Daily Practice · Higher Plus
May 1986 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1986The probability of winning a game is 2/5. A player expects 26 wins. How many games did they play?
- 2nd May 1986A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 3rd May 1986A car covers 470 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th May 1986Write x^2 + 10x + 5 in the form (x + a)^2 + b.
- 5th May 1986y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 64.
- 6th May 1986In a vector proof you find that vector PQ = 6a + b and vector RS = 30a + 5b. What does this show about PQ and RS?
- 7th May 1986A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 8th May 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?
- 9th May 1986Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.
- 10th May 1986Work out the coordinates of the turning point of y = x^2 + 2x - 3.
- 11th May 1986A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 12th May 1986A cuboid measures 4 cm by 15 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th May 1986A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th May 1986A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 15th May 1986Simplify sqrt(72) + sqrt(32), giving your answer in the form a sqrt(b).
- 16th May 1986Simplify (x^2 - 5x + 4)/(x - 4).
- 17th May 1986y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 18th May 1986A cuboid measures 7 cm by 5 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th May 1986A bag holds 6 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th May 1986On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st May 1986A rectangle is 24 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd May 1986In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 23rd May 1986y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 24th May 1986The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 25th May 1986A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 26th May 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?
- 27th May 1986Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 28th May 1986Make x the subject of 7x + 5 = y(x + 5).
- 29th May 1986y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 16.
- 30th May 1986In 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.
- 31st May 1986The probability of winning a game is 3/5. A player expects 6 wins. How many games did they play?