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1. A tap drips about 3 times a minute. Roughly how many drips is that in one day?[3]
2. Which capital letter, printed plainly, has both a horizontal and a vertical line of symmetry?[3]
3. A sequence starts 4, 7, 10, 13 and continues in the same way. What is the 20th term?[4]
4. A price goes up by 20%, then down by 20%. Compared with the original price, the final price is:[4]
A 20% lowerB 4% lowerC the sameD 4% higherE 40% higher5. Two similar triangles have areas of 9 and 25 square units. A side of the smaller one is 6 units. How long is the matching side of the larger one?[4]
6. A sequence starts 1, 1, and every term after that is the sum of the two before it. What is the eighth term?[4]
7. What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
8. A number is 4 more than a third of itself. Which of the choices is that number?[5]
9. A box holds 4 red, 5 blue and 6 green balls, mixed up. How many must be taken out without looking to be sure of having 3 of the same colour?[5]
10. A cube 3 units on each side is painted all over and then cut into unit cubes. How many of them have exactly two painted faces?[5]
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1. D — 4320 KA-0059 Estimation and order of magnitude
A I worked out the drips in an hour and stopped there.B I multiplied by the 24 hours but forgot the 60 minutes in each one.C I used 6 hours in a day, thinking of waking hours rather than a whole day.E I used 600 minutes in an hour rather than 60.2. C — H KA-0142 Line and rotational symmetry
A I found the vertical fold and assumed a horizontal one must work too.B I found the horizontal fold and stopped without testing the vertical one.D I counted the vertical fold twice rather than testing a horizontal one.E I mistook turning the letter upside down for folding it, which is rotation rather than symmetry about a line.3. C — 61 KA-0030 Arithmetic sequences and the nth term
A I added the step 18 times, counting the gaps between terms one too few.B I multiplied the step of 3 by 20 and forgot that the first term is already in place.D I used a first term of 3 instead of 4 while adding 20 steps.E I added the step 20 times to the first term instead of 19 times.4. B — 4% lower KA-0065 Percentages and simple discounts
A I applied only the decrease and forgot that the price had already risen.C I assumed a rise and a fall of the same percentage cancel each other out exactly.D I got the size of the change right but the direction wrong.E I added the two percentages together instead of applying them one after the other.5. B — 10 KA-0087 Scaling and similar figures
A I added the difference between the areas' square roots to the side rather than multiplying by their ratio.C I doubled the side because the larger area is roughly double the smaller.D I used the ratio of the areas as if it were the ratio of the lengths, then adjusted.E I multiplied the side by the ratio of the areas divided by three, mixing up which ratio applies to lengths.6. B — 21 KA-0104 Recursive rules
A I counted the two starting terms as one, so I stopped at the seventh term.C I added the two before it but slipped once in the middle of the chain.D I generated one term too many and gave the ninth.E I doubled each term instead of adding the two before it.7. D — 120 KA-0148 Clock geometry: hands, angles, times
A I gave the angle for a single hour mark rather than the four marks between the hands.B I counted two hour marks instead of four.C I assumed any gap of a few hours is a right angle, as it is at three o'clock.E I measured the angle the long way round the clock face instead of the smaller one.8. B — 6 KA-0045 Back-solve from the answer choices
A I tested the smallest choice first and stopped at the first one that felt about right.C I read a third of itself as three times itself and solved the wrong equation.D I reversed the comparison, finding a number whose third is 4 less than itself in the wrong direction.E I picked the largest choice because dividing by three made me expect a big starting number.9. C — 7 KA-0077 The pigeonhole principle
A I answered with the luckiest case, where the first three balls happen to match.B I found the worst case of two of each colour and forgot to take one more.D I multiplied the three colours by the three balls I need, rather than thinking about the worst case.E I worked from the number of balls of each colour rather than from the number of colours.10. C — 12 KA-0090 Counting cubes in a stack, including hidden ones
A I counted the middle cube of each face, which has exactly one painted face rather than two.B I counted the corner cubes, which have three painted faces.D I counted every cube that is painted at all except the corners, without separating one face from two.E I gave the total number of small cubes rather than the ones with exactly two painted faces.