⏱️ Ten-minute starters — Foundation

Answer key

1. (b) 5/9 — Add the parts of the ratio to find how many equal shares make up the whole: 4 + 5 = 9 shares. The blue counters take 5 of those 9 shares, so 5/9 of the counters are blue. 4/9 is the fraction that are red, 4/5 is the ratio copied straight down as a fraction, and 5/4 compares the blue counters with the red counters instead of with the whole box.
2. (b) RHS - right angle, hypotenuse and one side equal — A right angle, the hypotenuse (13 cm) and one other side (5 cm) are equal in both triangles, so this is RHS. SAS would need the equal angle to be the one INCLUDED between the two equal sides, but the right angle at B is not between AB and the hypotenuse AC — it is opposite the hypotenuse instead, so SAS does not apply directly here. SSS needs all three sides, but only two sides are stated. ASA needs two angles, but only one angle (the right angle) is given.
3. (a) 0.8 — Method: the spinner cannot land on red and blue at the same time, so the two events are mutually exclusive and their probabilities are added. Working: 0.3 + 0.5, lining the decimal points up. Answer: 0.8, which also tells you that the remaining colour, green, has probability 0.2 because the three must add to 1. The distractors: 0.2 comes from subtracting 0.3 from 0.5 instead of adding the two probabilities; 0.15 comes from multiplying 0.3 by 0.5 instead of adding them; 0.4 comes from finding the mean of 0.3 and 0.5 rather than their total.
4. (d) 56 — Method: count the trials over the whole period first, then multiply the number of trials by the probability. Working: 4 weeks is 4 × 7 = 28 days, and at 25 trains a day that is 25 × 28 = 700 trains. The expected number of late trains is 700 × 0.08 = 56. Answer: about 56 late trains over the 4 weeks. The distractors: 2 is the expected number for a single day, 25 × 0.08 = 2, with the 28 days never brought in; 14 uses one week instead of four, 25 × 7 × 0.08 = 14; 644 is 700 − 56 and counts the trains expected to be on time.
5. (d) No — angles must be equal too — A regular polygon must have both all sides equal and all angles equal. This tile has all six sides equal, but its interior angles are not all equal, so it fails the angle condition and is not regular — 'No — angles must be equal too' is correct. 'Yes — all sides are equal' is wrong because equal sides alone are not enough; a shape can have equal sides but unequal angles, as here. 'Yes — six equal sides means regular' is wrong for the same reason: equal sides do not automatically guarantee equal angles. 'No — hexagons can't be regular' is wrong because regular hexagons certainly exist (six equal sides and six equal 120° angles); it is this particular tile that fails to be regular, not hexagons in general.
6. (d) Correlation is a link; causation is one causing the other — Method: the two words describe different claims — one is about a pattern in the data, the other is about what produced that pattern. Working: correlation says only that two quantities tend to change together, which is something a scatter graph can display; causation says that a change in one quantity actually brings about the change in the other, which needs evidence a scatter graph cannot supply, because a third quantity may be driving both. Answer: correlation is a link between the quantities, while causation is one quantity causing the change in another. The distractors: the statement giving causation as the link and correlation as the cause simply swaps the two words over; the statement that the words mean the same thing is the classic error of reading a correlation as proof of cause; the statement that a scatter graph shows causation but not correlation reverses what a scatter graph can do, since the pattern it displays is exactly the correlation.
7. (d) 5:3:2 — German = 100% − 50% − 30% = 20%. The ratio 50 : 30 : 20 simplifies by dividing every part by 10 to give 5 : 3 : 2.
8. (c) 19 — Without any restriction there would be 5 × 4 = 20 different sandwiches. The restriction removes exactly one combination, cheese and mustard on gluten-free bread, so subtract 1: 20 − 1 = 19. 20 comes from ignoring the restriction completely. 15 comes from removing the gluten-free bread altogether, as if none of the fillings were available on it, 5 × 3 = 15. 16 comes from removing the cheese and mustard filling completely, as if it were not available on any bread, 4 × 4 = 16.
9. (c) 8 hours 35 minutes — From 21:35 to midnight is 2 hours 25 minutes, and from midnight to 06:10 is a further 6 hours 10 minutes, giving a total of 8 hours 35 minutes. Misreading the departure time as 22:35 instead of 21:35 loses an hour from the calculation and gives 7 hours 35 minutes. Misreading the departure time as 20:35 instead of 21:35 gains an hour and gives 9 hours 35 minutes. Subtracting the times as if both fell on the same day, without crossing midnight, gives 15 hours 25 minutes.
10. (c) < — Method: compare the two negative numbers by their position on a number line, not by the size of the digit. Working: −9 is nine places to the left of zero and −4 is four places to the left of zero, so −9 is further from zero in the negative direction, which makes it the smaller number. Answer: −9 < −4, so the symbol is <. > comes from comparing 9 and 4 as if both numbers were positive, ignoring the negative signs. = comes from treating both numbers as equal simply because they are both negative. ≥ combines > (false) with = (also false).
11. (a) 22p — First convert the hourly rate to pence: £13.20 = 1320p. Then convert from per hour to per minute by dividing by 60, since there are 60 minutes in an hour: 1320 ÷ 60 = 22p per minute. Working out 1320 × 60 = 79200p multiplies by 60 instead of dividing, going the wrong way between per hour and per minute. Working out 13.20 × 10 = 132p converts pounds to pence using the wrong power of ten, and dividing that by 60 carries the error through to give 2.2p. Working out 13.20 × 100 = 1320p converts the currency correctly but stops there, leaving the rate as pence per hour rather than completing the second conversion to pence per minute. The rate of pay is 22p per minute.
12. (d) 13/20 — Method: write both fractions over a common denominator, then add the numerators. Working: 2/5 = 8/20 and 1/4 = 5/20, so 2/5 + 1/4 = 8/20 + 5/20 = 13/20, which is already in its simplest form. Answer: 13/20. 1/3 comes from adding the numerators and the denominators separately: (2+1)/(5+4) = 3/9 = 1/3. 13/40 comes from converting both fractions to twentieths correctly but then adding the denominators as well as the numerators: (8+5)/(20+20) = 13/40. 3/20 comes from adding the original numerators (2+1) but keeping them over the common denominator without converting them first: 3/20.