Daily Practice · Higher Plus

May 1985 5-a-day

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May 1985

31 sheets · 155 questions · Grades 8-9

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Every sheet in May 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 May 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?
  2. 2nd May 1985Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).
  3. 3rd May 1985f(x) = 5x + 2. Work out the inverse function f^-1(x).
  4. 4th May 1985y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
  5. 5th May 1985In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  6. 6th May 1985The probability of winning a game is 5/8. A player expects 45 wins. How many games did they play?
  7. 7th May 1985A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
  8. 8th May 1985A rectangle is 7 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
  9. 9th May 1985Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
  10. 10th May 1985y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
  11. 11th May 1985In a vector proof you find that vector PQ = 6a - b and vector RS = 30a - 5b. What does this show about PQ and RS?
  12. 12th May 1985A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  13. 13th May 1985On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
  14. 14th May 1985Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
  15. 15th May 1985Use the iteration x(n+1) = cube root of (3x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
  16. 16th May 1985A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
  17. 17th May 1985A cuboid measures 3 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  18. 18th May 1985A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  19. 19th May 1985A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
  20. 20th May 1985A block has mass 260 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.
  21. 21st May 1985Work out the nth term of the quadratic sequence 7, 13, 25, 43, ...
  22. 22nd May 1985y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
  23. 23rd May 1985A cuboid measures 9 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  24. 24th May 1985A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  25. 25th May 1985On 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?
  26. 26th May 1985x = 61 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
  27. 27th May 1985The point (3, 0) lies on y = f(x). Write down its image on y = -f(x).
  28. 28th May 1985y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
  29. 29th May 1985The 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.
  30. 30th May 1985A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
  31. 31st May 1985A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?

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