Daily Practice · Higher Plus
October 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1955 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1955A car covers 260 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd October 1955Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 3rd October 1955y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 4th October 1955The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 5th October 1955A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 6th October 1955On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th October 1955Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 8th October 1955Use the iteration x(n+1) = cube root of (5x(n) + 4) with x(0) = 1. Work out x(1) to 3 decimal places.
- 9th October 1955y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 10th October 1955In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 11th October 1955The probability of winning a game is 7/8. A player expects 91 wins. How many games did they play?
- 12th October 1955A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 13th October 1955Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
- 14th October 1955Work out the nth term of the quadratic sequence -6, -2, 8, 24, ...
- 15th October 1955y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 16.
- 16th October 1955In a vector proof you find that vector PQ = 2a + b and vector RS = 10a + 5b. What does this show about PQ and RS?
- 17th October 1955A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 18th October 1955On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th October 1955A rectangle is 11 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th October 1955The point (5, 5) lies on y = f(x). Write down its image on y = f(x) - 1.
- 21st October 1955A train slows steadily from 23 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd October 1955A cuboid measures 12 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd October 1955A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th October 1955A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 25th October 1955Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
- 26th October 1955Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 27th October 1955y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 28th October 1955A cuboid measures 7 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th October 1955A bag holds 3 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th October 1955On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 31st October 1955A block has mass 710 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.