Daily Practice · Higher Plus

September 1960 5-a-day

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September 1960

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' September 1960 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 1960

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 1960A cuboid measures 10 cm by 6 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  2. 2nd September 1960A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  3. 3rd September 1960A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
  4. 4th September 1960x = 134 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
  5. 5th September 1960Simplify (x^2 + x - 56)/(x + 8).
  6. 6th September 1960y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
  7. 7th September 1960The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
  8. 8th September 1960A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
  9. 9th September 1960On 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?
  10. 10th September 1960A car covers 690 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  11. 11th September 1960In an algebraic proof, how would you write a multiple of 4 in terms of an integer n?
  12. 12th September 1960y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
  13. 13th September 1960In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
  14. 14th September 1960The probability of winning a game is 1/10. A player expects 6 wins. How many games did they play?
  15. 15th September 1960A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
  16. 16th September 1960Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
  17. 17th September 1960Make x the subject of 4x + 7 = y(x + 7).
  18. 18th September 1960y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 36.
  19. 19th September 1960In a vector proof you find that vector PQ = 2a - 4b and vector RS = 6a - 12b. What does this show about PQ and RS?
  20. 20th September 1960A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  21. 21st September 1960On 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?
  22. 22nd September 1960Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
  23. 23rd September 1960Write 4/(x + 4) + 4/(x - 3) as a single fraction.
  24. 24th September 1960A train slows steadily from 36 m/s to rest in 10 seconds. Work out its deceleration.
  25. 25th September 1960A cuboid measures 7 cm by 12 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  26. 26th September 1960A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  27. 27th September 1960A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
  28. 28th September 1960A rectangle is 7 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
  29. 29th September 1960Solve 12x^2 - 11x - 15 = 0.
  30. 30th September 1960y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.

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