Daily Practice · Higher Plus
August 1975 5-a-day
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The batch download puts all 5 tiers' August 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1975A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 2nd August 1975In a vector proof you find that vector PQ = a - 3b and vector RS = 2a - 6b. What does this show about PQ and RS?
- 3rd August 1975A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 4th August 1975A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 5th August 1975Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 6th August 1975Use the iteration x(n+1) = cube root of (11x(n) + 1) with x(0) = 5. Work out x(1) to 3 decimal places.
- 7th August 1975y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 8th August 1975A cuboid measures 8 cm by 11 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th August 1975A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th August 1975On 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?
- 11th August 1975A block has mass 470 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th August 1975Work out the nth term of the quadratic sequence 5, 20, 43, 74, ...
- 13th August 1975y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 14th August 1975A cuboid measures 6 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 1975A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th August 1975A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 17th August 1975x = 110 and y = 82, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th August 1975The point (4, -3) lies on y = f(x). Write down its image on y = f(x) - 2.
- 19th August 1975y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 9.
- 20th August 1975The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 21st August 1975A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 22nd August 1975On 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?
- 23rd August 1975A car covers 280 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th August 1975Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 25th August 1975A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 26th August 1975In 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.
- 27th August 1975The probability of winning a game is 5/8. A player expects 45 wins. How many games did they play?
- 28th August 1975A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 29th August 1975Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 30th August 1975f(x) = 4x - 2 and g(x) = 4x + 3. Work out fg(-3).
- 31st August 1975y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.