Daily Practice · Higher Plus
June 1982 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1982 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1982A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 2nd June 1982A cuboid measures 5 cm by 11 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd June 1982A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th June 1982A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 5th June 1982A 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.
- 6th June 1982Write x^2 - 14x + 15 in the form (x + a)^2 + b.
- 7th June 1982y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 8th June 1982A cuboid measures 10 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th June 1982A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th June 1982On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 11th June 1982Rationalise the denominator of 10/sqrt(5), giving your answer in its simplest form.
- 12th June 1982Work out the coordinates of the turning point of y = x^2 + 4x + 4.
- 13th June 1982y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 14th June 1982The 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.
- 15th June 1982A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 16th June 1982A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 17th June 1982Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 18th June 1982Simplify (x^2 - 5x - 14)/(x - 7).
- 19th June 1982y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 81.
- 20th June 1982In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 21st June 1982The probability of winning a game is 3/4. A player expects 78 wins. How many games did they play?
- 22nd June 1982On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd June 1982A rectangle is 14 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th June 1982In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 25th June 1982A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 26th June 1982In a vector proof you find that vector PQ = 5a - 4b and vector RS = 20a - 16b. What does this show about PQ and RS?
- 27th June 1982A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 28th June 1982A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 29th June 1982Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 30th June 1982Make x the subject of 2x + 6 = y(x + 6).