Daily Practice · Higher Plus

May 1983 5-a-day

← Today's Higher Plus sheet

May 1983

31 sheets · 155 questions · Grades 8-9

Printing for a group?

The batch download puts all 5 tiers' May 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in May 1983

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 1983x = 117 and y = 74, each correct to the nearest whole number. Work out the upper bound of x - y.
  2. 2nd May 1983Make x the subject of 7x + 4 = y(x + 4).
  3. 3rd May 1983A train slows steadily from 34 m/s to rest in 5 seconds. Work out its deceleration.
  4. 4th May 1983A cuboid measures 8 cm by 13 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  5. 5th May 1983A bag holds 7 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  6. 6th May 1983A 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?
  7. 7th May 1983A car covers 680 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  8. 8th May 1983Write 5/(x - 6) + 6/(x - 5) as a single fraction.
  9. 9th May 1983y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
  10. 10th May 1983The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
  11. 11th May 1983A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
  12. 12th May 1983On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  13. 13th May 1983Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
  14. 14th May 1983Solve 16x^2 + 24x + 5 = 0.
  15. 15th May 1983y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
  16. 16th May 1983In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
  17. 17th May 1983The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
  18. 18th May 1983A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
  19. 19th May 1983Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
  20. 20th May 1983f(x) = 5x - 1. Work out the inverse function f^-1(x).
  21. 21st May 1983y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 36.
  22. 22nd May 1983In a vector proof you find that vector PQ = a + 2b and vector RS = 5a + 10b. What does this show about PQ and RS?
  23. 23rd May 1983A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
  24. 24th May 1983On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  25. 25th May 1983A rectangle is 22 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
  26. 26th May 1983Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
  27. 27th May 1983A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
  28. 28th May 1983A cuboid measures 11 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  29. 29th May 1983A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  30. 30th May 1983A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
  31. 31st May 1983Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).

The same month at another level