Worksheet generator

1.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.

2.C — 16KA-0019Multi-step arithmetic word problems

• AI found what one child has left and gave that instead of the total for all four.
• BI divided 24 by 4 and then subtracted 2 twice, mixing up per-child steps with total steps.
• DI subtracted 2 pencils once from the whole pack instead of once from each of the four children.
• EI subtracted the 2 before sharing, so only one lot of 2 ever came out of the total.

3.D — 75KA-0023The multiplication principle

• AI added the number of options at each step instead of multiplying them.
• BI treated the two digits as one choice of ten rather than two independent choices of five.
• CI assumed the two digits had to be different, so I used 5 times 4 for them.
• EI used 5 choices for the letter position as well, forgetting there are only three letters.

4.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.

5.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.

6.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.

7.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.

8.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.

9.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.

10.D — 6KA-0085Line and rotational symmetry

• AI checked only the vertical and horizontal folds and stopped there.
• BI counted the lines through opposite corners and forgot the ones through opposite edges.
• CI assumed a hexagon behaves like a rectangle with a couple of extra folds.
• EI counted each line twice, once from each end.

11.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.

12.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.

13.C — CalKA-0091Elimination grids

• AI used Bo's clue and forgot the very first clue, which rules Ana out directly.
• BI read Bo's clue as telling me what Bo has rather than what Bo does not have.
• DI stopped after using each clue once, without going back to see what the ticks had ruled out.
• EI applied Bo's clue but never came back to Ana's, so I left two people in the running.

14.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.

15.C — 65KA-0103Recursive rules

• AI stopped at the fourth term, counting the starting number as the first step rather than the first term.
• BI generated one term too few, giving the fifth term instead of the sixth.
• DI doubled six times and subtracted 1 only once at the end.
• EI generated one term too many, giving the seventh instead of the sixth.

16.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.

17.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.

18.B — 21.5KA-0115Multi-step arithmetic word problems

• AI halved the 60 pencils before giving any away.
• CI subtracted 17 from one box of 12 rather than from the whole 60.
• DI gave the number of pencils left over rather than what each child gets.
• EI gave the starting number of pencils without doing either of the steps.

19.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.

20.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.

21.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.

22.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.

23.C — 28KA-0123Eliminate impossible choices by bounding

• AI ruled out the square 6 by 6, forgetting that a square is a rectangle.
• BI did not think to try 4 by 9, so I judged this perimeter impossible.
• DI missed the 3 by 12 rectangle when listing the factor pairs.
• EI stopped listing factor pairs before reaching 2 by 18.

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.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.

26.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.

27.A — 64KA-0156Growth patterns and figurate numbers

• BI gave the number of dots in the eighth ROW instead of the whole figure.
• CI added the row numbers 1 through 8 instead of the odd numbers of dots.
• DI multiplied 8 rows by 9, using a rough average row that is one too large.
• EI counted the rows starting from zero and used the ninth square number.

28.A — 40 percentKA-0165Mixtures and weighted averages

• BI averaged 25 and 50 without weighting by how much of each solution there was.
• CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
• DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
• EI used only the acid from the weaker solution and spread it over all ten litres.

29.A — 60KA-0172Selections of a few objects

• BI chose any 4 from all 9 people and ignored the two-and-two requirement.
• CI added the two counts instead of multiplying them.
• DI treated the choices as ordered, counting the same committee several times.
• EI used 5 x 4 x 2 or a similar shortcut rather than counting each selection properly.

30.A — 6KA-0173Counting up to symmetry

• BI counted every colouring of the four edges and forgot that rotations make some of them identical.
• CI divided 16 by 4, but that only works when no painting is left unchanged by a rotation, and some are.
• DI halved 16, treating only the 180 degree turn as a symmetry.
• EI listed by how many edges are black but forgot that two black edges can be adjacent or opposite.