Daily Practice · Higher Plus
December 1952 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1952 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1952
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1952A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 2nd December 1952A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 3rd December 1952A rectangle is 15 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th December 1952Solve 8x^2 - 10x - 25 = 0.
- 5th December 1952y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 6th December 1952A cuboid measures 14 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th December 1952A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th December 1952On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th December 1952Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 10th December 1952f(x) = 4x + 1. Work out the inverse function f^-1(x).
- 11th December 1952y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 12th December 1952A cuboid measures 9 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th December 1952A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th December 1952A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 15th December 1952A block has mass 680 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th December 1952Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 17th December 1952y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 49.
- 18th December 1952The 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.
- 19th December 1952A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 20th December 1952On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st December 1952x = 115 and y = 82, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd December 1952Use the iteration x(n+1) = cube root of (2x(n) + 6) with x(0) = 5. Work out x(1) to 3 decimal places.
- 23rd December 1952A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 24th December 1952In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 25th December 1952The probability of winning a game is 7/10. A player expects 70 wins. How many games did they play?
- 26th December 1952A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 27th December 1952A car covers 820 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th December 1952Work out the nth term of the quadratic sequence 7, 15, 27, 43, ...
- 29th December 1952y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 30th December 1952In a vector proof you find that vector PQ = 5a - 3b and vector RS = 20a - 12b. What does this show about PQ and RS?
- 31st December 1952A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.