Daily Practice · Higher Plus

March 1991 5-a-day

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March 1991

31 sheets · 155 questions · Grades 8-9

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Every sheet in March 1991

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

  1. 1st March 1991A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
  2. 2nd March 1991A car covers 620 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.
  3. 3rd March 1991Write 3/(x + 1) + 4/(x - 2) as a single fraction.
  4. 4th March 1991y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
  5. 5th March 1991In 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.
  6. 6th March 1991The probability of winning a game is 4/5. A player expects 80 wins. How many games did they play?
  7. 7th March 1991On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
  8. 8th March 1991Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
  9. 9th March 1991Solve 10x^2 + 27x + 18 = 0.
  10. 10th March 1991y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
  11. 11th March 1991In a vector proof you find that vector PQ = 4a + 2b and vector RS = 12a + 6b. What does this show about PQ and RS?
  12. 12th March 1991A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
  13. 13th March 1991A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
  14. 14th March 1991Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
  15. 15th March 1991f(x) = 4x - 11. Work out the inverse function f^-1(x).
  16. 16th March 1991y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 16.
  17. 17th March 1991A cuboid measures 6 cm by 5 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  18. 18th March 1991A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  19. 19th March 1991On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
  20. 20th March 1991A rectangle is 12 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
  21. 21st March 1991Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
  22. 22nd March 1991A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
  23. 23rd March 1991A cuboid measures 11 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  24. 24th March 1991A bag holds 5 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  25. 25th March 1991A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
  26. 26th March 1991Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
  27. 27th March 1991Use the iteration x(n+1) = cube root of (11x(n) + 2) with x(0) = 5. Work out x(1) to 3 decimal places.
  28. 28th March 1991y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
  29. 29th March 1991The 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.
  30. 30th March 1991A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
  31. 31st March 1991On 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?

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