Daily Practice · Higher Plus
May 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1983x = 117 and y = 74, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd May 1983Make x the subject of 7x + 4 = y(x + 4).
- 3rd May 1983A train slows steadily from 34 m/s to rest in 5 seconds. Work out its deceleration.
- 4th May 1983A cuboid measures 8 cm by 13 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th May 1983A bag holds 7 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th May 1983A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 7th May 1983A car covers 680 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.
- 8th May 1983Write 5/(x - 6) + 6/(x - 5) as a single fraction.
- 9th May 1983y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 10th May 1983The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 11th May 1983A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 12th May 1983On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th May 1983Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 14th May 1983Solve 16x^2 + 24x + 5 = 0.
- 15th May 1983y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 16th May 1983In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 17th May 1983The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
- 18th May 1983A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 19th May 1983Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 20th May 1983f(x) = 5x - 1. Work out the inverse function f^-1(x).
- 21st May 1983y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 36.
- 22nd May 1983In a vector proof you find that vector PQ = a + 2b and vector RS = 5a + 10b. What does this show about PQ and RS?
- 23rd May 1983A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 24th May 1983On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th May 1983A rectangle is 22 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th May 1983Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 27th May 1983A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 28th May 1983A cuboid measures 11 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th May 1983A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th May 1983A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 31st May 1983Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).