Worksheet generator

1.C — 110KA-0029Unit conversion

• AI subtracted correctly in metres but then gave the answer in metres when centimetres were asked for.
• BI converted 3.5 metres to 35 centimetres instead of 350.
• DI subtracted without converting at all, taking 3.5 away from 240.
• EI added the two lengths instead of finding the difference between them.

2.B — 7KA-0064Fractions of a quantity

• AI divided 28 by 7 instead of taking a quarter of it.
• CI found three quarters of 16 by mistake, mixing up the class size.
• DI found how many did travel by bus and gave that instead of how many did not.
• EI subtracted the 4 quarters as if they were 4 students.

3.B — 75KA-0088Angles on lines, in triangles, in polygons

• AI added the three angles wrongly, getting 295 instead of 285.
• CI used an angle sum of 370, mis-remembering the total for a quadrilateral.
• DI repeated one of the given angles instead of computing the missing one.
• EI used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.

4.C — 750KA-0113Unit conversion

• AI worked in kilograms and gave the answer in kilograms when grams were asked for.
• BI converted 2.5 kg to 250 g rather than 2500 g.
• DI subtracted 1750 from 3000, mis-converting 2.5 kg as three thousand grams.
• EI subtracted without converting at all, taking 2.5 away from 1750.

5.E — (7, 3)KA-0145Grid coordinates and lattice reasoning

• AI moved left instead of right, subtracting the 4 rather than adding it.
• BI moved left and up, reversing both directions.
• CI swapped the two coordinates round before moving.
• DI moved up instead of down, adding the 2 rather than subtracting it.

6.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.

7.B — 40KA-0080Properties of triangles and quadrilaterals

• AI subtracted 100 from 180 and then divided by four instead of by two.
• CI assumed the two equal angles are always 45 degrees.
• DI gave what is left after taking 100 from 180 without splitting it between the two angles.
• EI made the 100 one of the equal pair, which would already exceed 180 degrees on its own.

8.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.

9.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.

10.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.

11.C — 6KA-0025Counting up to symmetry

• AI also treated bracelets that are mirror images as the same, but only rotations were allowed.
• BI divided the number of beads by itself rather than dividing the number of arrangements by the number of rotations.
• DI divided the 24 arrangements by 2 instead of by the 4 rotations of a circle of four beads.
• EI counted every arrangement in a line and forgot that rotating a bracelet gives the same bracelet.

12.E — No, it is impossibleKA-0028Parity arguments

• AI found a sequence that turned over most of the cups and assumed the last one could be fixed somehow.
• BI matched the number of moves to the number of cups without checking whether the target is reachable at all.
• CI assumed that with enough moves any arrangement can be reached.
• DI thought the choice of which cups to flip could change whether the target is reachable.

13.A — 8KA-0031Counting paths on a grid

• BI assumed closing one junction removes about half the routes and halved the total of 20.
• CI counted the routes that pass through the closed junction and gave that instead of the ones that avoid it.
• DI subtracted only the 2 routes that reach the closed junction, not all the routes that continue through it.
• EI counted every route on the open grid and forgot to remove the ones through the closed junction.

14.D — 30KA-0047Counting by position (sliding window)

• AI counted only the sixteen smallest squares and stopped there.
• BI counted the small squares and the single big one, and forgot every size in between.
• CI counted the 2 by 2 squares as four rather than nine, splitting the board into blocks.
• EI used 4 by 4 positions for every size instead of shrinking the range as the square grows.

15.D — 12KA-0060Operation puzzles and cryptarithms

• AI added the digits of 132 instead of working out what A and B must be.
• BI found A + B correctly and then halved it, as if the question wanted one digit.
• CI spotted the 11 in the working and gave that instead of the sum it multiplies.
• EI found a pair of digits by trial and misadded them by one.

16.A — 12KA-0071Overcount, then correct

• BI divided the 120 arrangements by 6 rather than by the 10 movements that leave a bracelet looking the same.
• CI allowed for turning the bracelet but forgot it can also be flipped over.
• DI halved the 120 for flipping but forgot that turning also gives the same bracelet.
• EI counted every arrangement in a line, as if the bracelet had a fixed first bead.

17.B — 10KA-0082Shortest paths on and around shapes

• AI measured the straight line through the middle of the room, but the ant has to stay on the surfaces.
• CI unfolded the room but folded out the short wall rather than the one that makes the shortest route.
• DI chose an unfolding that gives a longer straight line and did not compare it with the others.
• EI walked along the edges of the room, 8 then 4 then 2, instead of cutting straight across the surfaces.

18.D — No, because the number of moves is oddKA-0097Parity arguments

• AI assumed enough moves can undo anything, without asking what each move preserves.
• BI tried a few sequences that nearly worked and assumed a better choice would finish the job.
• CI reached for the number of items rather than for what a single swap actually changes.
• EI thought the choice of swaps could change the outcome, when every swap has the same effect.

19.D — No, because the two colours cannot balanceKA-0101Coloring arguments

• AI checked that 100 divides by 4 and treated that as proof that a covering exists.
• BI assumed a covering must exist somewhere and that I simply had not found it yet.
• CI gave a reason that is not even true, since 100 really is a multiple of 4.
• EI thought orientation could rescue it, but every turn of a T covers the same mixture of colours.

20.D — 25KA-0106Inferring a rule from examples

• AI used the rule add 4, which fits the first example but not the others.
• BI found a rule from two examples only and never tested it against the third.
• CI doubled the input and forgot the extra one that every example needs.
• EI used double and add five, which fits none of the examples exactly.