Daily Practice · Higher Plus
March 1986 5-a-day
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The batch download puts all 5 tiers' March 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1986In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 2nd March 1986The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
- 3rd March 1986A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 4th March 1986Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 5th March 1986f(x) = 3x + 6. Work out the inverse function f^-1(x).
- 6th March 1986y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 7th March 1986In a vector proof you find that vector PQ = 3a + 6b and vector RS = 6a + 12b. What does this show about PQ and RS?
- 8th March 1986A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 9th March 1986On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th March 1986A block has mass 350 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th March 1986Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 12th March 1986y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 13th March 1986A cuboid measures 13 cm by 10 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th March 1986A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th March 1986A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 16th March 1986x = 90 and y = 76, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th March 1986Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
- 18th March 1986y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 4.
- 19th March 1986A cuboid measures 12 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th March 1986A bag holds 6 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st March 1986On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd March 1986A car covers 680 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.
- 23rd March 1986Work out the nth term of the quadratic sequence 7, 10, 15, 22, ...
- 24th March 1986A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 25th March 1986The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 26th March 1986A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 27th March 1986A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 28th March 1986Rationalise the denominator of 110/sqrt(11), giving your answer in its simplest form.
- 29th March 1986The point (1, -2) lies on y = f(x). Write down its image on y = -f(x).
- 30th March 1986y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 31st March 1986In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.