Daily Practice · Higher Plus

May 1972 5-a-day

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May 1972

31 sheets · 155 questions · Grades 8-9

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Every sheet in May 1972

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 1972A cuboid measures 13 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  2. 2nd May 1972A bag holds 4 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  3. 3rd May 1972A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
  4. 4th May 1972Simplify sqrt(8) + sqrt(72), giving your answer in the form a sqrt(b).
  5. 5th May 1972A quadratic sequence starts 10, 15, 22, 31. Work out the second difference, and the coefficient of n^2.
  6. 6th May 1972y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 81.
  7. 7th May 1972The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
  8. 8th May 1972A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
  9. 9th May 1972On 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?
  10. 10th May 1972A rectangle is 11 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
  11. 11th May 1972Solve x^2 + 2x - 15 < 0.
  12. 12th May 1972A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
  13. 13th May 1972In 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.
  14. 14th May 1972The probability of winning a game is 3/4. A player expects 45 wins. How many games did they play?
  15. 15th May 1972A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
  16. 16th May 1972Expand and simplify (7 + sqrt(6))(7 - sqrt(6)).
  17. 17th May 1972Write x^2 + 4x - 13 in the form (x + a)^2 + b.
  18. 18th May 1972y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
  19. 19th May 1972In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
  20. 20th May 1972A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
  21. 21st May 1972On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  22. 22nd May 1972A block has mass 640 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  23. 23rd May 1972Work out the coordinates of the turning point of y = x^2 - 2x - 14.
  24. 24th May 1972y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
  25. 25th May 1972A cuboid measures 8 cm by 11 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  26. 26th May 1972A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  27. 27th May 1972A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
  28. 28th May 1972x = 111 and y = 91, each correct to the nearest whole number. Work out the upper bound of x - y.
  29. 29th May 1972Simplify (x^2 - 7x + 10)/(x - 2).
  30. 30th May 1972y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 4.
  31. 31st May 1972A cuboid measures 14 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.

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