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.B — 24KA-0083Perimeter and area of rectilinear shapes

• AI subtracted 6 from 20 and gave that, which is neither a side nor an area.
• CI took the other side to be 20 minus 6 divided by 2, forgetting there are two sides of each length.
• DI multiplied the perimeter by half the known side instead of finding the missing side first.
• EI used 16 as the other side, taking 20 minus 6 plus 2 rather than working from the perimeter properly.

4.B — 2KA-0011Divisibility rules: 2, 3, 4, 5, 9, 10

• AI added the known digits to get 13 and then checked whether the missing digit itself was a multiple of 3.
• CI chose 3 because the question mentioned dividing by 3, without testing the digit sum at all.
• DI tested the last two digits, which is the rule for 4, not the rule for 3.
• EI added the digits but left out the 4 at the end, so my sum was four too small.

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.C — 25KA-0109Arithmetic sequences and the nth term

• AI added the step of 3 six times instead of seven, stopping at the seventh step.
• BI multiplied 3 by 8 without adding the first step's blocks.
• DI multiplied the step of 3 by 8 and added 4, taking one step too many.
• EI multiplied the first step's 4 blocks by the step number instead of following the pattern.

7.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.

8.B — 6KA-0045Back-solve from the answer choices

• AI tested the smallest choice first and stopped at the first one that felt about right.
• CI read a third of itself as three times itself and solved the wrong equation.
• DI reversed the comparison, finding a number whose third is 4 less than itself in the wrong direction.
• EI picked the largest choice because dividing by three made me expect a big starting number.

9.D — 8KA-0134Paper folding and hole punching

• AI forgot that the punch goes through every layer, not just the top one.
• BI undid only one of the two folds before counting.
• CI doubled twice for the folds but added the second hole instead of doubling for it too.
• EI counted three folds instead of two, doubling one time too many.

10.B — 7KA-0157The pigeonhole principle

• AI thought that one more than the number of colours must give three of a kind, which only guarantees a PAIR.
• CI got to two of each colour, then added one more for each colour instead of one more in total.
• DI assumed the worst case meant emptying the largest pile of 12 reds first.
• EI answered with the number of socks I want rather than the number I must take to be sure of them.