Daily Practice · Higher Plus

October 1964 5-a-day

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October 1964

31 sheets · 155 questions · Grades 8-9

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

Every sheet in October 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 October 1964Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
  2. 2nd October 1964Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
  3. 3rd October 1964y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
  4. 4th October 1964A cuboid measures 12 cm by 13 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  5. 5th October 1964A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  6. 6th October 1964On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  7. 7th October 1964A rectangle is 10 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  8. 8th October 1964f(x) = 4x + 7 and g(x) = 3x + 5. Work out fg(-2).
  9. 9th October 1964y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
  10. 10th October 1964A cuboid measures 13 cm by 5 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  11. 11th October 1964A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  12. 12th October 1964A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
  13. 13th October 1964Expand and simplify (9 + sqrt(2))(9 - sqrt(2)).
  14. 14th October 1964The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
  15. 15th October 1964y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 49.
  16. 16th October 1964The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
  17. 17th October 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 October 1964On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
  19. 19th October 1964A block has mass 840 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  20. 20th October 1964A quadratic sequence starts 10, 25, 46, 73. Work out the second difference, and the coefficient of n^2.
  21. 21st October 1964A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
  22. 22nd October 1964In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
  23. 23rd October 1964The probability of winning a game is 3/4. A player expects 15 wins. How many games did they play?
  24. 24th October 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?
  25. 25th October 1964x = 181 and y = 70, each correct to the nearest whole number. Work out the upper bound of x - y.
  26. 26th October 1964Solve x^2 - 8x + 15 < 0.
  27. 27th October 1964y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
  28. 28th October 1964In a vector proof you find that vector PQ = 3a - 3b and vector RS = 12a - 12b. What does this show about PQ and RS?
  29. 29th October 1964A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  30. 30th October 1964On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
  31. 31st October 1964A car covers 810 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

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