Daily Practice · Higher Plus
October 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1954 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1954A quadratic sequence starts 12, 26, 46, 72. Work out the second difference, and the coefficient of n^2.
- 2nd October 1954A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd October 1954A cuboid measures 4 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th October 1954A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th October 1954A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 6th October 1954A rectangle is 25 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th October 1954Solve x^2 + 5x - 6 > 0.
- 8th October 1954y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 9th October 1954The 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.
- 10th October 1954A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 11th October 1954On 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?
- 12th October 1954Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 13th October 1954Write x^2 - 4x + 8 in the form (x + a)^2 + b.
- 14th October 1954y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 15th October 1954In 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.
- 16th October 1954The probability of winning a game is 4/5. A player expects 120 wins. How many games did they play?
- 17th October 1954A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 18th October 1954A block has mass 520 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th October 1954Work out the coordinates of the turning point of y = x^2 - 14x - 14.
- 20th October 1954y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 9.
- 21st October 1954In a vector proof you find that vector PQ = 5a - 4b and vector RS = 20a - 16b. What does this show about PQ and RS?
- 22nd October 1954A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 23rd October 1954On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th October 1954x = 167 and y = 133, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th October 1954Simplify (x^2 + 7x + 10)/(x + 5).
- 26th October 1954A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 27th October 1954A cuboid measures 11 cm by 10 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th October 1954A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th October 1954A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 30th October 1954A car covers 670 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.
- 31st October 1954In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?