Daily Practice · Higher Plus
April 1982 5-a-day
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The batch download puts all 5 tiers' April 1982 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1982Solve 6x^2 - 7x - 20 = 0.
- 2nd April 1982y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 3rd April 1982A cuboid measures 11 cm by 9 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th April 1982A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th April 1982A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 6th April 1982Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 7th April 1982f(x) = 7x - 11. Work out the inverse function f^-1(x).
- 8th April 1982y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 16.
- 9th April 1982A cuboid measures 13 cm by 13 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th April 1982A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th April 1982On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th April 1982A block has mass 390 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th April 1982Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 14th April 1982A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 15th April 1982The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 16th April 1982A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 17th April 1982A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 18th April 1982x = 145 and y = 11, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th April 1982Use the iteration x(n+1) = cube root of (8x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.
- 20th April 1982y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 21st April 1982In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 22nd April 1982The probability of winning a game is 5/8. A player expects 25 wins. How many games did they play?
- 23rd April 1982On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th April 1982A car covers 310 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th April 1982Work out the nth term of the quadratic sequence 3, 9, 17, 27, ...
- 26th April 1982y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 27th April 1982In a vector proof you find that vector PQ = 2a - 2b and vector RS = 6a - 6b. What does this show about PQ and RS?
- 28th April 1982A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 29th April 1982A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 30th April 1982Rationalise the denominator of 6/sqrt(2), giving your answer in its simplest form.