Daily Practice · Higher Plus
December 1966 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1966 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1966A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 2nd December 1966Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 3rd December 1966Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 4th December 1966y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 5th December 1966The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 6th December 1966A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 7th December 1966On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 8th December 1966Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 9th December 1966Use the iteration x(n+1) = cube root of (7x(n) + 8) with x(0) = 1. Work out x(1) to 3 decimal places.
- 10th December 1966y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 11th December 1966In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 12th December 1966The probability of winning a game is 3/10. A player expects 21 wins. How many games did they play?
- 13th December 1966A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 14th December 1966A rectangle is 4 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th December 1966Work out the nth term of the quadratic sequence 2, 11, 24, 41, ...
- 16th December 1966y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 64.
- 17th December 1966In a vector proof you find that vector PQ = a - 4b and vector RS = 3a - 12b. What does this show about PQ and RS?
- 18th December 1966A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 19th December 1966On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th December 1966Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 21st December 1966The point (1, -2) lies on y = f(x). Write down its image on y = f(x + 1).
- 22nd December 1966A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd December 1966A cuboid measures 12 cm by 10 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th December 1966A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th December 1966A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 26th December 1966A block has mass 620 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th December 1966Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 28th December 1966y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 29th December 1966A cuboid measures 5 cm by 12 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th December 1966A bag holds 4 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st December 1966On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?