Daily Practice · Higher Plus
April 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1988 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1988A cuboid measures 9 cm by 9 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd April 1988A 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?
- 3rd April 1988On 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?
- 4th April 1988A block has mass 740 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th April 1988A quadratic sequence starts 15, 23, 33, 45. Work out the second difference, and the coefficient of n^2.
- 6th April 1988A train slows steadily from 36 m/s to rest in 5 seconds. Work out its deceleration.
- 7th April 1988A cuboid measures 8 cm by 12 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th April 1988A bag holds 5 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th April 1988A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 10th April 1988x = 69 and y = 48, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th April 1988Solve x^2 - 4x + 3 > 0.
- 12th April 1988y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 13th April 1988The 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.
- 14th April 1988A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 15th April 1988On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th April 1988A car covers 830 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.
- 17th April 1988Write x^2 - 4x + 9 in the form (x + a)^2 + b.
- 18th April 1988y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 19th April 1988In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 20th April 1988The probability of winning a game is 2/5. A player expects 14 wins. How many games did they play?
- 21st April 1988A 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?
- 22nd April 1988Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
- 23rd April 1988Work out the coordinates of the turning point of y = x^2 - 10x + 6.
- 24th April 1988y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 64.
- 25th April 1988In a vector proof you find that vector PQ = a - 6b and vector RS = 2a - 12b. What does this show about PQ and RS?
- 26th April 1988A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 27th April 1988On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th April 1988Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 29th April 1988Simplify (x^2 + 3x - 40)/(x - 5).
- 30th April 1988A train slows steadily from 32 m/s to rest in 10 seconds. Work out its deceleration.