Worksheet generator

1.B — square 3KA-0005Nets and folding, 2D to 3D

• AI picked the square directly next to the shaded one in the net, but neighbours in the net share an edge on the cube.
• CI counted to the far end of the column, assuming the square furthest away in the net is the one opposite.
• DI picked one of the side flaps because it is not touching the shaded square in the drawing.
• EI picked the other side flap for the same reason, without tracking what happens as the net folds.

2.B — 2KA-0011Divisibility rules: 2, 3, 4, 5, 9, 10

• AI added the known digits to get 13 and then checked whether the missing digit itself was a multiple of 3.
• CI chose 3 because the question mentioned dividing by 3, without testing the digit sum at all.
• DI tested the last two digits, which is the rule for 4, not the rule for 3.
• EI added the digits but left out the 4 at the end, so my sum was four too small.

3.B — greenKA-0014Repeating cycles and position mod n

• AI got a remainder of 2 but started counting the colours at zero, which shifted me back one bead.
• CI counted the seven whole repeats and then counted three more beads instead of two.
• DI divided 30 by 4, got 7 remainder 2, and used the last colour of a repeat as though the remainder were zero.
• EI thought the repeating pattern had no fixed starting point, even though bead one is given.

4.C — 61KA-0030Arithmetic sequences and the nth term

• AI added the step 18 times, counting the gaps between terms one too few.
• BI multiplied the step of 3 by 20 and forgot that the first term is already in place.
• DI used a first term of 3 instead of 4 while adding 20 steps.
• EI added the step 20 times to the first term instead of 19 times.

5.D — 120KA-0036Rate, time, distance

• AI worked out the cycling leg and gave that as the answer, forgetting the walk entirely.
• BI worked out the walking leg and gave that as the answer, forgetting the cycling entirely.
• CI wrote half an hour as 15 minutes instead of 30 and added it to the 90 minute walk.
• EI rounded the cycling leg up to a whole hour instead of keeping it as half an hour.

6.C — 9 timesKA-0042Scaling and similar figures

• AI applied the length scale factor straight to the area.
• BI doubled the scale factor because area involves two dimensions, instead of squaring it.
• DI multiplied the scale factor by four, as though area scaled with the number of sides.
• EI cubed the scale factor, which is the rule for volume rather than area.

7.B — 2 hoursKA-0044Combined work rates

• AI subtracted the two times from each other rather than adding the rates.
• CI averaged the two times, which would only be right if the taps took turns instead of running together.
• DI added the two times together, which makes the tank slower with two taps than with one.
• EI used the faster tap's time alone and ignored the contribution of the slower one.

8.D — 9KA-0046Counting by position (sliding window)

• AI cut the board into four separate 2 by 2 blocks instead of sliding the square one step at a time.
• BI counted the three sliding positions along the top and doubled them for two rows.
• CI counted the positions along the top row and down the left column and added them.
• EI counted the sixteen small squares on the board rather than the 2 by 2 squares.

9.A — 1KA-0053Remainders and modular cycles

• BI found the cycle 2, 4, 1 but read the remainder of 30 divided by 3 as one instead of zero.
• CI counted the cycle positions from zero, which shifted my answer one step along.
• DI divided 30 by 7 and used that remainder rather than the remainder of the powers.
• EI assumed the remainder would be one less than the divisor because the power is large.

10.C — 12KA-0062Factors, multiples, LCM and GCD by listing

• AI found a number that divides both but not the largest one, stopping at the first that worked.
• BI used the difference between 36 and 24 divided by 2 rather than a common factor.
• DI used a factor of 36 without checking that it also divides 24.
• EI found the least common multiple instead of the greatest common divisor.

11.D — 144KA-0063Divisibility rules: 2, 3, 4, 5, 9, 10

• AI checked that it divides by 4 and stopped without testing the 9.
• BI checked the digit sum for 9 and stopped without testing the 4.
• CI saw an even number with a digit sum of 6 and treated 6 as good enough for 9.
• EI tested 9 with the digit sum and assumed any odd multiple of 9 also divides by 4.

12.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.

13.B — 4KA-0069Inclusion–exclusion with two sets

• AI added 18 and 14 without removing the overlap, then subtracted from 30.
• CI subtracted the 6 who play both twice instead of once.
• DI subtracted only the footballers from the class and forgot the chess players entirely.
• EI found how many play at least one sport and gave that instead of how many play neither.

14.D — 24KA-0073Arrangements of a few objects

• AI counted the letters rather than their arrangements.
• BI multiplied 4 by 3 and stopped, forgetting the last two positions.
• CI used 4 choices for every position, as if letters could repeat.
• EI used 4 choices in each of four positions, which allows every letter to repeat.

