This is an original CREST Champs practice paper modelled on the CMO's published format. It is not a CMO paper and is not affiliated with or endorsed by the organiser. Modelled on the format of the CREST Mathematics Olympiad (CMO). Print this page for exam-style practice — the answer key stays on screen.

Practical Mathematics

25 questions × 1 mark

Q1. In the number 47 743, what is the difference between the values of the two digits 7?

A0B630C6 300D7 700

Q2. Look at the pattern: 2, 3, 5, 8, 12, ... What is the next number?

A14B16C17D18

Q3. What is the smallest whole number that gives 5 000 when it is rounded to the nearest hundred?

A4 500B4 950C4 999D5 049

Q4. A baker in Paris made 425 croissants. She sold 178 in the morning and 159 in the afternoon. How many croissants were left at the end of the day?

A78B88C98D247

Q5. A film show in Sydney starts at 4:45 p.m. and ends at 6:20 p.m. The show included a 15-minute interval. For how long did the film itself play?

A1 h 5 minB1 h 20 minC1 h 35 minD1 h 50 min

Q6. In Singapore, Mei buys a toy robot for 8.75 Singapore dollars and a puzzle for $6.50. She pays with a $20 note. How much change should she get?

A$4.75B$5.25C$11.25D$15.25

Q7. In Istanbul, one ferry carries 145 passengers per trip and makes 6 trips a day. A second ferry carries 210 passengers per trip and makes 4 trips a day. How many more passengers does the first ferry carry in a day than the second?

A30B65C870D1 710

Q8. Ravi ate 2/8 of a chocolate bar and his sister ate 1/4 of the same bar. What fraction of the bar did they eat altogether?

A3/12B3/8C1/2D3/4

Q9. At which of these times do the two hands of a clock make a straight angle?

A3 o'clockB6 o'clockC9 o'clockD12 o'clock

Q10. A recipe needs 1 kg 250 g of flour. Ana has a full 2 kg bag. After she makes the recipe once, how many grams of flour are left in the bag?

A250 gB750 gC850 gD1 250 g

Q11. A farmer in Kenya collects 178 eggs. She packs them into boxes that each hold exactly 6 eggs. After she fills as many boxes as possible, how many eggs are left over?

A2B4C5D29

Q12. Sara in Mumbai has 36 red beads and 48 blue beads. She makes identical bracelets, using every bead, so that each bracelet has the same number of red beads and the same number of blue beads. What is the greatest number of bracelets she can make?

A4B6C12D16

Q13. Which of these numbers is a multiple of 6 but NOT a multiple of 4?

A24B30C32D36

Q14. A rope is 4.5 m long. Tom cuts off a piece 1.75 m long, and then another piece 0.8 m long. What length of rope is left?

A1.05 mB1.95 mC2.05 mD2.75 m

Q15. Which is greater: 1/3 of 60 or 1/4 of 84?

A1/3 of 60 — it is greater by 1B1/4 of 84 — it is greater by 1CThey are equalD1/4 of 84 — it is greater by 4

Q16. A rectangular garden is 12 m long and 8 m wide. A fence is built all the way around it, except for a gate 2 m wide. What length of fencing is needed?

A36 mB38 mC40 mD94 m

Q17. A train leaves Cape Town at 09:35 and arrives in George at 14:10. Along the way it stands still at stations for a total of 20 minutes. For how long is the train actually moving?

A4 h 15 minB4 h 35 minC4 h 55 minD5 h 25 min

Q18. A jug holds 2 litres of juice. Riya fills 6 glasses from it, each holding 250 mL. How much juice is left in the jug?

A250 mLB500 mLC750 mLD1 500 mL

Q19. In London, a notebook costs £2.35 and a pen costs £1.20. Sam buys 3 notebooks and 2 pens and pays with a £10 note. How much change should he get?

A£0.45B£0.55C£2.95D£9.45

Q20. In a survey of 96 children, 1/4 of them chose football, 30 chose cricket, 18 chose tennis, and the rest chose swimming. How many children chose swimming?

A22B24C48D72

Q21. Which of these capital letters has exactly 2 lines of symmetry?

AABECHDT

Q22. When a number is doubled and then 36 is added, the result is 94. What is the number?

A11B29C58D65

Q23. 438 students and 27 adults are going on a school trip. Each bus can seat exactly 50 people. What is the smallest number of buses needed so that everyone gets a seat?

A8B9C10D12

Q24. Two rectangles each have an area of 36 cm². Rectangle P is 9 cm long, and rectangle Q is 6 cm long. How much longer is the perimeter of P than the perimeter of Q?

