Daily Practice · Higher Plus

December 1962 5-a-day

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December 1962

31 sheets · 155 questions · Grades 8-9

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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.

  1. 1st December 1962y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
  2. 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.
  3. 3rd December 1962The probability of winning a game is 1/4. A player expects 15 wins. How many games did they play?
  4. 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?
  5. 5th December 1962A rectangle is 17 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
  6. 6th December 1962In an algebraic proof, how would you write an odd number in terms of an integer n?
  7. 7th December 1962y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
  8. 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?
  9. 9th December 1962A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
  10. 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?
  11. 11th December 1962Expand and simplify (7 + sqrt(6))(7 - sqrt(6)).
  12. 12th December 1962Make x the subject of 4x + 3 = y(x + 3).
  13. 13th December 1962y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
  14. 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.
  15. 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?
  16. 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?
  17. 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.
  18. 18th December 1962Write 4/(x - 2) + 2/(x - 4) as a single fraction.
  19. 19th December 1962A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
  20. 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.
  21. 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?
  22. 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?
  23. 23rd December 1962x = 168 and y = 139, each correct to the nearest whole number. Work out the upper bound of x - y.
  24. 24th December 1962Solve 9x^2 + 9x + 2 = 0.
  25. 25th December 1962y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
  26. 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.
  27. 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.
  28. 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?
  29. 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.
  30. 30th December 1962f(x) = 5x - 10. Work out the inverse function f^-1(x).
  31. 31st December 1962y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.

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