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1. A rope is 3.5 metres long. A second rope is 240 centimetres long. How much longer is the first rope, in centimetres?[3]
2. A bag of flour holds 2.5 kg. 1750 g are used. How many grams are left?[3]
3. Three more than twice a number is 19. What is the number?[3]
4. Ravi cycles 12 km at 24 km per hour, then walks 6 km at 4 km per hour. How many minutes does the whole journey take?[4]
5. One tap fills a tank in 6 hours and another fills it in 3 hours. With both running, how long does the tank take to fill?[4]
A 1 hourB 2 hoursC 4.5 hoursD 9 hoursE 3 hours6. A mother is 32 and her child is 8. In how many years will the mother be exactly three times as old as the child?[4]
7. One pipe fills a pool in 12 hours and another fills it in 4 hours. With both running, how many hours does the pool take to fill?[4]
8. A train covers 150 km at a steady 60 km per hour. How many minutes does the journey take?[4]
9. A class of 12 scored an average of 8. Another class of 18 scored an average of 13. What is the average for all 30 students together?[5]
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1. C — 110 KA-0029 Unit conversion
A I subtracted correctly in metres but then gave the answer in metres when centimetres were asked for.B I converted 3.5 metres to 35 centimetres instead of 350.D I subtracted without converting at all, taking 3.5 away from 240.E I added the two lengths instead of finding the difference between them.2. C — 750 KA-0113 Unit conversion
A I worked in kilograms and gave the answer in kilograms when grams were asked for.B I converted 2.5 kg to 250 g rather than 2500 g.D I subtracted 1750 from 3000, mis-converting 2.5 kg as three thousand grams.E I subtracted without converting at all, taking 2.5 away from 1750.3. A — 8 KA-0144 Translating a sentence into an equation
B I subtracted 8 from 19 rather than working the two steps backwards.C I subtracted the 3 from 19 and gave that without halving it.D I added the 3 to 19 instead of subtracting it.E I doubled 19 and added 3, applying the machine forwards instead of undoing it.4. D — 120 KA-0036 Rate, time, distance
A I worked out the cycling leg and gave that as the answer, forgetting the walk entirely.B I worked out the walking leg and gave that as the answer, forgetting the cycling entirely.C I wrote half an hour as 15 minutes instead of 30 and added it to the 90 minute walk.E I rounded the cycling leg up to a whole hour instead of keeping it as half an hour.5. B — 2 hours KA-0044 Combined work rates
A I subtracted the two times from each other rather than adding the rates.C I averaged the two times, which would only be right if the taps took turns instead of running together.D I added the two times together, which makes the tank slower with two taps than with one.E I used the faster tap's time alone and ignored the contribution of the slower one.6. B — 4 KA-0111 Age problems
A I aged only the child and left the mother's age unchanged.C I looked for when the mother is four times as old rather than three times.D I used the age difference of 24 and halved it, without checking the ratio it gives.E I gave the difference between their ages, which never changes, instead of a number of years.7. A — 3 KA-0116 Combined work rates
B I gave the faster pipe's time on its own, forgetting the slower one helps as well.C I halved the slower pipe's time rather than adding the two rates.D I averaged the two times, which would only be right if the pipes took turns.E I added the two times, which makes two pipes slower than one - an impossible answer.8. C — 150 KA-0117 Rate, time, distance
A I divided 150 by 60 and read the answer as minutes rather than hours.B I used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.D I converted 2.5 hours as two hours and fifty minutes.E I multiplied the distance by 60 instead of dividing, then converted.9. B — 11 KA-0112 Mixtures and weighted averages
A I averaged the two averages, ignoring that the classes are different sizes.C I weighted the averages but used the wrong class size against each one.D I leaned towards the larger class's average without computing the totals.E I added the two averages together instead of combining them.