Daily Practice · Higher Plus
June 1987 5-a-day
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The batch download puts all 5 tiers' June 1987 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1987A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 2nd June 1987A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 3rd June 1987A rectangle is 21 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th June 1987A quadratic sequence starts 10, 24, 44, 70. Work out the second difference, and the coefficient of n^2.
- 5th June 1987y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 6th June 1987A cuboid measures 13 cm by 12 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th June 1987A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th June 1987On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th June 1987Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 10th June 1987Solve x^2 - 6x < 0.
- 11th June 1987y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 12th June 1987A cuboid measures 10 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th June 1987A bag holds 3 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th June 1987A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 15th June 1987A block has mass 700 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th June 1987Write x^2 + 12x + 6 in the form (x + a)^2 + b.
- 17th June 1987y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 36.
- 18th June 1987The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 19th June 1987A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 20th June 1987On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st June 1987x = 52 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd June 1987Work out the coordinates of the turning point of y = x^2 + 6x - 14.
- 23rd June 1987A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 24th June 1987In 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.
- 25th June 1987The probability of winning a game is 1/4. A player expects 9 wins. How many games did they play?
- 26th June 1987A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 27th June 1987A car covers 760 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th June 1987Simplify (x^2 - 4x + 3)/(x - 1).
- 29th June 1987y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 30th June 1987In a vector proof you find that vector PQ = 6a - 2b and vector RS = 12a - 4b. What does this show about PQ and RS?