Daily Practice · Higher Plus
August 1981 5-a-day
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The batch download puts all 5 tiers' August 1981 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1981A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 2nd August 1981On 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?
- 3rd August 1981A block has mass 750 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th August 1981Write x^2 - 2x - 11 in the form (x + a)^2 + b.
- 5th August 1981y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 6th August 1981A cuboid measures 8 cm by 14 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th August 1981A 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?
- 8th August 1981A 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?
- 9th August 1981x = 32 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th August 1981Work out the coordinates of the turning point of y = x^2 - 10x + 8.
- 11th August 1981y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 64.
- 12th August 1981A cuboid measures 14 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th August 1981A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th August 1981On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th August 1981A car covers 390 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 16th August 1981Simplify (x^2 - 8x + 15)/(x - 5).
- 17th August 1981A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 18th August 1981The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 19th August 1981A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 20th August 1981A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 21st August 1981Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 22nd August 1981In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 6 in terms of an integer n?
- 23rd August 1981y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 24th August 1981In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 25th August 1981The probability of winning a game is 5/8. A player expects 75 wins. How many games did they play?
- 26th August 1981On 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?
- 27th August 1981Simplify sqrt(72) + sqrt(8), giving your answer in the form a sqrt(b).
- 28th August 1981Make x the subject of 6x + 4 = y(x + 4).
- 29th August 1981y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 30th August 1981In a vector proof you find that vector PQ = 3a - 6b and vector RS = 9a - 18b. What does this show about PQ and RS?
- 31st August 1981A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.