paper details　P6 Mathematics practice paper with 12 questions on fractions, percentages, speed, area and perimeter, 100 marks in 50 minutes, with marking points and printable PDFs.

Section A: Fractions and Percentages

Answer all questions. Give answers in simplest form and show your working.

#	Question	Answer and marking notes
1	Mother bought 3 1/4 kg of sugar and used 5/8 kg of it to make rice cakes. (a) How much sugar is left? Give the answer as a fraction in its simplest form. (b) If the remaining sugar is packed into small bags of 1/8 kg each, how many bags can be filled?	Answer: (a) 3 1/4 – 5/8 = 26/8 – 5/8 = 21/8 = 2 5/8 kg. (b) 21/8 divided by 1/8 = 21 bags. Marking: 2 marks for a common denominator, 3 marks for the subtraction and the mixed number, 3 marks for the division; no marks if 3 1/4 is misread as 3.14.
2	Class 6A has 40 pupils and 3/5 of them are girls. (a) How many girls are there? (b) One quarter of the girls wear glasses. How many girls wear glasses? (c) What percentage of the class are boys?	Answer: (a) 40 x 3/5 = 24 girls. (b) 24 x 1/4 = 6 girls. (c) Boys 40 – 24 = 16; 16 / 40 x 100% = 40%. Marking: 2 marks for each part; deduct 1 mark where the working is missing.
3	A toy has a marked price of 250 dollars and is now sold at 80% of the marked price. (a) Find the selling price. (b) How much less than the marked price is paid? (c) What is the discount percentage?	Answer: (a) 250 x 0.8 = 200 dollars. (b) 250 – 200 = 50 dollars. (c) 50 / 250 x 100% = 20%. Marking: 80% of the marked price is 0.8, so no marks in (a) and (b) for using 0.2; 2 marks in (c) with the marked price as the denominator.
4	A book cost 80 dollars last year and its price is increased by 15% this year. (a) Find this year price. (b) Find the increase in dollars. (c) If the price rises by a further 10% next year, taking this year price as the base, find next year price.	Answer: (a) 80 x 1.15 = 92 dollars. (b) 92 – 80 = 12 dollars. (c) 92 x 1.10 = 101.2 dollars. Marking: (a) 3 marks, (b) 2 marks, (c) 3 marks; only 1 mark in (c) if 80 is used as the base.

Section B: Speed and Area of Shapes

Answer all questions. Write down the formula used and state the units.

#	Question	Answer and marking notes
5	A bus travels 27 km in 45 minutes. (a) Find its average speed in km/h. (b) At the same speed, how many minutes does the bus take to travel 45 km? (c) At the same speed, how far does it travel in 2 hours?	Answer: (a) 45 minutes is 0.75 hour, so 27 / 0.75 = 36 km/h. (b) 45 / 36 x 60 = 75 minutes, that is 1 hour 15 minutes. (c) 36 x 2 = 72 km. Marking: 3 marks for the time conversion, 2 marks each for (a), (b) and (c); deduct 1 mark for wrong units.
6	Ming walks 3.5 km to school at a speed of 5 km/h. (a) How many minutes does the journey take? (b) He leaves home at 07:35. At what time does he arrive at school? (c) He walks home along the same road at 4 km/h. How many minutes does the return journey take?	Answer: (a) 3.5 / 5 x 60 = 42 minutes. (b) 07:35 plus 42 minutes is 08:17. (c) 3.5 / 4 x 60 = 52.5 minutes, that is 52 minutes 30 seconds. Marking: 3 marks for each part; an answer of 52 minutes in (c) loses 1 mark.
7	A rectangle is 12 cm long and 8 cm wide. (a) Find its perimeter. (b) Find its area. (c) A square has sides of 9 cm. By how many square centimetres is its area less than the area of the rectangle?	Answer: (a) (12 + 8) x 2 = 40 cm. (b) 12 x 8 = 96 square centimetres. (c) 9 x 9 = 81, and 96 – 81 = 15 square centimetres. Marking: 3 marks each for the perimeter and the area, 3 marks for the comparison; deduct 1 mark for each missing unit, up to 2 marks.
8	A triangle has a base of 15 cm and a height of 8 cm. (a) Find its area. (b) A parallelogram has the same base and the same height. Find its area. (c) How many times the area of the triangle is the area of the parallelogram?	Answer: (a) 15 x 8 / 2 = 60 square centimetres. (b) 15 x 8 = 120 square centimetres. (c) 120 / 60 = 2 times. Marking: only 1 mark in (a) if the division by 2 is missing; 3 marks in (b); 3 marks in (c).

Section C: Circles, Volume and Data Handling

Answer all questions. Take pi as 3.14.

#	Question	Answer and marking notes
9	A circular flower bed has a diameter of 20 m. Take pi as 3.14. (a) Find the circumference of the flower bed. (b) The bed is rebuilt as a semicircle with the same diameter. Find the perimeter of the semicircle, including the straight edge.	Answer: (a) 3.14 x 20 = 62.8 m. (b) 62.8 / 2 + 20 = 31.4 + 20 = 51.4 m. Marking: 4 marks in (a); 2 marks for the arc and 2 marks for adding the diameter in (b), so only 2 marks if the straight edge is omitted.
10	A rectangular water tank is 20 cm long, 15 cm wide and 10 cm high. (a) Find its capacity in cubic centimetres. (b) Express the capacity in litres. (c) The tank already contains 1.8 L of water. Find the depth of the water.	Answer: (a) 20 x 15 x 10 = 3000 cubic centimetres. (b) 3000 / 1000 = 3 litres. (c) 1.8 L is 1800 cubic centimetres, and 1800 / (20 x 15) = 1800 / 300 = 6 cm. Marking: 3 marks in (a), 2 marks in (b), 3 marks in (c); no marks in (c) if litres are not converted.
11	Ken scores 78, 85, 90 and 79 in four mathematics tests. (a) Find his mean score for the four tests. (b) What must he score in the fifth test so that the mean of the five tests is 85? (c) If he scores only 80 in the fifth test, find the mean of the five tests.	Answer: (a) (78 + 85 + 90 + 79) / 4 = 332 / 4 = 83. (b) 85 x 5 = 425 and 425 – 332 = 93. (c) (332 + 80) / 5 = 412 / 5 = 82.4. Marking: 2 marks in (a), 3 marks in (b), 3 marks in (c); no marks in (b) for simply doing 85 – 83.
12	To make orange drink, concentrated orange juice is mixed with water in the ratio 1 : 4. (a) How much concentrated juice is needed to make 600 mL of drink? (b) How much water is needed? (c) How much concentrated juice is there in a 250 mL cup of the drink?	Answer: (a) 600 / (1 + 4) = 120, so 120 mL of concentrated juice. (b) 120 x 4 = 480 mL of water. (c) 250 / 5 = 50 mL. Marking: 3 marks in (a), 2 marks in (b), 3 marks in (c); no marks in (a) and (b) if 1 : 4 is read as four parts of juice.

Find a tutor — free Tutor Registration →

A TutorZone practice paper; original questions and passages, not publisher material.