Daily Practice · Higher Plus

October 1982 5-a-day

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October 1982

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' October 1982 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in October 1982

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st October 1982A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  2. 2nd October 1982A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
  3. 3rd October 1982x = 61 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
  4. 4th October 1982In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
  5. 5th October 1982y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
  6. 6th October 1982A cuboid measures 13 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  7. 7th October 1982A bag holds 4 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  8. 8th October 1982On 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?
  9. 9th October 1982A car covers 730 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  10. 10th October 1982Make x the subject of 3x + 8 = y(x + 8).
  11. 11th October 1982y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
  12. 12th October 1982The 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.
  13. 13th October 1982A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
  14. 14th October 1982A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
  15. 15th October 1982Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
  16. 16th October 1982Write 5/(x + 1) + 6/(x + 2) as a single fraction.
  17. 17th October 1982y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 4.
  18. 18th October 1982In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
  19. 19th October 1982The probability of winning a game is 3/5. A player expects 6 wins. How many games did they play?
  20. 20th October 1982On 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?
  21. 21st October 1982Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
  22. 22nd October 1982Solve 5x^2 + 9x + 4 = 0.
  23. 23rd October 1982A train slows steadily from 26 m/s to rest in 8 seconds. Work out its deceleration.
  24. 24th October 1982In a vector proof you find that vector PQ = a + b and vector RS = 5a + 5b. What does this show about PQ and RS?
  25. 25th October 1982A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
  26. 26th October 1982A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
  27. 27th October 1982A rectangle is 5 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
  28. 28th October 1982f(x) = 6x - 11. Work out the inverse function f^-1(x).
  29. 29th October 1982y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
  30. 30th October 1982A cuboid measures 10 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  31. 31st October 1982A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?

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