Daily Practice · Higher Plus

May 1968 5-a-day

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May 1968

31 sheets · 155 questions · Grades 8-9

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Every sheet in May 1968

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st May 1968A rectangle is 16 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
  2. 2nd May 1968Use the iteration x(n+1) = cube root of (4x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
  3. 3rd May 1968y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 9.
  4. 4th May 1968In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
  5. 5th May 1968The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
  6. 6th May 1968On 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 May 1968Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
  8. 8th May 1968Work out the nth term of the quadratic sequence 14, 22, 32, 44, ...
  9. 9th May 1968A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
  10. 10th May 1968In a vector proof you find that vector PQ = 5a - 5b and vector RS = 10a - 10b. What does this show about PQ and RS?
  11. 11th May 1968A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
  12. 12th May 1968A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
  13. 13th May 1968A block has mass 680 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  14. 14th May 1968The point (5, -1) lies on y = f(x). Write down its image on y = -f(x).
  15. 15th May 1968y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
  16. 16th May 1968A cuboid measures 6 cm by 7 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  17. 17th May 1968A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  18. 18th May 1968On 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?
  19. 19th May 1968x = 40 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
  20. 20th May 1968Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
  21. 21st May 1968y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
  22. 22nd May 1968A cuboid measures 10 cm by 9 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  23. 23rd May 1968A bag holds 3 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  24. 24th May 1968A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
  25. 25th May 1968A car covers 890 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.
  26. 26th May 1968f(x) = 3x - 6 and g(x) = 6x + 7. Work out fg(-2).
  27. 27th May 1968y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 64.
  28. 28th May 1968The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
  29. 29th May 1968A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
  30. 30th May 1968On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
  31. 31st May 1968Rationalise the denominator of 56/sqrt(7), giving your answer in its simplest form.

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