Daily Practice · Higher Plus
April 1989 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1989 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1989A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 2nd April 1989A cuboid measures 5 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd April 1989A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th April 1989A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 5th April 1989A rectangle is 30 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th April 1989Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 7th April 1989y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 8th April 1989The 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.
- 9th April 1989A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 10th April 1989On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th April 1989Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 12th April 1989Use the iteration x(n+1) = cube root of (3x(n) + 9) with x(0) = 2. Work out x(1) to 3 decimal places.
- 13th April 1989y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 14th April 1989In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 15th April 1989The probability of winning a game is 1/4. A player expects 7 wins. How many games did they play?
- 16th April 1989A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 17th April 1989A block has mass 530 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th April 1989Work out the nth term of the quadratic sequence 11, 21, 37, 59, ...
- 19th April 1989y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 4.
- 20th April 1989In a vector proof you find that vector PQ = 2a + 3b and vector RS = 6a + 9b. What does this show about PQ and RS?
- 21st April 1989A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 22nd April 1989On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd April 1989x = 156 and y = 48, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th April 1989The point (3, 3) lies on y = f(x). Write down its image on y = -f(x).
- 25th April 1989A train slows steadily from 25 m/s to rest in 4 seconds. Work out its deceleration.
- 26th April 1989A cuboid measures 13 cm by 3 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th April 1989A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th April 1989A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 29th April 1989A car covers 650 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 30th April 1989Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.