A0 cmB2 cmC3 cmD26 cm

Q25. In a pattern, each number is double the previous number plus 1. The 4th number in the pattern is 47. What is the 2nd number?

A5B11C23D95

Achiever's Section

10 questions × 2 marks

Q26. Anya, who lives in Toronto, had 60 Canadian dollars. She spent 1/4 of her money on a book, and then spent 1/3 of the money she had LEFT on lunch. How much money does she have now?

A$25B$30C$35D$45

Q27. In a Vienna bakery, Oven A bakes 24 buns every 15 minutes, and Oven B bakes 40 buns every 30 minutes. In 1 and a half hours, how many more buns does Oven A bake than Oven B?

A8B24C120D144

Q28. A straight path in an Amsterdam park is 180 m long. Lampposts are placed every 15 m along BOTH sides of the path, with a lamppost at each end of each side. How many lampposts are needed altogether?

A13B24C25D26

Q29. Marco's book has 208 pages. He starts reading on Monday 1 June. On weekdays (Monday to Friday) he reads 16 pages a day, but on Saturdays and Sundays he reads 24 pages a day. On which date does he finish the book?

A11 JuneB12 JuneC13 JuneD14 June

Q30. Two pizzas are each cut into 8 equal slices, making 16 slices in total. Leo eats 3 slices of the first pizza, and Zara eats half of the second pizza. What fraction of ALL the pizza is left?

A7/16B1/2C9/16D5/8

Q31. A rectangle has a perimeter of 40 cm. Its length is 4 cm more than its width. What is its area?

A64 cm²B84 cm²C96 cm²D100 cm²

Q32. At a post office in Berlin, three parcels A, B and C together weigh 27 kg. Parcel A weighs twice as much as parcel B, and parcel C weighs 3 kg more than parcel B. How much does the heaviest parcel weigh?

A6 kgB9 kgC12 kgD15 kg

Q33. At a market in Nairobi, Amara buys 6 mangoes, all at the same price, and one basket costing 60 Kenyan shillings. She pays with a 500-shilling note and receives 140 shillings in change. What is the price of one mango?

A40 shillingsB50 shillingsC60 shillingsD300 shillings

Q34. The sum of two numbers is 36, and the larger number is three times the smaller number. What is the difference between the two numbers?

A9B12C18D27

Q35. In Auckland, a ferry departs every 25 minutes, and the first ferry of the day leaves at 08:00. Nina arrives at the pier at 09:50. How long must she wait for the next ferry?

