Daily Practice · Higher Plus

October 1969 5-a-day

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October 1969

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' October 1969 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in October 1969

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 1969y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
  2. 2nd October 1969In a vector proof you find that vector PQ = 5a + 4b and vector RS = 15a + 12b. What does this show about PQ and RS?
  3. 3rd October 1969A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
  4. 4th October 1969On 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?
  5. 5th October 1969x = 71 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
  6. 6th October 1969The point (-2, 1) lies on y = f(x). Write down its image on y = f(-x).
  7. 7th October 1969y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
  8. 8th October 1969A cuboid measures 9 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  9. 9th October 1969A 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?
  10. 10th October 1969A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
  11. 11th October 1969A car covers 160 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.
  12. 12th October 1969Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
  13. 13th October 1969y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 64.
  14. 14th October 1969A cuboid measures 11 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  15. 15th October 1969A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  16. 16th October 1969On 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?
  17. 17th October 1969Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
  18. 18th October 1969f(x) = 2x - 1 and g(x) = 2x + 6. Work out fg(6).
  19. 19th October 1969A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
  20. 20th October 1969The 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 October 1969A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
  22. 22nd October 1969A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
  23. 23rd October 1969Simplify sqrt(80) + sqrt(5), giving your answer in the form a sqrt(b).
  24. 24th October 1969The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  25. 25th October 1969y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
  26. 26th October 1969In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  27. 27th October 1969The probability of winning a game is 5/8. A player expects 20 wins. How many games did they play?
  28. 28th October 1969On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  29. 29th October 1969A rectangle is 5 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
  30. 30th October 1969A quadratic sequence starts 13, 27, 51, 85. Work out the second difference, and the coefficient of n^2.
  31. 31st October 1969y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.

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