Daily Practice · Higher Plus
August 1987 5-a-day
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The batch download puts all 5 tiers' August 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1987A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 2nd August 1987x = 149 and y = 62, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd August 1987Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 4th August 1987y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 4.
- 5th August 1987A cuboid measures 4 cm by 9 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th August 1987A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th August 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?
- 8th August 1987A car covers 550 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th August 1987Use the iteration x(n+1) = cube root of (10x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
- 10th August 1987A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 11th August 1987A cuboid measures 14 cm by 11 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th August 1987A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th August 1987A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 14th August 1987Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 15th August 1987Work out the nth term of the quadratic sequence 12, 23, 38, 57, ...
- 16th August 1987y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 17th August 1987The 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.
- 18th August 1987A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
- 19th August 1987On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th August 1987Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 21st August 1987The point (-2, 2) lies on y = f(x). Write down its image on y = f(x + 2).
- 22nd August 1987y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 23rd August 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.
- 24th August 1987The probability of winning a game is 1/2. A player expects 18 wins. How many games did they play?
- 25th August 1987A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 26th August 1987A rectangle is 29 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th August 1987Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 28th August 1987y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 64.
- 29th August 1987In a vector proof you find that vector PQ = 6a - 4b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 30th August 1987A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 31st August 1987On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?