Daily Practice · Higher Plus
May 1978 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1978 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1978A bag holds 5 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd May 1978On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd May 1978A rectangle is 9 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th May 1978Solve 20x^2 - x - 12 = 0.
- 5th May 1978A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 6th May 1978The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 7th May 1978A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 8th May 1978A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 9th May 1978Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 10th May 1978f(x) = 4x + 8. Work out the inverse function f^-1(x).
- 11th May 1978y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 12th May 1978In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 13th May 1978The probability of winning a game is 3/8. A player expects 42 wins. How many games did they play?
- 14th May 1978On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th May 1978A block has mass 780 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th May 1978Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 17th May 1978y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 18th May 1978In a vector proof you find that vector PQ = 3a - 4b and vector RS = 12a - 16b. What does this show about PQ and RS?
- 19th May 1978A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 20th May 1978A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 21st May 1978x = 47 and y = 31, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd May 1978Use the iteration x(n+1) = cube root of (12x(n) + 1) with x(0) = 1. Work out x(1) to 3 decimal places.
- 23rd May 1978y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 16.
- 24th May 1978A cuboid measures 11 cm by 13 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th May 1978A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th May 1978On 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?
- 27th May 1978A car covers 840 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.
- 28th May 1978Work out the nth term of the quadratic sequence -5, -7, -7, -5, ...
- 29th May 1978A train slows steadily from 16 m/s to rest in 10 seconds. Work out its deceleration.
- 30th May 1978A cuboid measures 4 cm by 4 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st May 1978A bag holds 3 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?