Worksheet generator

1.D — 15KA-0024Ratio as parts of a whole

• AI found what one part is worth and gave that as my answer instead of multiplying it back up.
• BI divided 40 by the five blue parts instead of by the eight parts that make the whole.
• CI read the ratio 3 to 5 as meaning 3 out of every 5 and worked from that.
• EI found the value of one part correctly but then multiplied by 5 instead of 3, giving the blue counters.

2.C — 84KA-0027Area by subtraction (shaded regions)

• AI gave the area of the square that was cut out instead of the area that remains.
• BI subtracted the side length of the small square from the area of the big one.
• DI subtracted 4 rather than the small square's area of 16.
• EI gave the area of the whole square and forgot that a piece had been removed.

3.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.

4.D — 16KA-0033Means, and working backwards from a mean

• AI subtracted the two means from each other and gave the difference as the removed number.
• BI assumed the removed number must be the new mean, since the mean dropped to 11.
• CI assumed removing a number equal to the old mean is what changes the mean.
• EI added the two totals instead of subtracting one from the other.

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.A — the pole points right and the triangle is below itKA-0039Reflections, rotations, translations

• BI turned the pole the right way but kept the triangle on the side it started on.
• CI turned the shape anticlockwise instead of clockwise.
• DI turned the shape half a turn instead of a quarter turn.
• EI reflected the shape in a vertical line instead of rotating it.

7.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.

8.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.

9.D — 2550KA-0058Clever regrouping (pair to round numbers)

• AI found the sum of 1 to 50 and forgot that every term here is twice as big.
• BI used 49 pairs instead of 25, losing one pair from the count.
• CI estimated the answer as a round number rather than pairing properly.
• EI paired the terms but forgot that pairing counts every number twice, so I never halved.

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.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.

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.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.

16.C — 18KA-0084Area by dissection and rearrangement

• AI added the two different side lengths without doubling for the opposite pair.
• BI halved the square's perimeter of 24 and adjusted by three, treating the cut as if it removed length.
• DI gave the perimeter of the whole square instead of one of the pieces.
• EI gave the area of the square rather than the perimeter of a piece.

17.B — 10KA-0087Scaling and similar figures

• AI added the difference between the areas' square roots to the side rather than multiplying by their ratio.
• CI doubled the side because the larger area is roughly double the smaller.
• DI used the ratio of the areas as if it were the ratio of the lengths, then adjusted.
• EI multiplied the side by the ratio of the areas divided by three, mixing up which ratio applies to lengths.

18.B — BoKA-0092Ordering and ranking from clues

• AI gave the child who is first rather than the one who is second.
• CI placed Cal directly after Ana, reading ahead of Dee as meaning immediately ahead.
• DI built the order backwards from the last position instead of forwards from the first.
• EI assumed the clues left several orders open without checking that they chain into a single one.

19.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.

20.B — 21KA-0104Recursive rules

• AI counted the two starting terms as one, so I stopped at the seventh term.
• CI added the two before it but slipped once in the middle of the chain.
• DI generated one term too many and gave the ninth.
• EI doubled each term instead of adding the two before it.

21.C — 55KA-0107Growth patterns and figurate numbers

• AI stopped at the eighth triangle, losing count while adding the rows.
• BI gave the ninth triangle instead of the tenth, being one row short.
• DI gave the eleventh triangle, adding one row too many.
• EI squared the position number, which describes square patterns rather than triangular ones.

22.B — 4KA-0111Age problems

• AI aged only the child and left the mother's age unchanged.
• CI looked for when the mother is four times as old rather than three times.
• DI used the age difference of 24 and halved it, without checking the ratio it gives.
• EI gave the difference between their ages, which never changes, instead of a number of years.

23.A — 3KA-0116Combined work rates

• BI gave the faster pipe's time on its own, forgetting the slower one helps as well.
• CI halved the slower pipe's time rather than adding the two rates.
• DI averaged the two times, which would only be right if the pipes took turns.
• EI added the two times, which makes two pipes slower than one - an impossible answer.

24.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.

25.B — 12KA-0121Try small cases first

• AI used the number of hands each person shakes rather than the number of people.
• CI doubled the answer, forgetting that the halving has already been done.
• DI halved 66 and treated that as the number of people.
• EI gave the number of handshakes back as the number of people.

26.A — 12KA-0122Back-solve from the answer choices

• BI assumed a number with two different prime factors always has six factors.
• CI counted the factors of 16 as six by including a number twice.
• DI assumed a square number has six factors without listing them.
• EI counted the powers of 3 up to 27 and thought there were six of them.

27.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.

28.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.

29.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.

30.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.