Daily Practice · Higher Plus
June 1986 5-a-day
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The batch download puts all 5 tiers' June 1986 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1986On 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?
- 2nd June 1986A block has mass 470 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.
- 3rd June 1986Write 3/(x + 1) + 5/(x + 3) as a single fraction.
- 4th June 1986A train slows steadily from 31 m/s to rest in 4 seconds. Work out its deceleration.
- 5th June 1986In a vector proof you find that vector PQ = 2a - b and vector RS = 4a - 2b. What does this show about PQ and RS?
- 6th June 1986A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 7th June 1986A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 8th June 1986x = 68 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th June 1986Solve 8x^2 + 18x - 5 = 0.
- 10th June 1986y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 11th June 1986A cuboid measures 7 cm by 5 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th June 1986A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th June 1986On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th June 1986A car covers 620 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th June 1986f(x) = 6x - 5. Work out the inverse function f^-1(x).
- 16th June 1986y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 17th June 1986A cuboid measures 7 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th June 1986A bag holds 6 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th June 1986A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 20th June 1986Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
- 21st June 1986Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 22nd June 1986y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 36.
- 23rd June 1986The 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.
- 24th June 1986A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 25th June 1986On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th June 1986Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 27th June 1986Use the iteration x(n+1) = cube root of (2x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 28th June 1986A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 29th June 1986In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 30th June 1986The probability of winning a game is 1/8. A player expects 7 wins. How many games did they play?