A5 minutesB10 minutesC15 minutesD25 minutes
Answer key & worked solutions — open after attempting
Q1 — C · One 7 is in the thousands place (value 7 000) and the other is in the hundreds place (value 700). Their difference is 7 000 - 700 = 6 300. (7 700 is the trap answer if you add the two values instead of subtracting, and 0 is the trap if you think equal digits must have equal values.)
Q2 — C · The gaps between the numbers grow by 1 each time: +1, +2, +3, +4. So the next gap is +5, and 12 + 5 = 17. (16 is the trap answer if you repeat the last gap of +4.)
Q3 — B · Numbers from 4 950 up to 5 049 all round to 5 000 to the nearest hundred, because 4 950 rounds up and 5 049 rounds down. The smallest of these is 4 950. (4 500 is the trap for rounding to the nearest thousand, and 5 049 is the largest such number, not the smallest.)
Q4 — B · First subtract the morning sales: 425 - 178 = 247. Then subtract the afternoon sales: 247 - 159 = 88 croissants left. (247 is the trap answer if you stop after the first step.)
Q5 — B · From 4:45 p.m. to 6:20 p.m. is 1 hour 35 minutes. Taking away the 15-minute interval leaves 1 h 35 min - 15 min = 1 h 20 min of film. (1 h 35 min is the trap if you forget the interval; 1 h 50 min is the trap if you add it instead.)
Q6 — A · The total cost is 8.75 + 6.50 = $15.25. The change is 20.00 - 15.25 = $4.75. ($11.25 is the trap if you subtract only the robot's price, and $15.25 is the total spent, not the change.)
Q7 — A · First ferry: 145 x 6 = 870 passengers. Second ferry: 210 x 4 = 840 passengers. The first carries 870 - 840 = 30 more. (65 is the trap answer 210 - 145, and 1 710 is the trap if you add the two totals.)
Q8 — C · 2/8 is equivalent to 1/4, so together they ate 1/4 + 1/4 = 2/4 = 1/2 of the bar. (3/12 is the trap if you add numerators and denominators separately, and 3/8 is the trap if you treat 1/4 as 1/8.)
Q9 — B · At 6 o'clock the hour hand points to 6 and the minute hand points to 12, so the hands lie in a straight line — a straight angle (180 degrees). At 3 o'clock and 9 o'clock they make right angles, and at 12 o'clock the hands lie together (no angle between them).
Q10 — B · Convert both amounts to grams: 2 kg = 2 000 g and 1 kg 250 g = 1 250 g. Then 2 000 - 1 250 = 750 g left. (850 g is the trap if you regroup wrongly, and 1 250 g is the amount used, not the amount left.)
Q11 — B · 178 divided by 6 = 29 remainder 4, because 6 x 29 = 174 and 178 - 174 = 4. So 4 eggs are left over. (29 is the number of full boxes, not the leftover eggs.)
Q12 — C · The number of bracelets must divide both 36 and 48. The common factors of 36 and 48 are 1, 2, 3, 4, 6 and 12, so the greatest number of bracelets is 12 (each with 3 red and 4 blue beads). (6 is a common factor but not the greatest; 16 divides 48 but not 36.)
Q13 — B · 30 = 6 x 5, but 30 divided by 4 = 7 remainder 2, so 30 is a multiple of 6 and not of 4. Both 24 and 36 are multiples of 6 AND of 4, and 32 is a multiple of 4 but not of 6.
Q14 — B · First cut: 4.5 - 1.75 = 2.75 m. Second cut: 2.75 - 0.8 = 1.95 m left. (2.75 m is the trap if you stop after the first cut, and 2.05 m is the trap if you line up the decimal points wrongly when subtracting 0.8.)
Q15 — B · 1/3 of 60 = 60 divided by 3 = 20, and 1/4 of 84 = 84 divided by 4 = 21. So 1/4 of 84 is greater, by 21 - 20 = 1. (It is tempting to think 1/3 must beat 1/4 because 1/3 is the bigger fraction, but the wholes are different.)
Q16 — B · The full perimeter is 2 x (12 + 8) = 40 m. The 2 m gate needs no fencing, so 40 - 2 = 38 m of fencing is needed. (40 m is the trap if you forget the gate, and 94 comes from muddling the area, 96 m², with the gate.)
Q17 — A · From 09:35 to 14:10 is 4 h 35 min (09:35 to 13:35 is 4 h, then 35 more minutes to 14:10). Subtracting the 20 minutes of stops gives 4 h 35 min - 20 min = 4 h 15 min of moving time. (4 h 55 min is the trap if you add the stops instead of subtracting.)
Q18 — B · 2 litres = 2 000 mL. The six glasses take 6 x 250 = 1 500 mL, so 2 000 - 1 500 = 500 mL is left. (1 500 mL is the amount poured out, not the amount left.)
Q19 — B · Notebooks: 3 x £2.35 = £7.05. Pens: 2 x £1.20 = £2.40. Total: £7.05 + £2.40 = £9.45. Change: £10.00 - £9.45 = £0.55. (£2.95 is the money left after the notebooks alone, and £9.45 is the total spent, not the change.)
Q20 — B · 1/4 of 96 = 24 chose football. So 24 + 30 + 18 = 72 children chose football, cricket or tennis, leaving 96 - 72 = 24 for swimming. (72 is the trap if you stop at the subtotal; it is a coincidence that swimming matches football's 24 — the check 24 + 30 + 18 + 24 = 96 confirms it.)
