Daily Practice · Higher Plus
April 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1992 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1992A rectangle is 29 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd April 1992In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 3rd April 1992y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 4th April 1992In a vector proof you find that vector PQ = 2a + 6b and vector RS = 10a + 30b. What does this show about PQ and RS?
- 5th April 1992A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 6th April 1992On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th April 1992Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 8th April 1992Make x the subject of 5x + 8 = y(x + 8).
- 9th April 1992A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 10th April 1992A cuboid measures 5 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th April 1992A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th April 1992A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 13th April 1992A block has mass 220 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th April 1992Write 3/(x + 3) + 4/(x - 5) as a single fraction.
- 15th April 1992y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 16th April 1992A cuboid measures 11 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th April 1992A bag holds 6 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th April 1992On 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?
- 19th April 1992x = 199 and y = 63, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th April 1992Solve 4x^2 - 13x - 12 = 0.
- 21st April 1992y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 22nd April 1992The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 23rd April 1992A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 24th April 1992A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 25th April 1992A car covers 350 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.
- 26th April 1992f(x) = 3x + 3. Work out the inverse function f^-1(x).
- 27th April 1992y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 64.
- 28th April 1992In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 29th April 1992The probability of winning a game is 3/4. A player expects 27 wins. How many games did they play?
- 30th April 1992On 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?