Daily Practice · Higher Plus

March 1987 5-a-day

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March 1987

31 sheets · 155 questions · Grades 8-9

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Every sheet in March 1987

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 1987y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
  2. 2nd March 1987In a vector proof you find that vector PQ = 6a - 6b and vector RS = 18a - 18b. What does this show about PQ and RS?
  3. 3rd March 1987A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
  4. 4th March 1987On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
  5. 5th March 1987Simplify sqrt(8) + sqrt(72), giving your answer in the form a sqrt(b).
  6. 6th March 1987Write x^2 - 12x + 14 in the form (x + a)^2 + b.
  7. 7th March 1987y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
  8. 8th March 1987A cuboid measures 8 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  9. 9th March 1987A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  10. 10th March 1987A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
  11. 11th March 1987A rectangle is 13 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
  12. 12th March 1987Work out the coordinates of the turning point of y = x^2 - 4x + 8.
  13. 13th March 1987y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 49.
  14. 14th March 1987A 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.
  15. 15th March 1987A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  16. 16th March 1987On 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?
  17. 17th March 1987Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
  18. 18th March 1987Simplify (x^2 - 9x + 8)/(x - 8).
  19. 19th March 1987A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
  20. 20th March 1987The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
  21. 21st March 1987A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
  22. 22nd March 1987A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
  23. 23rd March 1987A block has mass 240 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  24. 24th March 1987In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
  25. 25th March 1987y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
  26. 26th March 1987In 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 March 1987The probability of winning a game is 9/10. A player expects 135 wins. How many games did they play?
  28. 28th March 1987On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  29. 29th March 1987x = 37 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
  30. 30th March 1987Make x the subject of 3x + 6 = y(x + 6).
  31. 31st March 1987y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.

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