Daily Practice · Higher Plus
December 1962 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1962 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1962
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1962y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 2nd December 1962In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 3rd December 1962The probability of winning a game is 1/4. A player expects 15 wins. How many games did they play?
- 4th December 1962On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th December 1962A rectangle is 17 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th December 1962In an algebraic proof, how would you write an odd number in terms of an integer n?
- 7th December 1962y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 8th December 1962In a vector proof you find that vector PQ = 3a - 2b and vector RS = 9a - 6b. What does this show about PQ and RS?
- 9th December 1962A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 10th December 1962A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 11th December 1962Expand and simplify (7 + sqrt(6))(7 - sqrt(6)).
- 12th December 1962Make x the subject of 4x + 3 = y(x + 3).
- 13th December 1962y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
- 14th December 1962A cuboid measures 5 cm by 7 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th December 1962A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th December 1962On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th December 1962A block has mass 350 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th December 1962Write 4/(x - 2) + 2/(x - 4) as a single fraction.
- 19th December 1962A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 20th December 1962A cuboid measures 12 cm by 4 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st December 1962A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd December 1962A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 23rd December 1962x = 168 and y = 139, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th December 1962Solve 9x^2 + 9x + 2 = 0.
- 25th December 1962y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 26th December 1962The 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.
- 27th December 1962A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 28th December 1962On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 29th December 1962A car covers 440 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 30th December 1962f(x) = 5x - 10. Work out the inverse function f^-1(x).
- 31st December 1962y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.