Daily Practice · Higher Plus

September 1982 5-a-day

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September 1982

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' September 1982 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 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 September 1982A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  2. 2nd September 1982On 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?
  3. 3rd September 1982Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
  4. 4th September 1982A quadratic sequence starts 1, 12, 29, 52. Work out the second difference, and the coefficient of n^2.
  5. 5th September 1982A train slows steadily from 13 m/s to rest in 4 seconds. Work out its deceleration.
  6. 6th September 1982A cuboid measures 11 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  7. 7th September 1982A bag holds 7 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  8. 8th September 1982A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
  9. 9th September 1982Simplify sqrt(72) + sqrt(8), giving your answer in the form a sqrt(b).
  10. 10th September 1982Solve x^2 - 6x + 8 > 0.
  11. 11th September 1982y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
  12. 12th September 1982The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
  13. 13th September 1982A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
  14. 14th September 1982On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  15. 15th September 1982A rectangle is 18 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
  16. 16th September 1982Write x^2 - 8x - 4 in the form (x + a)^2 + b.
  17. 17th September 1982y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
  18. 18th September 1982In 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.
  19. 19th September 1982The probability of winning a game is 1/5. A player expects 6 wins. How many games did they play?
  20. 20th September 1982A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
  21. 21st September 1982Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
  22. 22nd September 1982Work out the coordinates of the turning point of y = x^2 - 2x + 9.
  23. 23rd September 1982y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 4.
  24. 24th September 1982In a vector proof you find that vector PQ = 2a - 2b and vector RS = 10a - 10b. What does this show about PQ and RS?
  25. 25th September 1982A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
  26. 26th September 1982On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
  27. 27th September 1982A block has mass 640 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  28. 28th September 1982Simplify (x^2 - 2x - 48)/(x + 6).
  29. 29th September 1982A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
  30. 30th September 1982A cuboid measures 5 cm by 10 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.

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