15.A — 3KA-0076Casework

• BI included 0 and 7 as a pair, even though both numbers have to be bigger than zero.
• CI counted both orders of each pair, even though swapping does not make a new way.
• DI counted every starting number from 1 to 7 without checking which pairs repeat.
• EI counted both orders and also allowed pairs of equal numbers.

16.C — 6KA-0081Views of a solid: top, front, side

• AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
• BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
• DI added an extra cube that neither view requires.
• EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.

17.B — 1KA-0089Building and counting with unit cubes

• AI assumed every small cube touches the outside somewhere.
• CI counted the cubes at the centre of each face, which are painted on one side.
• DI counted the corner cubes, which are the most painted rather than the least.
• EI gave the total number of small cubes instead of the unpainted ones.

18.B — 60KA-0093Weighing and balance puzzles

• AI halved the apple's weight, as if one apple balanced two pears.
• CI assumed a pear must weigh the same as an apple because the two sides balance.
• DI multiplied the apple's weight by three halves the wrong way round, making the pear heavier.
• EI gave the total weight of the two apples rather than the weight of one pear.

19.B — Box X is not redKA-0099Reading a logical statement precisely

• AI read the rule backwards, as if being heavy were what makes a box red.
• CI assumed not red must mean one particular other colour, when the rule says nothing about which.
• DI contradicted the rule I was given rather than applying it to box X.
• EI decided one fact could not settle anything, without testing what would follow if X were red.

20.B — 8KA-0100Working backwards

• AI undid the operations in the order they were written instead of in reverse order.
• CI gave the final answer back, assuming the three steps cancelled each other out.
• DI doubled the 11 and subtracted the 6 but forgot the final halving that undoes the doubling.
• EI undid only the halving and stopped there without touching the other two steps.

21.D — 1200KA-0128Check units and re-read before bubbling

• AI worked entirely in metres and gave the answer in square metres.
• BI multiplied 30 by 0.4 without converting the metres to centimetres at all.
• CI converted 0.4 m to 4 cm rather than 40 cm.
• EI converted 0.4 m to 400 cm, moving the decimal point one place too far.

22.E — 408KA-0129Sanity-check with a second method

• AI worked out 17 times 20 and forgot to add the 17 times 4 part.
• BI worked out 17 times 4 as 28 instead of 68 when adding the parts together.
• CI worked out 17 times 4 as 48 instead of 68 when adding the parts together.
• DI made a carrying slip of ten in the final addition of the two parts.

23.B — 7KA-0131Back-solve from the answer choices

• AI tested the first choice, got 13, and picked it anyway because it was close.
• CI added the 3 to 17 instead of subtracting it, then halved the 20 that gave me.
• DI subtracted 3 from 17 and gave that without halving it.
• EI added 3 to 17 instead of undoing the addition by subtracting it.

24.D — 21KA-0132Eliminate impossible choices by bounding

• AI did not try one five and four twos, so I judged this total impossible.
• BI missed the combination of two fives and three twos.
• CI stopped listing after two fives and never reached three fives and two twos.
• EI forgot the case where every coin is a five, which is allowed by the wording.

25.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.

26.A — 1KA-0149Last-digit behavior of products and powers

• BI assumed every power of 3 ends in 3.
• CI found the cycle 3, 9, 7, 1 but counted its positions from zero, landing one step early.
• DI used a remainder of 2 instead of 0 when dividing 100 by the cycle length of 4.
• EI assumed a number this large has no reachable last digit, rather than looking for a repeat.

27.B — 9KA-0150Try small cases first

• AI counted one diagonal from each corner and stopped there.
• CI counted three diagonals from each corner but forgot that each one gets counted from both ends.
• DI counted every line joining two corners, including the six sides.
• EI multiplied six corners by three diagonals each and never halved.

28.B — 30 cmKA-0155Scaling and similar figures

• AI kept the difference of 4 cm between the two sides instead of keeping their ratio.
• CI added 20 to 12 rather than scaling 12.
• DI used the scale factor upside down and multiplied 12 by 8/20 instead of 20/8.
• EI multiplied 12 by 1.5, the ratio between the original sides, instead of by the enlargement factor.

29.A — 56KA-0163Selections of a few objects

• BI counted ordered selections, so I counted the same three people once for every order they could stand in.
• CI multiplied the 8 members by the 3 places, which counts something quite different from a selection.
• DI divided the 336 ordered selections by 3 instead of by 3 factorial.
• EI chose 2 people rather than 3.

30.B — 50 sq cmKA-0164Scaling and similar figures

• AI scaled the area by 5/3, using the side ratio directly instead of its square.
• CI multiplied the area by 2.5, halfway between the side ratio and its square.
• DI scaled by 3/5 instead of 5/3, making the larger triangle smaller.
• EI multiplied by 5 and ignored the 3 in the ratio entirely.