Daily Practice · Higher Plus

October 1976 5-a-day

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October 1976

31 sheets · 155 questions · Grades 8-9

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Every sheet in October 1976

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 1976A cuboid measures 10 cm by 15 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  2. 2nd October 1976A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  3. 3rd October 1976On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  4. 4th October 1976A block has mass 670 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  5. 5th October 1976Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
  6. 6th October 1976A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
  7. 7th October 1976A cuboid measures 6 cm by 8 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  8. 8th October 1976A bag holds 4 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  9. 9th October 1976A 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?
  10. 10th October 1976x = 192 and y = 80, each correct to the nearest whole number. Work out the upper bound of x - y.
  11. 11th October 1976f(x) = 4x + 1 and g(x) = 5x - 9. Work out fg(2).
  12. 12th October 1976y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
  13. 13th October 1976The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
  14. 14th October 1976A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
  15. 15th October 1976On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  16. 16th October 1976A car covers 110 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  17. 17th October 1976The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  18. 18th October 1976y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
  19. 19th October 1976In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
  20. 20th October 1976The probability of winning a game is 2/5. A player expects 30 wins. How many games did they play?
  21. 21st October 1976A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
  22. 22nd October 1976Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
  23. 23rd October 1976A quadratic sequence starts 6, 12, 20, 30. Work out the second difference, and the coefficient of n^2.
  24. 24th October 1976y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 36.
  25. 25th October 1976In a vector proof you find that vector PQ = 3a - 4b and vector RS = 9a - 12b. What does this show about PQ and RS?
  26. 26th October 1976A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
  27. 27th October 1976On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  28. 28th October 1976Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
  29. 29th October 1976Solve x^2 + 4x + 3 < 0.
  30. 30th October 1976A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
  31. 31st October 1976A cuboid measures 6 cm by 10 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.

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