Daily Practice · Higher Plus

August 1964 5-a-day

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August 1964

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' August 1964 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in August 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 August 1964A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
  2. 2nd August 1964x = 52 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
  3. 3rd August 1964Simplify (x^2 - 2x - 3)/(x - 3).
  4. 4th August 1964y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 49.
  5. 5th August 1964A cuboid measures 15 cm by 5 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  6. 6th August 1964A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  7. 7th August 1964On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  8. 8th August 1964A car covers 640 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.
  9. 9th August 1964In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 8 in terms of an integer n?
  10. 10th August 1964A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
  11. 11th August 1964A cuboid measures 8 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  12. 12th August 1964A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  13. 13th August 1964A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
  14. 14th August 1964Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
  15. 15th August 1964Make x the subject of 2x + 7 = y(x + 7).
  16. 16th August 1964y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
  17. 17th August 1964The 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.
  18. 18th August 1964A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
  19. 19th August 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?
  20. 20th August 1964Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
  21. 21st August 1964Write 7/(x - 2) + 7/(x - 1) as a single fraction.
  22. 22nd August 1964y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
  23. 23rd August 1964In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
  24. 24th August 1964The probability of winning a game is 4/5. A player expects 72 wins. How many games did they play?
  25. 25th August 1964A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
  26. 26th August 1964A rectangle is 11 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
  27. 27th August 1964Solve 4x^2 + 17x + 4 = 0.
  28. 28th August 1964y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 16.
  29. 29th August 1964In a vector proof you find that vector PQ = 4a + 6b and vector RS = 12a + 18b. What does this show about PQ and RS?
  30. 30th August 1964A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
  31. 31st August 1964On 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?

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