Daily Practice · Higher Plus

October 1984 5-a-day

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October 1984

31 sheets · 155 questions · Grades 8-9

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Every sheet in October 1984

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

  1. 1st October 1984The 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.
  2. 2nd October 1984A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
  3. 3rd October 1984A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
  4. 4th October 1984Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
  5. 5th October 1984Solve 12x^2 + 5x - 3 = 0.
  6. 6th October 1984y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 81.
  7. 7th October 1984In 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.
  8. 8th October 1984The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
  9. 9th October 1984On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  10. 10th October 1984A rectangle is 29 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
  11. 11th October 1984f(x) = 3x - 5. Work out the inverse function f^-1(x).
  12. 12th October 1984A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
  13. 13th October 1984In a vector proof you find that vector PQ = 6a - 2b and vector RS = 30a - 10b. What does this show about PQ and RS?
  14. 14th October 1984A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
  15. 15th October 1984A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
  16. 16th October 1984Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
  17. 17th October 1984Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
  18. 18th October 1984y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
  19. 19th October 1984A cuboid measures 4 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  20. 20th October 1984A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  21. 21st October 1984On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
  22. 22nd October 1984A block has mass 410 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  23. 23rd October 1984Use the iteration x(n+1) = cube root of (11x(n) + 9) with x(0) = 2. Work out x(1) to 3 decimal places.
  24. 24th October 1984y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
  25. 25th October 1984A cuboid measures 6 cm by 14 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  26. 26th October 1984A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  27. 27th October 1984A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
  28. 28th October 1984x = 40 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
  29. 29th October 1984Work out the nth term of the quadratic sequence 3, 6, 11, 18, ...
  30. 30th October 1984y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 49.
  31. 31st October 1984The 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.

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