Daily Practice · Higher Plus

September 1962 5-a-day

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September 1962

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' September 1962 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 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 September 1962Make x the subject of 5x + 3 = y(x + 3).
  2. 2nd September 1962y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
  3. 3rd September 1962In 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.
  4. 4th September 1962The probability of winning a game is 7/10. A player expects 63 wins. How many games did they play?
  5. 5th September 1962A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
  6. 6th September 1962Simplify sqrt(32) + sqrt(2), giving your answer in the form a sqrt(b).
  7. 7th September 1962Write 7/(x - 4) + 6/(x - 6) as a single fraction.
  8. 8th September 1962y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 9.
  9. 9th September 1962In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
  10. 10th September 1962A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
  11. 11th September 1962On 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?
  12. 12th September 1962A rectangle is 14 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
  13. 13th September 1962Solve 6x^2 + 13x + 5 = 0.
  14. 14th September 1962A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
  15. 15th September 1962A cuboid measures 8 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  16. 16th September 1962A 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?
  17. 17th September 1962A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
  18. 18th September 1962Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
  19. 19th September 1962f(x) = 6x - 12. Work out the inverse function f^-1(x).
  20. 20th September 1962y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
  21. 21st September 1962A cuboid measures 5 cm by 5 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  22. 22nd September 1962A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  23. 23rd September 1962On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  24. 24th September 1962A block has mass 260 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  25. 25th September 1962Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
  26. 26th September 1962y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
  27. 27th September 1962The 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.
  28. 28th September 1962A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
  29. 29th September 1962A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
  30. 30th September 1962x = 55 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.

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