Daily Practice · Higher Plus
September 1986 5-a-day
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The batch download puts all 5 tiers' September 1986 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1986In an algebraic proof, how would you write a multiple of 7 in terms of an integer n?
- 2nd September 1986y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 16.
- 3rd September 1986In a vector proof you find that vector PQ = 4a + 3b and vector RS = 12a + 9b. What does this show about PQ and RS?
- 4th September 1986A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 5th September 1986On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th September 1986A car covers 830 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.
- 7th September 1986Make x the subject of 4x + 6 = y(x + 6).
- 8th September 1986A train slows steadily from 13 m/s to rest in 5 seconds. Work out its deceleration.
- 9th September 1986A cuboid measures 3 cm by 11 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th September 1986A bag holds 11 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th September 1986A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 12th September 1986Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 13th September 1986Write 7/(x - 1) + 4/(x + 1) as a single fraction.
- 14th September 1986y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 15th September 1986A cuboid measures 4 cm by 4 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th September 1986A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th September 1986On 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?
- 18th September 1986Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 19th September 1986Solve 12x^2 - 31x + 20 = 0.
- 20th September 1986y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 21st September 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.
- 22nd September 1986A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 23rd September 1986A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 24th September 1986A rectangle is 24 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th September 1986f(x) = 4x - 12. Work out the inverse function f^-1(x).
- 26th September 1986y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 9.
- 27th September 1986In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 28th September 1986The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 29th September 1986On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th September 1986Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).