Daily Practice · Higher Plus

June 1974 5-a-day

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June 1974

30 sheets · 150 questions · Grades 8-9

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Every sheet in June 1974

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

  1. 1st June 1974y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
  2. 2nd June 1974In 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.
  3. 3rd June 1974The probability of winning a game is 2/5. A player expects 52 wins. How many games did they play?
  4. 4th June 1974On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  5. 5th June 1974A rectangle is 18 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
  6. 6th June 1974Solve 15x^2 - 13x - 6 = 0.
  7. 7th June 1974y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
  8. 8th June 1974In a vector proof you find that vector PQ = 5a - 6b and vector RS = 25a - 30b. What does this show about PQ and RS?
  9. 9th June 1974A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  10. 10th June 1974A 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?
  11. 11th June 1974Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
  12. 12th June 1974f(x) = 7x - 12. Work out the inverse function f^-1(x).
  13. 13th June 1974y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 64.
  14. 14th June 1974A cuboid measures 11 cm by 11 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  15. 15th June 1974A 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 June 1974On 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?
  17. 17th June 1974A block has mass 400 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  18. 18th June 1974Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
  19. 19th June 1974A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
  20. 20th June 1974A cuboid measures 6 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 June 1974A bag holds 5 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  22. 22nd June 1974A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
  23. 23rd June 1974x = 138 and y = 118, each correct to the nearest whole number. Work out the upper bound of x - y.
  24. 24th June 1974Use the iteration x(n+1) = cube root of (3x(n) + 6) with x(0) = 1. Work out x(1) to 3 decimal places.
  25. 25th June 1974y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
  26. 26th June 1974The 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 June 1974A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
  28. 28th June 1974On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  29. 29th June 1974A car covers 430 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  30. 30th June 1974Work out the nth term of the quadratic sequence -3, -1, 5, 15, ...

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