Daily Practice · Higher Plus

August 1992 - Higher Plus 5-a-day

← Today's Higher Plus sheet

August 1992

31 sheets · 155 questions · Grades 8-9

Printing for a group?

The batch download puts all 5 tiers' August 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in August 1992

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

  1. 1st August 1992y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 4.
  2. 2nd August 1992In a vector proof you find that vector PQ = 4a - b and vector RS = 8a - 2b. What does this show about PQ and RS?
  3. 3rd August 1992A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
  4. 4th August 1992On 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?
  5. 5th August 1992A rectangle is 16 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
  6. 6th August 1992f(x) = 7x + 1. Work out the inverse function f^-1(x).
  7. 7th August 1992A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
  8. 8th August 1992A cuboid measures 14 cm by 14 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  9. 9th August 1992A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  10. 10th August 1992A 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?
  11. 11th August 1992Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
  12. 12th August 1992Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
  13. 13th August 1992y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
  14. 14th August 1992A cuboid measures 14 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  15. 15th August 1992A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  16. 16th August 1992On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  17. 17th August 1992A block has mass 820 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  18. 18th August 1992Use the iteration x(n+1) = cube root of (5x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
  19. 19th August 1992y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
  20. 20th August 1992The 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.
  21. 21st August 1992A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
  22. 22nd August 1992A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
  23. 23rd August 1992x = 91 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
  24. 24th August 1992Work out the nth term of the quadratic sequence -2, 5, 16, 31, ...
  25. 25th August 1992y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 4.
  26. 26th August 1992In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  27. 27th August 1992The probability of winning a game is 1/2. A player expects 6 wins. How many games did they play?
  28. 28th August 1992On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  29. 29th August 1992A car covers 120 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.
  30. 30th August 1992The point (0, -2) lies on y = f(x). Write down its image on y = f(x + 6).
  31. 31st August 1992A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.

The same month at another level