Daily Practice · Higher Plus
May 1981 5-a-day
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The batch download puts all 5 tiers' May 1981 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1981y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 2nd May 1981In a vector proof you find that vector PQ = a - b and vector RS = 2a - 2b. What does this show about PQ and RS?
- 3rd May 1981A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 4th May 1981A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 5th May 1981Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 6th May 1981Simplify (x^2 - 4x - 21)/(x + 3).
- 7th May 1981y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 81.
- 8th May 1981A cuboid measures 15 cm by 6 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th May 1981A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th May 1981On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th May 1981A block has mass 780 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th May 1981In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 13th May 1981A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
- 14th May 1981A cuboid measures 14 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th May 1981A bag holds 5 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th May 1981A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 17th May 1981x = 190 and y = 166, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th May 1981Make x the subject of 4x + 8 = y(x + 8).
- 19th May 1981y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 20th May 1981The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 21st May 1981A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 22nd May 1981On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd May 1981A car covers 300 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th May 1981Write 7/(x + 3) + 7/(x + 5) as a single fraction.
- 25th May 1981y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 26th May 1981In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 27th May 1981The probability of winning a game is 3/8. A player expects 12 wins. How many games did they play?
- 28th May 1981A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 29th May 1981Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 30th May 1981Solve 4x^2 + 5x + 1 = 0.
- 31st May 1981y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 81.