Daily Practice · Higher Plus
October 1977 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1977A train slows steadily from 18 m/s to rest in 4 seconds. Work out its deceleration.
- 2nd October 1977A cuboid measures 12 cm by 5 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd October 1977A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th October 1977A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 5th October 1977A rectangle is 17 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th October 1977Write 5/(x + 5) + 6/(x - 6) as a single fraction.
- 7th October 1977y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 8th October 1977The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 9th October 1977A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
- 10th October 1977On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th October 1977Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 12th October 1977Solve 12x^2 + 29x + 15 = 0.
- 13th October 1977y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 14th October 1977In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 15th October 1977The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 16th October 1977A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 17th October 1977A block has mass 710 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th October 1977f(x) = 5x + 12. Work out the inverse function f^-1(x).
- 19th October 1977y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 81.
- 20th October 1977In a vector proof you find that vector PQ = 4a - 2b and vector RS = 12a - 6b. What does this show about PQ and RS?
- 21st October 1977A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 22nd October 1977On 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?
- 23rd October 1977x = 89 and y = 27, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th October 1977Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 25th October 1977A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 26th October 1977A cuboid measures 14 cm by 3 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th October 1977A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th October 1977A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 29th October 1977A car covers 350 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.
- 30th October 1977Use the iteration x(n+1) = cube root of (4x(n) + 9) with x(0) = 1. Work out x(1) to 3 decimal places.
- 31st October 1977y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.