Daily Practice · Higher Plus
September 1987 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1987 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1987Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
- 2nd September 1987f(x) = 5x - 3 and g(x) = 4x + 2. Work out fg(5).
- 3rd September 1987A train slows steadily from 13 m/s to rest in 5 seconds. Work out its deceleration.
- 4th September 1987A cuboid measures 15 cm by 7 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th September 1987A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th September 1987A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 7th September 1987A block has mass 780 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th September 1987The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 9th September 1987y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 10th September 1987A cuboid measures 8 cm by 4 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th September 1987A bag holds 3 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th September 1987On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th September 1987x = 191 and y = 72, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th September 1987A quadratic sequence starts 9, 21, 43, 75. Work out the second difference, and the coefficient of n^2.
- 15th September 1987y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 16th September 1987The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 17th September 1987A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 18th September 1987A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 19th September 1987A car covers 850 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th September 1987Solve x^2 - x - 2 > 0.
- 21st September 1987y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 9.
- 22nd September 1987In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 23rd September 1987The probability of winning a game is 1/2. A player expects 26 wins. How many games did they play?
- 24th September 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?
- 25th September 1987Rationalise the denominator of 56/sqrt(7), giving your answer in its simplest form.
- 26th September 1987Write x^2 + 14x + 2 in the form (x + a)^2 + b.
- 27th September 1987A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 28th September 1987In a vector proof you find that vector PQ = 2a - 2b and vector RS = 8a - 8b. What does this show about PQ and RS?
- 29th September 1987A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 30th September 1987A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?