Worksheet generator

1.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.

2.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.

3.D — 9KA-0046Counting by position (sliding window)

• AI cut the board into four separate 2 by 2 blocks instead of sliding the square one step at a time.
• BI counted the three sliding positions along the top and doubled them for two rows.
• CI counted the positions along the top row and down the left column and added them.
• EI counted the sixteen small squares on the board rather than the 2 by 2 squares.

4.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.

5.C — 6KA-0081Views of a solid: top, front, side

• AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
• BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
• DI added an extra cube that neither view requires.
• EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.

6.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.

7.D — 120KA-0148Clock geometry: hands, angles, times

• AI gave the angle for a single hour mark rather than the four marks between the hands.
• BI counted two hour marks instead of four.
• CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
• EI measured the angle the long way round the clock face instead of the smaller one.

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.B — 9KA-0150Try small cases first

• AI counted one diagonal from each corner and stopped there.
• CI counted three diagonals from each corner but forgot that each one gets counted from both ends.
• DI counted every line joining two corners, including the six sides.
• EI multiplied six corners by three diagonals each and never halved.

10.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.