Daily Practice · Higher Plus

May 1975 5-a-day

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May 1975

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' May 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in May 1975

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 1975Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
  2. 2nd May 1975Work out the nth term of the quadratic sequence -7, -6, -1, 8, ...
  3. 3rd May 1975y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
  4. 4th May 1975In a vector proof you find that vector PQ = a + 4b and vector RS = 4a + 16b. What does this show about PQ and RS?
  5. 5th May 1975A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
  6. 6th May 1975On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  7. 7th May 1975A rectangle is 21 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  8. 8th May 1975The point (1, 4) lies on y = f(x). Write down its image on y = f(-x).
  9. 9th May 1975y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
  10. 10th May 1975A cuboid measures 10 cm by 9 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  11. 11th May 1975A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  12. 12th May 1975A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
  13. 13th May 1975Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
  14. 14th May 1975Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
  15. 15th May 1975y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 81.
  16. 16th May 1975A cuboid measures 8 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  17. 17th May 1975A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  18. 18th May 1975On 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?
  19. 19th May 1975A block has mass 750 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  20. 20th May 1975f(x) = 5x - 8 and g(x) = 2x + 3. Work out fg(-1).
  21. 21st May 1975A train slows steadily from 29 m/s to rest in 10 seconds. Work out its deceleration.
  22. 22nd May 1975The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
  23. 23rd May 1975A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
  24. 24th May 1975A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
  25. 25th May 1975x = 167 and y = 133, each correct to the nearest whole number. Work out the upper bound of x - y.
  26. 26th May 1975The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
  27. 27th May 1975y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
  28. 28th May 1975In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
  29. 29th May 1975The probability of winning a game is 7/10. A player expects 105 wins. How many games did they play?
  30. 30th May 1975On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  31. 31st May 1975A car covers 500 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

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