Daily Practice · Higher Plus
October 1953 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1953y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 25.
- 2nd October 1953A cuboid measures 4 cm by 13 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd October 1953A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th October 1953On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th October 1953A block has mass 510 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th October 1953Solve 15x^2 - 23x + 4 = 0.
- 7th October 1953A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 8th October 1953A cuboid measures 8 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th October 1953A bag holds 3 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th October 1953A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 11th October 1953x = 162 and y = 116, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th October 1953f(x) = 4x + 1. Work out the inverse function f^-1(x).
- 13th October 1953y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 14th October 1953The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 15th October 1953A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 16th October 1953On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th October 1953A car covers 560 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.
- 18th October 1953Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 19th October 1953y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 20th October 1953In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 21st October 1953The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
- 22nd October 1953A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 23rd October 1953Rationalise the denominator of 132/sqrt(11), giving your answer in its simplest form.
- 24th October 1953Use the iteration x(n+1) = cube root of (4x(n) + 9) with x(0) = 2. Work out x(1) to 3 decimal places.
- 25th October 1953y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 16.
- 26th October 1953In a vector proof you find that vector PQ = a + 4b and vector RS = 2a + 8b. What does this show about PQ and RS?
- 27th October 1953A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 28th October 1953On 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?
- 29th October 1953Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 30th October 1953Work out the nth term of the quadratic sequence -1, 12, 33, 62, ...
- 31st October 1953A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.