Daily Practice · Higher Plus
October 1952 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1952 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1952
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1952In a vector proof you find that vector PQ = 4a - 3b and vector RS = 20a - 15b. What does this show about PQ and RS?
- 2nd October 1952A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
- 3rd October 1952A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 4th October 1952A car covers 900 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th October 1952f(x) = 5x - 2 and g(x) = 3x - 1. Work out fg(4).
- 6th October 1952y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 81.
- 7th October 1952A cuboid measures 13 cm by 8 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th October 1952A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th October 1952On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th October 1952Rationalise the denominator of 24/sqrt(2), giving your answer in its simplest form.
- 11th October 1952The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 12th October 1952A train slows steadily from 17 m/s to rest in 8 seconds. Work out its deceleration.
- 13th October 1952A cuboid measures 4 cm by 9 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th October 1952A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th October 1952A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 16th October 1952Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).
- 17th October 1952A quadratic sequence starts -4, 4, 20, 44. Work out the second difference, and the coefficient of n^2.
- 18th October 1952y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 19th October 1952The 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.
- 20th October 1952A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 21st October 1952On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 22nd October 1952A rectangle is 16 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd October 1952Solve x^2 - 6x < 0.
- 24th October 1952y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 25th October 1952In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 26th October 1952The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?
- 27th October 1952A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 28th October 1952Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 29th October 1952Write x^2 + 2x - 4 in the form (x + a)^2 + b.
- 30th October 1952y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 16.
- 31st October 1952In a vector proof you find that vector PQ = 2a - 5b and vector RS = 6a - 15b. What does this show about PQ and RS?