Daily Practice · Higher Plus
December 1964 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1964 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1964
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1964Write 3/(x + 5) + 5/(x + 6) as a single fraction.
- 2nd December 1964y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 9.
- 3rd December 1964A cuboid measures 13 cm by 8 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th December 1964A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th December 1964On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th December 1964x = 144 and y = 110, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th December 1964Solve 5x^2 + 17x + 6 = 0.
- 8th December 1964A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 9th December 1964A cuboid measures 10 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th December 1964A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th December 1964A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 12th December 1964A car covers 840 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th December 1964f(x) = 5x + 2. Work out the inverse function f^-1(x).
- 14th December 1964y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 15th December 1964The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 16th December 1964A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 17th December 1964On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th December 1964Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 19th December 1964Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 20th December 1964y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 21st December 1964In 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.
- 22nd December 1964The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 23rd December 1964A 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?
- 24th December 1964Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
- 25th December 1964Use the iteration x(n+1) = cube root of (9x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 26th December 1964y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 81.
- 27th December 1964In a vector proof you find that vector PQ = a + 3b and vector RS = 5a + 15b. What does this show about PQ and RS?
- 28th December 1964A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 29th December 1964On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th December 1964A rectangle is 21 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st December 1964Work out the nth term of the quadratic sequence 3, 11, 21, 33, ...