Daily Practice · Higher Plus

October 1985 5-a-day

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October 1985

31 sheets · 155 questions · Grades 8-9

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Every sheet in October 1985

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 1985y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 36.
  2. 2nd October 1985In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
  3. 3rd October 1985The probability of winning a game is 3/5. A player expects 90 wins. How many games did they play?
  4. 4th October 1985On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  5. 5th October 1985A car covers 770 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  6. 6th October 1985Solve x^2 + 5x - 6 > 0.
  7. 7th October 1985A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
  8. 8th October 1985In a vector proof you find that vector PQ = 2a - 2b and vector RS = 10a - 10b. What does this show about PQ and RS?
  9. 9th October 1985A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  10. 10th October 1985A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
  11. 11th October 1985Rationalise the denominator of 132/sqrt(11), giving your answer in its simplest form.
  12. 12th October 1985Write x^2 + 14x - 14 in the form (x + a)^2 + b.
  13. 13th October 1985y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
  14. 14th October 1985A cuboid measures 9 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  15. 15th October 1985A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  16. 16th October 1985On 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?
  17. 17th October 1985Simplify sqrt(75) + sqrt(108), giving your answer in the form a sqrt(b).
  18. 18th October 1985Work out the coordinates of the turning point of y = x^2 - 16x + 11.
  19. 19th October 1985y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
  20. 20th October 1985A cuboid measures 11 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  21. 21st October 1985A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  22. 22nd October 1985A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
  23. 23rd October 1985A rectangle is 18 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  24. 24th October 1985Simplify (x^2 - 16)/(x + 4).
  25. 25th October 1985y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 4.
  26. 26th October 1985The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
  27. 27th October 1985A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
  28. 28th October 1985On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  29. 29th October 1985Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
  30. 30th October 1985In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
  31. 31st October 1985A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.

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