Daily Practice · Higher Plus
December 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1955 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1955Work out the coordinates of the turning point of y = x^2 - 14x + 9.
- 2nd December 1955y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 4.
- 3rd December 1955The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 4th December 1955A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 5th December 1955On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th December 1955Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 7th December 1955Simplify (x^2 - 2x - 3)/(x - 3).
- 8th December 1955A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 9th December 1955In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 10th December 1955The probability of winning a game is 4/5. A player expects 88 wins. How many games did they play?
- 11th December 1955A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 12th December 1955A block has mass 620 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th December 1955In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 14th December 1955y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 15th December 1955In a vector proof you find that vector PQ = a - 2b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 16th December 1955A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 17th December 1955On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th December 1955x = 161 and y = 21, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th December 1955Make x the subject of 3x + 4 = y(x + 4).
- 20th December 1955y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 21st December 1955A cuboid measures 4 cm by 9 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd December 1955A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd December 1955A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 24th December 1955A car covers 630 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th December 1955Write 2/(x + 1) + 6/(x + 4) as a single fraction.
- 26th December 1955y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 49.
- 27th December 1955A cuboid measures 4 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th December 1955A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th December 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th December 1955Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 31st December 1955Solve 2x^2 + 9x - 5 = 0.