Daily Practice · Higher Plus
October 1967 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1967 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1967The 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.
- 2nd October 1967A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 3rd October 1967On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th October 1967A rectangle is 9 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th October 1967Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 6th October 1967A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.
- 7th October 1967In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 8th October 1967The probability of winning a game is 1/5. A player expects 8 wins. How many games did they play?
- 9th October 1967A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 10th October 1967Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 11th October 1967Use the iteration x(n+1) = cube root of (5x(n) + 5) with x(0) = 4. Work out x(1) to 3 decimal places.
- 12th October 1967y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 13th October 1967In a vector proof you find that vector PQ = 4a - 6b and vector RS = 8a - 12b. What does this show about PQ and RS?
- 14th October 1967A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 15th October 1967On 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?
- 16th October 1967A block has mass 570 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th October 1967Work out the nth term of the quadratic sequence 14, 31, 56, 89, ...
- 18th October 1967y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 19th October 1967A cuboid measures 6 cm by 12 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th October 1967A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st October 1967A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 22nd October 1967x = 138 and y = 126, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd October 1967The point (0, 1) lies on y = f(x). Write down its image on y = f(x) + 5.
- 24th October 1967y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 16.
- 25th October 1967A cuboid measures 7 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th October 1967A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th October 1967On 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?
- 28th October 1967A car covers 800 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th October 1967Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 30th October 1967A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
- 31st October 1967The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.