Worksheet generator

1.B — 3 centsKA-0010Money and change

• AI found the smallest amount that cannot be made rather than the largest one.
• CI did not notice that 7 is 2 plus 5, so I marked it as impossible without testing it.
• DI only tried using coins of one kind at a time and never mixed the two denominations.
• EI assumed odd amounts are impossible because one of the coins is even.

2.E — 60KA-0026Percentages and simple discounts

• AI worked out the size of the discount and gave that as the new price instead of subtracting it.
• BI treated a quarter off as half off and took the price down to 40.
• CI applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.
• DI subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.

3.B — 28KA-0035Handshakes and pairs

• AI doubled the number of people, as if each person made two handshakes in total.
• CI let each person shake hands with all eight people including themselves before halving.
• DI multiplied 8 by 7 and forgot that each handshake was counted from both sides.
• EI multiplied 8 by 8, counting every ordered pair including a person with themselves.

4.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing

• AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
• BI added the two intervals together rather than looking for a time that is a multiple of both.
• DI found a common multiple but not the least one, landing on a later coincidence.
• EI multiplied the two intervals together instead of finding their least common multiple.

5.C — 4KA-0161Remainders and modular cycles

• AI assumed the cycle ends on 1 at every exponent that is a multiple of 2.
• BI used a remainder of 1 rather than 2 when dividing 50 by 3.
• DI doubled my way to 2 cubed = 8 and used 8 minus 2.
• EI assumed a large power of 2 must eventually be divisible by 7.

6.A — 2 hoursKA-0162Rate, time, distance

• BI used only the slower car's speed and divided 300 by 90 the wrong way round.
• CI averaged the two speeds to 75 km/h and divided 300 by it, which ignores that both cars move at once.
• DI divided 300 by 60, using only the slower car.
• EI halved the distance to 150 and then divided by 150, applying the closing speed twice.

7.B — 4% lowerKA-0065Percentages and simple discounts

• AI applied only the decrease and forgot that the price had already risen.
• CI assumed a rise and a fall of the same percentage cancel each other out exactly.
• DI got the size of the change right but the direction wrong.
• EI added the two percentages together instead of applying them one after the other.

8.C — 11KA-0066Means, and working backwards from a mean

• AI assumed the missing number must be the mean itself.
• BI averaged the three known numbers instead of working from the total.
• DI repeated one of the numbers already given rather than computing the missing one.
• EI used a total of 37 instead of 36, adding the mean in once too often.

9.B — 15KA-0074Selections of a few objects

• AI doubled the group size instead of counting pairs.
• CI allowed a student to be paired with themselves, adding six impossible pairs.
• DI counted each pair twice, once in each order, and forgot to halve.
• EI multiplied 6 by 6, counting every ordered pair including a student with themselves.

10.C — 150KA-0117Rate, time, distance

• AI divided 150 by 60 and read the answer as minutes rather than hours.
• BI used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.
• DI converted 2.5 hours as two hours and fifty minutes.
• EI multiplied the distance by 60 instead of dividing, then converted.

11.C — 8KA-0147Circles: radius, diameter, and touching circles

• AI subtracted the radii, which is the answer when one circle sits inside the other.
• BI averaged the two radii instead of adding them.
• DI multiplied the radii together rather than adding them.
• EI added the two diameters instead of the two radii.

12.D — 120KA-0148Clock geometry: hands, angles, times

• AI gave the angle for a single hour mark rather than the four marks between the hands.
• BI counted two hour marks instead of four.
• CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
• EI measured the angle the long way round the clock face instead of the smaller one.

13.D — 19KA-0018Complementary counting

• AI counted the codes that avoid 3 entirely and gave that as my answer without subtracting.
• BI counted the codes with a 3 in the first position only and forgot the other two positions.
• CI counted the codes with exactly one 3 and forgot the ones with two or three of them.
• EI counted every possible code and forgot to remove the ones with no 3 at all.

14.C — 4KA-0020Paper folding and hole punching

• AI forgot that the punch goes through every layer at once, not just the top one.
• BI undid only one of the two folds before counting the holes.
• DI doubled for the first fold and then added two more rather than doubling a second time.
• EI counted a fold that was never made, doubling three times instead of twice.

15.B — 252KA-0075Complementary counting

• AI counted the numbers made entirely of digits other than 7 in every position, including a leading zero.
• CI counted the numbers with a 7 in each position separately and forgot that some were counted twice.
• DI added three lots of 90 and one extra hundred, double counting the 700s.
• EI counted the numbers with no 7 at all and gave that instead of subtracting it.