Daily Practice · Higher Plus
September 1981 5-a-day
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The batch download puts all 5 tiers' September 1981 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1981A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 2nd September 1981A rectangle is 4 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd September 1981Write 6/(x - 4) + 6/(x + 3) as a single fraction.
- 4th September 1981y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 16.
- 5th September 1981A cuboid measures 3 cm by 15 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th September 1981A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th September 1981On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th September 1981Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 9th September 1981Solve 4x^2 - 17x + 4 = 0.
- 10th September 1981A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.
- 11th September 1981A cuboid measures 6 cm by 7 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th September 1981A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th September 1981A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 14th September 1981A block has mass 730 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th September 1981f(x) = 2x - 9. Work out the inverse function f^-1(x).
- 16th September 1981y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 17th September 1981The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 18th September 1981A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 19th September 1981On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th September 1981x = 172 and y = 67, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st September 1981Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 22nd September 1981y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 23rd September 1981In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 24th September 1981The probability of winning a game is 5/8. A player expects 45 wins. How many games did they play?
- 25th September 1981A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 26th September 1981A car covers 750 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th September 1981Use the iteration x(n+1) = cube root of (10x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 28th September 1981y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 4.
- 29th September 1981In a vector proof you find that vector PQ = 4a + 4b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 30th September 1981A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.