Daily Practice · Higher Plus
June 1981 5-a-day
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The batch download puts all 5 tiers' June 1981 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1981In a vector proof you find that vector PQ = 4a - 4b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 2nd June 1981A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 3rd June 1981On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th June 1981Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
- 5th June 1981f(x) = 3x - 10. Work out the inverse function f^-1(x).
- 6th June 1981A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 7th June 1981A cuboid measures 4 cm by 11 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th June 1981A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th June 1981A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 10th June 1981A rectangle is 23 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th June 1981Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 12th June 1981y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 13th June 1981A cuboid measures 12 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th June 1981A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th June 1981On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th June 1981Expand and simplify (8 + sqrt(6))(8 - sqrt(6)).
- 17th June 1981Use the iteration x(n+1) = cube root of (4x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.
- 18th June 1981y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 19th June 1981The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 20th June 1981A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 21st June 1981A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 22nd June 1981A block has mass 890 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd June 1981Work out the nth term of the quadratic sequence -5, 3, 19, 43, ...
- 24th June 1981y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 9.
- 25th June 1981In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 26th June 1981The probability of winning a game is 7/8. A player expects 35 wins. How many games did they play?
- 27th June 1981On 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?
- 28th June 1981x = 195 and y = 140, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th June 1981The point (-3, 6) lies on y = f(x). Write down its image on y = -f(x).
- 30th June 1981A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.