Daily Practice · Higher Plus
October 1972 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1972 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1972x = 180 and y = 89, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd October 1972Solve 9x^2 + 18x + 8 = 0.
- 3rd October 1972A train slows steadily from 28 m/s to rest in 4 seconds. Work out its deceleration.
- 4th October 1972The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 5th October 1972A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 6th October 1972A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 7th October 1972A car covers 440 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th October 1972f(x) = 7x - 6. Work out the inverse function f^-1(x).
- 9th October 1972y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 10th October 1972In 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.
- 11th October 1972The probability of winning a game is 1/4. A player expects 15 wins. How many games did they play?
- 12th October 1972On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th October 1972Rationalise the denominator of 45/sqrt(5), giving your answer in its simplest form.
- 14th October 1972Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 15th October 1972y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 16th October 1972In a vector proof you find that vector PQ = 3a - 2b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 17th October 1972A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 18th October 1972A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 19th October 1972Simplify sqrt(18) + sqrt(18), giving your answer in the form a sqrt(b).
- 20th October 1972Use the iteration x(n+1) = cube root of (10x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 21st October 1972y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 25.
- 22nd October 1972A cuboid measures 6 cm by 10 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd October 1972A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th October 1972On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th October 1972A rectangle is 26 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th October 1972Work out the nth term of the quadratic sequence 12, 20, 30, 42, ...
- 27th October 1972A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 28th October 1972A cuboid measures 12 cm by 9 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th October 1972A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th October 1972A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 31st October 1972Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).