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.D — ThursdayKA-0021Remainders and modular cycles

• AI found the remainder 2 but counted the two days starting from today rather than starting from tomorrow.
• BI divided 100 by 7 and used the quotient of 14, treating the leftover days as if there were none.
• CI remembered there was a remainder but used a remainder of 1 instead of working it out.
• EI counted 100 divided by 7 as 14 remainder 3 instead of remainder 2.

3.C — 55 degreesKA-0022Angles on lines, in triangles, in polygons

• AI assumed the triangle was isosceles because it had a right angle, so I repeated the 35.
• BI assumed a right-angled triangle always has two 45 degree angles.
• DI subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.
• EI subtracted only the 35 from 180 and forgot to take off the right angle as well.

4.E — 24KA-0038Building and counting with unit cubes

• AI added the three measurements together instead of multiplying them.
• BI counted one layer of 4 by 3 and forgot that the block is two layers tall.
• CI read the block as 3 by 3 by 2 because the drawing hid the far column.
• DI counted only the cubes whose faces I could actually see in the picture.

5.B — the straight line of sixKA-0048Nets and folding, 2D to 3D

• AI assumed any arrangement that is not a simple line must fail to fold.
• CI thought a staircase would overlap when folded, without tracking a single face through the fold.
• DI picked the cross because it looks unusual, even though it is the most familiar cube net there is.
• EI checked that each arrangement had six squares and assumed six squares is enough.

6.C — 14KA-0051Complementary counting

• AI counted the multiples of 3 and gave that instead of the numbers that are not multiples.
• BI counted 21 as a multiple of 3 inside the range, so I removed one too many.
• DI removed only the multiples of 3 that are also even, so I subtracted three instead of six.
• EI gave the size of the whole range and forgot to remove anything at all.

7.C — 70KA-0055Place value and digit positions

• AI gave the last digit of the number instead of looking at the 7 at all.
• BI gave the digit itself rather than what it is worth in the position it sits in.
• DI counted the positions from the left, so I read the 7 as being in the hundreds place.
• EI gave the value of the largest digit instead of the value of the 7.

8.B — Write an answer for every one of themKA-0127Never leave a blank — there is no penalty

• AI treated guessing as dishonest, but the rules of the paper explicitly allow it and cost nothing.
• CI answered one and left two blanks that could each have scored, at no risk.
• DI tried to communicate with the marker, but only the answers are scored.
• EI offered working on a paper where only the chosen letter is marked.

9.E — 8KA-0143Systematic listing

• AI counted the two available digits rather than the numbers they can build.
• BI counted the three positions instead of the numbers.
• CI used only two of the three positions when multiplying.
• DI multiplied 2 by 3, mixing the number of digits with the number of positions.

10.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.

11.A — 1KA-0169Remainders and modular cycles

• BI reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.
• CI read the cycle backwards and landed on the entry before the right one.
• DI used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.
• EI assumed a power that large must be divisible by 5.

12.A — 150 degreesKA-0170Angles on lines, in triangles, in polygons

• BI found the exterior angle and answered with that instead of the interior one.
• CI used 360 divided by 12 subtracted from 195, or otherwise slipped a step in the arithmetic.
• DI gave the total of all twelve interior angles rather than one of them.
• EI used a ten-sided polygon by mistake.

13.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.

14.D — 30KA-0007Working backwards

• AI added the 6 and the 9 and stopped, forgetting to undo the halving at the start.
• BI undid the steps in the order they were written instead of reversing the order as well as the operations.
• CI doubled the 9 first and then added the 6, which reverses the steps in the wrong order.
• EI doubled twice because giving half away felt like it should be undone more than once.

15.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.

16.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.

17.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.

18.B — Bo onlyKA-0096Truth-tellers and liars

• AI took Ana's statement at face value without checking whether a truthful person could say it.
• CI decided nobody was lying without testing Ana's statement against that assumption.
• DI believed Ana's statement even after concluding she was a liar, which is what a liar's statement cannot be.
• EI gave up when Ana's statement looked circular, instead of testing one assumption all the way through.

19.A — Yes, alwaysKA-0102Informal proof by contradiction

• BI found one pair that works and assumed the argument depended on that particular card.
• CI tried a couple of selections, did not find a pair, and stopped looking.
• DI looked for a pattern in the numbers rather than at how many pairs there are to avoid.
• EI thought the answer depended on which six were taken, when the counting settles it for every choice.

20.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.

21.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.

22.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.

23.A — 48 km/hKA-0174Rate, time, distance

• BI averaged the two speeds, which would only be right if equal TIME were spent at each, not equal distance.
• CI weighted the two speeds by their own values instead of by the time each leg took.
• DI halved the correct answer, dividing by the total distance twice.
• EI added the two speeds together, which gives a number faster than either leg and so cannot be an average of them.

24.B — 1KA-0017Truth-tellers and liars

• AI assumed everyone could be lying at once without checking that Cal's statement would then be true.
• CI found one consistent truth-teller and added another without testing whether both could hold together.
• DI assumed everyone was telling the truth without noticing that Ana's statement then contradicts Bo's.
• EI gave up after one assumption led to a contradiction, instead of trying the other assumption.

25.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.

26.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.

27.C — No, the last number is always evenKA-0098Invariants and monovariants

• AI found sequences ending in small numbers and assumed 1 was among the reachable ones.
• BI assumed a hard-looking question must have exactly one answer.
• DI found one sequence ending in 0 and assumed every sequence must end there.
• EI thought the order could change the outcome, when the quantity that decides it never changes.

28.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.

29.B — 11KA-0112Mixtures and weighted averages

• AI averaged the two averages, ignoring that the classes are different sizes.
• CI weighted the averages but used the wrong class size against each one.
• DI leaned towards the larger class's average without computing the totals.
• EI added the two averages together instead of combining them.

30.A — 2 hours 24 minutesKA-0159Combined work rates

• BI averaged the two times, but two taps together must be faster than either one alone.
• CI added the two times, which would be right for filling two tanks one after the other.
• DI halved the smaller of the two times, guessing that two taps must simply be twice as fast as one.
• EI found 2 hours 24 minutes correctly and then halved it a second time.