Daily Practice · Higher Plus
August 1952 5-a-day
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The batch download puts all 5 tiers' August 1952 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1952
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1952A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 2nd August 1952In a vector proof you find that vector PQ = a - 3b and vector RS = 3a - 9b. What does this show about PQ and RS?
- 3rd August 1952A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 4th August 1952A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 5th August 1952Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 6th August 1952In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 7th August 1952y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 8th August 1952A cuboid measures 11 cm by 12 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th August 1952A 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?
- 10th August 1952On 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?
- 11th August 1952A block has mass 550 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th August 1952Make x the subject of 7x + 3 = y(x + 3).
- 13th August 1952y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 14th August 1952A cuboid measures 6 cm by 8 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th August 1952A bag holds 6 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th August 1952A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 17th August 1952x = 44 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th August 1952Write 4/(x + 3) + 5/(x + 2) as a single fraction.
- 19th August 1952y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 81.
- 20th August 1952The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 21st August 1952A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 22nd August 1952On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd August 1952A car covers 150 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th August 1952Solve 4x^2 - 1 = 0.
- 25th August 1952A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 26th August 1952In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 27th August 1952The probability of winning a game is 1/4. A player expects 9 wins. How many games did they play?
- 28th August 1952A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 29th August 1952Rationalise the denominator of 12/sqrt(3), giving your answer in its simplest form.
- 30th August 1952f(x) = 3x - 7. Work out the inverse function f^-1(x).
- 31st August 1952y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.