Daily Practice · Higher Plus

November 1987 5-a-day

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November 1987

30 sheets · 150 questions · Grades 8-9

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Every sheet in November 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 November 1987Solve 8x^2 - 30x + 25 = 0.
  2. 2nd November 1987y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
  3. 3rd November 1987A cuboid measures 14 cm by 5 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  4. 4th November 1987A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  5. 5th November 1987A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
  6. 6th November 1987Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
  7. 7th November 1987f(x) = 2x + 11. Work out the inverse function f^-1(x).
  8. 8th November 1987y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 16.
  9. 9th November 1987A cuboid measures 5 cm by 5 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  10. 10th November 1987A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  11. 11th November 1987On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  12. 12th November 1987Simplify sqrt(27) + sqrt(48), giving your answer in the form a sqrt(b).
  13. 13th November 1987Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
  14. 14th November 1987A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
  15. 15th November 1987The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
  16. 16th November 1987A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
  17. 17th November 1987A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
  18. 18th November 1987A rectangle is 25 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
  19. 19th November 1987Use the iteration x(n+1) = cube root of (10x(n) + 1) with x(0) = 1. Work out x(1) to 3 decimal places.
  20. 20th November 1987y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
  21. 21st November 1987In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
  22. 22nd November 1987The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
  23. 23rd November 1987On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
  24. 24th November 1987Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
  25. 25th November 1987Work out the nth term of the quadratic sequence 2, 14, 34, 62, ...
  26. 26th November 1987y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
  27. 27th November 1987In a vector proof you find that vector PQ = 2a - 2b and vector RS = 10a - 10b. What does this show about PQ and RS?
  28. 28th November 1987A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
  29. 29th November 1987A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
  30. 30th November 1987A block has mass 620 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

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