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1. Everyone at a meeting shakes hands with everyone else exactly once. There are 66 handshakes in total. How many people are there?[4]
2. Which of these numbers has exactly 6 different whole-number factors, counting 1 and the number itself?[4]
3. A rectangle has an area of 36 and sides that are whole numbers. Which of these could NOT be its perimeter?[4]
4. A rectangle measures 30 cm by 0.4 m. What is its area in square centimetres?[4]
5. Work out 17 x 24, then check it a second way before you commit to an answer.[4]
6. Twice a number, with 3 added, gives 17. Which of the choices is the number?[4]
7. Ana has exactly 5 coins, each worth either 2 cents or 5 cents. Which of these could NOT be her total?[4]
8. A diagonal joins two corners of a shape that are not next to each other. How many diagonals does a hexagon have?[4]
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1. B — 12 KA-0121 Try small cases first
A I used the number of hands each person shakes rather than the number of people.C I doubled the answer, forgetting that the halving has already been done.D I halved 66 and treated that as the number of people.E I gave the number of handshakes back as the number of people.2. A — 12 KA-0122 Back-solve from the answer choices
B I assumed a number with two different prime factors always has six factors.C I counted the factors of 16 as six by including a number twice.D I assumed a square number has six factors without listing them.E I counted the powers of 3 up to 27 and thought there were six of them.3. C — 28 KA-0123 Eliminate impossible choices by bounding
A I ruled out the square 6 by 6, forgetting that a square is a rectangle.B I did not think to try 4 by 9, so I judged this perimeter impossible.D I missed the 3 by 12 rectangle when listing the factor pairs.E I stopped listing factor pairs before reaching 2 by 18.4. D — 1200 KA-0128 Check units and re-read before bubbling
A I worked entirely in metres and gave the answer in square metres.B I multiplied 30 by 0.4 without converting the metres to centimetres at all.C I converted 0.4 m to 4 cm rather than 40 cm.E I converted 0.4 m to 400 cm, moving the decimal point one place too far.5. E — 408 KA-0129 Sanity-check with a second method
A I worked out 17 times 20 and forgot to add the 17 times 4 part.B I worked out 17 times 4 as 28 instead of 68 when adding the parts together.C I worked out 17 times 4 as 48 instead of 68 when adding the parts together.D I made a carrying slip of ten in the final addition of the two parts.6. B — 7 KA-0131 Back-solve from the answer choices
A I tested the first choice, got 13, and picked it anyway because it was close.C I added the 3 to 17 instead of subtracting it, then halved the 20 that gave me.D I subtracted 3 from 17 and gave that without halving it.E I added 3 to 17 instead of undoing the addition by subtracting it.7. D — 21 KA-0132 Eliminate impossible choices by bounding
A I did not try one five and four twos, so I judged this total impossible.B I missed the combination of two fives and three twos.C I stopped listing after two fives and never reached three fives and two twos.E I forgot the case where every coin is a five, which is allowed by the wording.8. B — 9 KA-0150 Try small cases first
A I counted one diagonal from each corner and stopped there.C I counted three diagonals from each corner but forgot that each one gets counted from both ends.D I counted every line joining two corners, including the six sides.E I multiplied six corners by three diagonals each and never halved.