Daily Practice · Higher Plus
August 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1992y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 4.
- 2nd August 1992In a vector proof you find that vector PQ = 4a - b and vector RS = 8a - 2b. What does this show about PQ and RS?
- 3rd August 1992A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 4th August 1992On 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?
- 5th August 1992A rectangle is 16 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th August 1992f(x) = 7x + 1. Work out the inverse function f^-1(x).
- 7th August 1992A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
- 8th August 1992A cuboid measures 14 cm by 14 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th August 1992A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th August 1992A 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?
- 11th August 1992Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 12th August 1992Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 13th August 1992y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 14th August 1992A cuboid measures 14 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th August 1992A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th August 1992On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th August 1992A block has mass 820 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th August 1992Use the iteration x(n+1) = cube root of (5x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
- 19th August 1992y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 20th August 1992The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 21st August 1992A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 22nd August 1992A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 23rd August 1992x = 91 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th August 1992Work out the nth term of the quadratic sequence -2, 5, 16, 31, ...
- 25th August 1992y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 4.
- 26th August 1992In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 27th August 1992The probability of winning a game is 1/2. A player expects 6 wins. How many games did they play?
- 28th August 1992On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th August 1992A car covers 120 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.
- 30th August 1992The point (0, -2) lies on y = f(x). Write down its image on y = f(x + 6).
- 31st August 1992A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.