Daily Practice · Higher Plus
August 1971 5-a-day
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The batch download puts all 5 tiers' August 1971 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1971A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 2nd August 1971A block has mass 810 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.
- 3rd August 1971In an algebraic proof, how would you write a multiple of 3 in terms of an integer n?
- 4th August 1971y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 5th August 1971A cuboid measures 6 cm by 10 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th August 1971A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th August 1971On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th August 1971x = 131 and y = 73, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th August 1971Make x the subject of 8x + 8 = y(x + 8).
- 10th August 1971y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 11th August 1971The 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.
- 12th August 1971A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 13th August 1971A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 14th August 1971A car covers 740 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.
- 15th August 1971Write 6/(x - 6) + 5/(x + 3) as a single fraction.
- 16th August 1971y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 25.
- 17th August 1971In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 18th August 1971The probability of winning a game is 1/2. A player expects 75 wins. How many games did they play?
- 19th August 1971On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th August 1971Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 21st August 1971Solve 12x^2 + 23x + 10 = 0.
- 22nd August 1971A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd August 1971In a vector proof you find that vector PQ = 6a - 4b and vector RS = 30a - 20b. What does this show about PQ and RS?
- 24th August 1971A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 25th August 1971A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 26th August 1971Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).
- 27th August 1971f(x) = 7x + 6. Work out the inverse function f^-1(x).
- 28th August 1971y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 29th August 1971A cuboid measures 3 cm by 15 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th August 1971A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st August 1971On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?