Daily Practice · Higher Plus
April 1987 5-a-day
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The batch download puts all 5 tiers' April 1987 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1987In a vector proof you find that vector PQ = a - 6b and vector RS = 3a - 18b. What does this show about PQ and RS?
- 2nd April 1987A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 3rd April 1987A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 4th April 1987A car covers 640 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.
- 5th April 1987Write 4/(x + 5) + 2/(x - 5) as a single fraction.
- 6th April 1987y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 81.
- 7th April 1987A cuboid measures 8 cm by 7 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th April 1987A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th April 1987On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th April 1987Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 11th April 1987Solve 16x^2 + 24x + 5 = 0.
- 12th April 1987A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
- 13th April 1987A cuboid measures 8 cm by 10 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th April 1987A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th April 1987A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 16th April 1987Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 17th April 1987f(x) = 4x + 11. Work out the inverse function f^-1(x).
- 18th April 1987y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 19th April 1987The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 20th April 1987A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 21st April 1987On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd April 1987A rectangle is 24 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd April 1987Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.
- 24th April 1987y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 25th April 1987In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 26th April 1987The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 27th April 1987A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 28th April 1987Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 29th April 1987Use the iteration x(n+1) = cube root of (6x(n) + 4) with x(0) = 3. Work out x(1) to 3 decimal places.
- 30th April 1987y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 25.