Daily Practice · Higher Plus
August 1972 5-a-day
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The batch download puts all 5 tiers' August 1972 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1972On 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?
- 2nd August 1972A rectangle is 8 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd August 1972f(x) = 4x + 1 and g(x) = 2x + 6. Work out fg(-2).
- 4th August 1972y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 5th August 1972The 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.
- 6th August 1972A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 7th August 1972A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 8th August 1972Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 9th August 1972The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 10th August 1972y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 64.
- 11th August 1972In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 12th August 1972The probability of winning a game is 1/2. A player expects 18 wins. How many games did they play?
- 13th August 1972On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th August 1972A block has mass 560 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.
- 15th August 1972A quadratic sequence starts 1, 6, 15, 28. Work out the second difference, and the coefficient of n^2.
- 16th August 1972A train slows steadily from 21 m/s to rest in 4 seconds. Work out its deceleration.
- 17th August 1972In a vector proof you find that vector PQ = a - 4b and vector RS = 4a - 16b. What does this show about PQ and RS?
- 18th August 1972A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 19th August 1972A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 20th August 1972x = 87 and y = 65, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st August 1972Solve x^2 + 11x + 24 > 0.
- 22nd August 1972y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 23rd August 1972A cuboid measures 14 cm by 9 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th August 1972A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th August 1972On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th August 1972A car covers 500 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th August 1972Write x^2 + 6x - 12 in the form (x + a)^2 + b.
- 28th August 1972y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 29th August 1972A cuboid measures 6 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th August 1972A bag holds 4 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st August 1972A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?