Daily Practice · Higher Plus

September 1988 5-a-day

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September 1988

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' September 1988 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 1988

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 1988Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
  2. 2nd September 1988Solve 8x^2 + 18x - 5 = 0.
  3. 3rd September 1988y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
  4. 4th September 1988A cuboid measures 6 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  5. 5th September 1988A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  6. 6th September 1988On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  7. 7th September 1988A rectangle is 27 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
  8. 8th September 1988f(x) = 7x + 7. Work out the inverse function f^-1(x).
  9. 9th September 1988y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
  10. 10th September 1988The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
  11. 11th September 1988A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
  12. 12th September 1988A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
  13. 13th September 1988Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
  14. 14th September 1988Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
  15. 15th September 1988y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 16.
  16. 16th September 1988In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
  17. 17th September 1988The probability of winning a game is 3/10. A player expects 15 wins. How many games did they play?
  18. 18th September 1988On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
  19. 19th September 1988A block has mass 670 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  20. 20th September 1988Use the iteration x(n+1) = cube root of (7x(n) + 3) with x(0) = 4. Work out x(1) to 3 decimal places.
  21. 21st September 1988A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
  22. 22nd September 1988In a vector proof you find that vector PQ = 6a + 6b and vector RS = 12a + 12b. What does this show about PQ and RS?
  23. 23rd September 1988A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
  24. 24th September 1988A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
  25. 25th September 1988x = 127 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
  26. 26th September 1988Work out the nth term of the quadratic sequence 3, 14, 33, 60, ...
  27. 27th September 1988y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
  28. 28th September 1988A cuboid measures 11 cm by 9 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  29. 29th September 1988A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  30. 30th September 1988On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?

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