Daily Practice · Higher Plus
December 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1954 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1954y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 2nd December 1954A cuboid measures 13 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd December 1954A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th December 1954A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 5th December 1954x = 184 and y = 104, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th December 1954Use the iteration x(n+1) = cube root of (9x(n) + 4) with x(0) = 3. Work out x(1) to 3 decimal places.
- 7th December 1954y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 64.
- 8th December 1954The 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.
- 9th December 1954A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 10th December 1954On 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?
- 11th December 1954A car covers 710 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th December 1954Work out the nth term of the quadratic sequence 7, 19, 39, 67, ...
- 13th December 1954A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 14th December 1954In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 15th December 1954The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?
- 16th December 1954A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 17th December 1954Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 18th December 1954The point (-4, -1) lies on y = f(x). Write down its image on y = f(x) - 2.
- 19th December 1954y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 20th December 1954In a vector proof you find that vector PQ = 3a + 5b and vector RS = 15a + 25b. What does this show about PQ and RS?
- 21st December 1954A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 22nd December 1954On 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?
- 23rd December 1954Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 24th December 1954Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 25th December 1954y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 26th December 1954A cuboid measures 8 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th December 1954A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th December 1954A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 29th December 1954A rectangle is 30 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th December 1954f(x) = 4x - 8 and g(x) = 3x + 4. Work out fg(5).
- 31st December 1954y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 25.