Daily Practice · Higher Plus
August 1973 5-a-day
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The batch download puts all 5 tiers' August 1973 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1973
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1973A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 2nd August 1973A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 3rd August 1973Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 4th August 1973Solve 4x^2 + 12x + 5 = 0.
- 5th August 1973y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 49.
- 6th August 1973In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 7th August 1973The probability of winning a game is 1/2. A player expects 52 wins. How many games did they play?
- 8th August 1973On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th August 1973Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
- 10th August 1973f(x) = 7x - 1. Work out the inverse function f^-1(x).
- 11th August 1973A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 12th August 1973In a vector proof you find that vector PQ = 2a + b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 13th August 1973A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 14th August 1973A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 15th August 1973A rectangle is 21 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th August 1973Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 17th August 1973y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 18th August 1973A cuboid measures 5 cm by 14 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th August 1973A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th August 1973On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st August 1973Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 22nd August 1973Use the iteration x(n+1) = cube root of (7x(n) + 1) with x(0) = 3. Work out x(1) to 3 decimal places.
- 23rd August 1973y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 24th August 1973A cuboid measures 4 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th August 1973A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th August 1973A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 27th August 1973A block has mass 630 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th August 1973Work out the nth term of the quadratic sequence 14, 28, 48, 74, ...
- 29th August 1973y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 36.
- 30th August 1973The 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.
- 31st August 1973A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.