Q21 — C · H has a vertical line of symmetry and a horizontal one — exactly 2. A and T have only a vertical line each, and E has only a horizontal line.
Q22 — B · Work backwards from 94. Undo the adding: 94 - 36 = 58. Undo the doubling: 58 divided by 2 = 29. Check forwards: 29 x 2 = 58, and 58 + 36 = 94. (58 is the trap if you forget to halve, 65 comes from adding 36 before halving, and 11 comes from halving before subtracting.)
Q23 — C · Altogether 438 + 27 = 465 people are travelling. 465 divided by 50 = 9 remainder 15, so 9 buses seat only 450 people and a 10th bus is needed for the remaining 15. (9 is the trap if you count only the students, since 438 people fit in 9 buses, or if you ignore the remainder.)
Q24 — B · P's width is 36 divided by 9 = 4 cm, so its perimeter is 2 x (9 + 4) = 26 cm. Q's width is 36 divided by 6 = 6 cm, so its perimeter is 2 x (6 + 6) = 24 cm. The difference is 26 - 24 = 2 cm. (0 cm is the trap answer — equal areas do NOT mean equal perimeters; 26 cm is P's whole perimeter.)
Q25 — B · Work backwards, undoing 'double and add 1' each time: 3rd number = (47 - 1) divided by 2 = 23; 2nd number = (23 - 1) divided by 2 = 11. Check forwards: 11 doubles-plus-1 to 23, and 23 doubles-plus-1 to 47. (23 is the trap if you stop one step early, 5 if you go one step too far, and 95 if you go forwards instead of backwards.)
Q26 — B · 1/4 of $60 is $15, so after the book she has 60 - 15 = $45. Lunch costs 1/3 of $45 = $15, leaving 45 - 15 = $30. ($25 is the trap if you take 1/3 of the original $60 for lunch, and $45 is the trap if you stop after the book.)
Q27 — B · 1 and a half hours = 90 minutes. Oven A: 90 divided by 15 = 6 batches, so 6 x 24 = 144 buns. Oven B: 90 divided by 30 = 3 batches, so 3 x 40 = 120 buns. Difference: 144 - 120 = 24 buns. (8 is the trap if you compare a single half-hour only — 48 against 40 — and 144 and 120 are the separate totals.)
Q28 — D · Along one side there are 180 divided by 15 = 12 gaps, and 12 gaps need 12 + 1 = 13 posts (one more post than gaps, because both ends have a post). Both sides together need 2 x 13 = 26 posts. (24 is the trap if you forget the extra end post on each side, and 13 is the trap if you count only one side.)
Q29 — B · Week 1: Monday 1st to Friday 5th is 5 x 16 = 80 pages; Saturday 6th and Sunday 7th add 2 x 24 = 48 pages, so 128 pages are done by Sunday 7 June. That leaves 208 - 128 = 80 pages. The next five weekdays give 16 pages each: 80 divided by 16 = 5 days, so he reads Monday 8th to Friday 12th and finishes on 12 June. (13 June is the trap if you assume 16 pages every day, since 208 divided by 16 = 13 days.)
Q30 — C · Zara's half of the second pizza is 4 slices, so together they eat 3 + 4 = 7 of the 16 slices. That leaves 16 - 7 = 9 slices, which is 9/16 of all the pizza. (7/16 is the fraction EATEN, and 1/2 is the trap if you think one whole pizza's worth must be gone.)
Q31 — C · Half the perimeter is length + width = 20 cm. Two numbers that add to 20 and differ by 4 are 12 and 8, so the rectangle is 12 cm by 8 cm. Check: 2 x (12 + 8) = 40 cm. Area = 12 x 8 = 96 cm². (100 cm² is the trap if you ignore the 4 cm difference and use a 10 x 10 square, and 84 cm² comes from wrongly splitting 20 into 14 and 6.)
Q32 — C · In terms of B's weight, the total is B + 2 x B + (B + 3) = 4 x B + 3 = 27 kg, so 4 x B = 24 and B = 6 kg. Then A = 12 kg and C = 9 kg. Check: 12 + 6 + 9 = 27 kg. The heaviest is parcel A at 12 kg. (6 kg is B's weight and 9 kg is C's — reading the question as asking for B or C is the trap.)
Q33 — B · Work backwards from the change: she spent 500 - 140 = 360 shillings. Take away the basket: 360 - 60 = 300 shillings for the mangoes. Each mango costs 300 divided by 6 = 50 shillings. Check: 6 x 50 + 60 = 360, and 500 - 360 = 140. (60 shillings is the trap if you forget the basket, since 360 divided by 6 = 60, and 300 is the cost of all six mangoes.)
Q34 — C · If the smaller number is one part, the larger is three parts, so 36 is four equal parts and each part is 36 divided by 4 = 9. The numbers are 9 and 27. Check: 9 + 27 = 36 and 27 = 3 x 9. Their difference is 27 - 9 = 18. (9 and 27 are the numbers themselves — the traps if you stop before subtracting — and 12 is the trap answer 36 divided by 3.)
Q35 — C · The departures run 08:00, 08:25, 08:50, 09:15, 09:40, 10:05, ... At 09:50 the most recent ferry left at 09:40, so the next one leaves at 10:05, and Nina waits 10:05 - 09:50 = 15 minutes. (10 minutes is the trap — that is how long AGO the last ferry left — and 25 minutes is simply the gap between ferries.)