Daily Practice · Higher Plus
December 1972 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1972 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1972Solve x^2 - 3x < 0.
- 2nd December 1972y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 3rd December 1972The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 4th December 1972A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 5th December 1972A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 6th December 1972A rectangle is 28 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th December 1972Write x^2 + 4x - 10 in the form (x + a)^2 + b.
- 8th December 1972y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 9.
- 9th December 1972In 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.
- 10th December 1972The probability of winning a game is 1/2. A player expects 10 wins. How many games did they play?
- 11th December 1972On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th December 1972Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 13th December 1972Work out the coordinates of the turning point of y = x^2 + 14x - 6.
- 14th December 1972A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 15th December 1972In a vector proof you find that vector PQ = 2a + 2b and vector RS = 4a + 4b. What does this show about PQ and RS?
- 16th December 1972A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 17th December 1972A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 18th December 1972A block has mass 520 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.
- 19th December 1972Simplify (x^2 - 2x - 48)/(x - 8).
- 20th December 1972y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 21st December 1972A cuboid measures 11 cm by 8 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd December 1972A bag holds 9 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 1972On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th December 1972x = 109 and y = 34, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th December 1972In an algebraic proof, how would you write an odd number in terms of an integer n?
- 26th December 1972y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 27th December 1972A cuboid measures 14 cm by 11 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th December 1972A 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?
- 29th December 1972A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 30th December 1972A car covers 530 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.
- 31st December 1972Make x the subject of 5x + 8 = y(x + 8).