Worksheet generator

1.C — 30KA-0006Number lines and betweenness

• AI counted the tick marks and gave the position number instead of reading the value on the scale.
• BI worked out that each gap is worth 10 but then counted only as far as the tick before the arrow.
• DI counted the tick marks rather than the gaps between them, so every gap came out one step too small.
• EI counted the gaps from the right-hand end instead of from zero.

2.E — 86400KA-0124Estimate to the nearest choice

• AI gave the number of minutes in a day instead of the number of seconds.
• BI gave the number of seconds in one hour rather than in a whole day.
• CI multiplied the 24 hours by a round thousand instead of converting properly.
• DI multiplied 60 by a round thousand, using one conversion and inventing the other.

3.C — 100 degreesKA-0152Angles on lines, in triangles, in polygons

• AI found the smaller of the two unknown angles and stopped before doubling it.
• BI split the remaining 150 degrees into two equal halves instead of a one-to-two split.
• DI split the remainder evenly into 75 and 75, then doubled one of them.
• EI assumed that the largest angle in a triangle like this must be a right angle.

4.C — 84KA-0027Area by subtraction (shaded regions)

• AI gave the area of the square that was cut out instead of the area that remains.
• BI subtracted the side length of the small square from the area of the big one.
• DI subtracted 4 rather than the small square's area of 16.
• EI gave the area of the whole square and forgot that a piece had been removed.

5.A — 1KA-0053Remainders and modular cycles

• BI found the cycle 2, 4, 1 but read the remainder of 30 divided by 3 as one instead of zero.
• CI counted the cycle positions from zero, which shifted my answer one step along.
• DI divided 30 by 7 and used that remainder rather than the remainder of the powers.
• EI assumed the remainder would be one less than the divisor because the power is large.

6.B — 4% lowerKA-0065Percentages and simple discounts

• AI applied only the decrease and forgot that the price had already risen.
• CI assumed a rise and a fall of the same percentage cancel each other out exactly.
• DI got the size of the change right but the direction wrong.
• EI added the two percentages together instead of applying them one after the other.

7.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.

8.A — 1/10KA-0125Spot the trick vs. decide to grind

• BI cancelled the chain but stopped one factor early, leaving a 9 on the bottom.
• CI worked out the first bracket and assumed the rest made no difference.
• DI gave the last bracket on its own instead of the whole product.
• EI assumed everything cancels completely, leaving nothing behind.

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.A — It is always oddKA-0167Parity arguments

• BI checked the parity of the count of numbers rather than of their sum.
• CI tried two examples, got different answers, and concluded nothing is forced.
• DI assumed differences must shrink all the way to nothing.
• EI found one sequence of moves ending at 1 and assumed every sequence must.