Daily Practice · Higher Plus
December 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1983A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd December 1983On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd December 1983A car covers 550 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th December 1983Solve 16x^2 - 1 = 0.
- 5th December 1983A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
- 6th December 1983The 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.
- 7th December 1983A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 8th December 1983A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 9th December 1983Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 10th December 1983f(x) = 8x - 7. Work out the inverse function f^-1(x).
- 11th December 1983y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 12th December 1983In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 13th December 1983The probability of winning a game is 3/4. A player expects 6 wins. How many games did they play?
- 14th December 1983On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th December 1983Simplify sqrt(48) + sqrt(147), giving your answer in the form a sqrt(b).
- 16th December 1983Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 17th December 1983y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 18th December 1983In a vector proof you find that vector PQ = 4a + 5b and vector RS = 16a + 20b. What does this show about PQ and RS?
- 19th December 1983A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th December 1983A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 21st December 1983A rectangle is 18 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd December 1983Use the iteration x(n+1) = cube root of (8x(n) + 1) with x(0) = 3. Work out x(1) to 3 decimal places.
- 23rd December 1983y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 81.
- 24th December 1983A cuboid measures 5 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th December 1983A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th December 1983On 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?
- 27th December 1983Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 28th December 1983Work out the nth term of the quadratic sequence -4, -6, -6, -4, ...
- 29th December 1983A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 30th December 1983A cuboid measures 11 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st December 1983A bag holds 4 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?