Daily Practice · Higher Plus

September 1964 5-a-day

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September 1964

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' September 1964 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 1964

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 1964Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
  2. 2nd September 1964f(x) = 3x - 2. Work out the inverse function f^-1(x).
  3. 3rd September 1964A train slows steadily from 32 m/s to rest in 10 seconds. Work out its deceleration.
  4. 4th September 1964A cuboid measures 3 cm by 5 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  5. 5th September 1964A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  6. 6th September 1964A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
  7. 7th September 1964A block has mass 250 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  8. 8th September 1964Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
  9. 9th September 1964y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
  10. 10th September 1964A cuboid measures 13 cm by 7 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  11. 11th September 1964A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  12. 12th September 1964On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  13. 13th September 1964x = 115 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
  14. 14th September 1964Use the iteration x(n+1) = cube root of (3x(n) + 1) with x(0) = 4. Work out x(1) to 3 decimal places.
  15. 15th September 1964y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
  16. 16th September 1964The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
  17. 17th September 1964A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
  18. 18th September 1964A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
  19. 19th September 1964A car covers 240 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.
  20. 20th September 1964Work out the nth term of the quadratic sequence -4, 0, 8, 20, ...
  21. 21st September 1964y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
  22. 22nd September 1964In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  23. 23rd September 1964The probability of winning a game is 1/2. A player expects 4 wins. How many games did they play?
  24. 24th September 1964On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  25. 25th September 1964Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
  26. 26th September 1964The point (0, 5) lies on y = f(x). Write down its image on y = f(x) + 5.
  27. 27th September 1964A train slows steadily from 21 m/s to rest in 4 seconds. Work out its deceleration.
  28. 28th September 1964In a vector proof you find that vector PQ = 2a - 6b and vector RS = 8a - 24b. What does this show about PQ and RS?
  29. 29th September 1964A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
  30. 30th September 1964A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?

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