Daily Practice · Higher Plus
October 1984 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1984 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1984The 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.
- 2nd October 1984A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 3rd October 1984A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 4th October 1984Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
- 5th October 1984Solve 12x^2 + 5x - 3 = 0.
- 6th October 1984y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 81.
- 7th October 1984In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 8th October 1984The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
- 9th October 1984On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th October 1984A rectangle is 29 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th October 1984f(x) = 3x - 5. Work out the inverse function f^-1(x).
- 12th October 1984A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
- 13th October 1984In a vector proof you find that vector PQ = 6a - 2b and vector RS = 30a - 10b. What does this show about PQ and RS?
- 14th October 1984A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 15th October 1984A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 16th October 1984Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 17th October 1984Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 18th October 1984y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 19th October 1984A cuboid measures 4 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th October 1984A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st October 1984On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd October 1984A block has mass 410 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd October 1984Use the iteration x(n+1) = cube root of (11x(n) + 9) with x(0) = 2. Work out x(1) to 3 decimal places.
- 24th October 1984y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 25th October 1984A cuboid measures 6 cm by 14 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th October 1984A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th October 1984A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 28th October 1984x = 40 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th October 1984Work out the nth term of the quadratic sequence 3, 6, 11, 18, ...
- 30th October 1984y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 49.
- 31st October 1984The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.