Worksheet generator

1.E — 60KA-0026Percentages and simple discounts

• AI worked out the size of the discount and gave that as the new price instead of subtracting it.
• BI treated a quarter off as half off and took the price down to 40.
• CI applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.
• DI subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.

2.C — 9KA-0072Systematic listing

• AI counted only the numbers with two identical digits, like 11, 22 and 33.
• BI required the two digits to be different, even though repeats are allowed.
• DI allowed a fourth digit that was not in the list.
• EI counted three-digit numbers instead of two-digit ones.

3.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.

4.A — 123KA-0160Arithmetic sequences and the nth term

• BI multiplied the step by 30 instead of by 29, forgetting that the first term needs no steps.
• CI used 4 times 30 and forgot to add the starting value.
• DI added 28 steps instead of 29, counting the gaps one short.
• EI treated the first term as the step and used 7 times 30 minus something close.

5.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.

6.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.

7.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.

8.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.

9.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.

10.E — 9KA-0037Last-digit behavior of products and powers

• AI assumed a number this large has no reachable last digit and gave up on the cycle.
• BI found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.
• CI found the cycle but counted its positions starting at zero, shifting my answer along by one.
• DI assumed the units digit of any power of 7 is always 7.

11.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.

12.B — 9KA-0095The extremal principle

• AI divided 100 by 12 and rounded down instead of up.
• CI rounded the division to a convenient number without checking that a packing with a smaller maximum exists.
• DI gave the number of boxes as the answer rather than a number of apples.
• EI described the case where one box holds everything, which is possible but not guaranteed.

13.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.

14.B — Answer it with your best guess, mark it, and move onKA-0126Time triage: now, later, or guess

• AI let the time already spent decide, but that time is gone whatever I do next.
• CI moved on but left a blank, which scores nothing if I never get back to it.
• DI spent time re-reading work I had no reason to doubt, while 21 unseen questions waited.
• EI assumed the hardest questions are the best use of time, when the unseen easy ones are worth the same each.

15.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.