Daily Practice · Higher Plus
December 1985 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1985 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1985In 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.
- 2nd December 1985The probability of winning a game is 2/5. A player expects 28 wins. How many games did they play?
- 3rd December 1985On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th December 1985A rectangle is 15 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th December 1985Use the iteration x(n+1) = cube root of (10x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
- 6th December 1985y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 7th December 1985In a vector proof you find that vector PQ = 6a - 4b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 8th December 1985A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 9th December 1985A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 10th December 1985Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 11th December 1985Work out the nth term of the quadratic sequence 3, 7, 15, 27, ...
- 12th December 1985y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 16.
- 13th December 1985A cuboid measures 4 cm by 13 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th December 1985A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th December 1985On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th December 1985A block has mass 470 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th December 1985The point (2, -5) lies on y = f(x). Write down its image on y = f(x) + 1.
- 18th December 1985A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 19th December 1985A cuboid measures 11 cm by 10 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th December 1985A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st December 1985A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 22nd December 1985x = 180 and y = 82, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd December 1985Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 24th December 1985y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 25th December 1985The 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.
- 26th December 1985A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 27th December 1985On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th December 1985A car covers 320 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 December 1985f(x) = 5x - 1 and g(x) = 2x + 2. Work out fg(-2).
- 30th December 1985y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 31st December 1985In 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.