Daily Practice · Higher Plus

November 1983 5-a-day

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November 1983

30 sheets · 150 questions · Grades 8-9

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Every sheet in November 1983

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  1. 1st November 1983A bag holds 3 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  2. 2nd November 1983A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
  3. 3rd November 1983Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
  4. 4th November 1983Work out the coordinates of the turning point of y = x^2 + 10x + 2.
  5. 5th November 1983y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 25.
  6. 6th November 1983The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
  7. 7th November 1983A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
  8. 8th November 1983On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  9. 9th November 1983A rectangle is 22 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
  10. 10th November 1983Simplify (x^2 - 7x - 8)/(x - 8).
  11. 11th November 1983A train slows steadily from 29 m/s to rest in 10 seconds. Work out its deceleration.
  12. 12th November 1983In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
  13. 13th November 1983The probability of winning a game is 3/8. A player expects 6 wins. How many games did they play?
  14. 14th November 1983A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
  15. 15th November 1983Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
  16. 16th November 1983In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
  17. 17th November 1983y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
  18. 18th November 1983In a vector proof you find that vector PQ = 6a - 3b and vector RS = 12a - 6b. What does this show about PQ and RS?
  19. 19th November 1983A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
  20. 20th November 1983On 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?
  21. 21st November 1983A block has mass 210 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  22. 22nd November 1983Make x the subject of 8x + 7 = y(x + 7).
  23. 23rd November 1983y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
  24. 24th November 1983A cuboid measures 7 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  25. 25th November 1983A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  26. 26th November 1983A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
  27. 27th November 1983x = 69 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
  28. 28th November 1983Write 7/(x - 5) + 5/(x + 6) as a single fraction.
  29. 29th November 1983y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 81.
  30. 30th November 1983A cuboid measures 10 cm by 12 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.

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