Daily Practice · Higher Plus

October 1966 5-a-day

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October 1966

31 sheets · 155 questions · Grades 8-9

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Every sheet in October 1966

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 1966A bag holds 4 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  2. 2nd October 1966A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
  3. 3rd October 1966A block has mass 560 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  4. 4th October 1966A quadratic sequence starts 7, 12, 19, 28. Work out the second difference, and the coefficient of n^2.
  5. 5th October 1966y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 49.
  6. 6th October 1966The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
  7. 7th October 1966A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
  8. 8th October 1966On 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?
  9. 9th October 1966x = 93 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
  10. 10th October 1966Solve x^2 + 11x + 30 > 0.
  11. 11th October 1966A train slows steadily from 28 m/s to rest in 10 seconds. Work out its deceleration.
  12. 12th October 1966In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  13. 13th October 1966The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
  14. 14th October 1966A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
  15. 15th October 1966A car covers 570 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  16. 16th October 1966Write x^2 - 8x - 8 in the form (x + a)^2 + b.
  17. 17th October 1966y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
  18. 18th October 1966In a vector proof you find that vector PQ = 5a - 3b and vector RS = 10a - 6b. What does this show about PQ and RS?
  19. 19th October 1966A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  20. 20th October 1966On 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?
  21. 21st October 1966Rationalise the denominator of 21/sqrt(7), giving your answer in its simplest form.
  22. 22nd October 1966Work out the coordinates of the turning point of y = x^2 - 8x - 13.
  23. 23rd October 1966y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
  24. 24th October 1966A cuboid measures 14 cm by 10 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  25. 25th October 1966A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  26. 26th October 1966A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
  27. 27th October 1966Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
  28. 28th October 1966Simplify (x^2 + 9x + 14)/(x + 7).
  29. 29th October 1966y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 25.
  30. 30th October 1966A cuboid measures 12 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  31. 31st October 1966A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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