Daily Practice · Higher Plus

January 1964 5-a-day

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January 1964

31 sheets · 155 questions · Grades 8-9

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

Every sheet in January 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 January 1964y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.
  2. 2nd January 1964In a vector proof you find that vector PQ = 2a + b and vector RS = 8a + 4b. What does this show about PQ and RS?
  3. 3rd January 1964A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
  4. 4th January 1964On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  5. 5th January 1964x = 60 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
  6. 6th January 1964Work out the coordinates of the turning point of y = x^2 - 10x + 13.
  7. 7th January 1964A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
  8. 8th January 1964A cuboid measures 12 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  9. 9th January 1964A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  10. 10th January 1964A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
  11. 11th January 1964A car covers 200 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  12. 12th January 1964Simplify (x^2 + 15x + 56)/(x + 7).
  13. 13th January 1964y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
  14. 14th January 1964A cuboid measures 11 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  15. 15th January 1964A bag holds 5 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  16. 16th January 1964On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  17. 17th January 1964Rationalise the denominator of 21/sqrt(7), giving your answer in its simplest form.
  18. 18th January 1964In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
  19. 19th January 1964y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
  20. 20th January 1964The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
  21. 21st January 1964A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
  22. 22nd January 1964A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
  23. 23rd January 1964Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
  24. 24th January 1964Make x the subject of 7x + 7 = y(x + 7).
  25. 25th January 1964y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 49.
  26. 26th January 1964In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
  27. 27th January 1964The probability of winning a game is 1/5. A player expects 24 wins. How many games did they play?
  28. 28th January 1964On 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?
  29. 29th January 1964A rectangle is 24 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
  30. 30th January 1964Write 6/(x - 2) + 4/(x - 6) as a single fraction.
  31. 31st January 1964A train slows steadily from 31 m/s to rest in 4 seconds. Work out its deceleration.

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