Daily Practice · Higher Plus

June 1984 5-a-day

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June 1984

30 sheets · 150 questions · Grades 8-9

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Every sheet in June 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 June 1984Simplify (x^2 - 4x - 5)/(x + 1).
  2. 2nd June 1984y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
  3. 3rd June 1984The 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.
  4. 4th June 1984A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
  5. 5th June 1984A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
  6. 6th June 1984A rectangle is 12 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
  7. 7th June 1984In an algebraic proof, how would you write an even number in terms of an integer n?
  8. 8th June 1984y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 64.
  9. 9th June 1984In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  10. 10th June 1984The probability of winning a game is 1/8. A player expects 12 wins. How many games did they play?
  11. 11th June 1984On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  12. 12th June 1984Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
  13. 13th June 1984Make x the subject of 3x + 6 = y(x + 6).
  14. 14th June 1984A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
  15. 15th June 1984In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
  16. 16th June 1984A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  17. 17th June 1984A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
  18. 18th June 1984A block has mass 680 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  19. 19th June 1984Write 3/(x - 6) + 4/(x + 6) as a single fraction.
  20. 20th June 1984y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
  21. 21st June 1984A cuboid measures 8 cm by 11 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  22. 22nd June 1984A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  23. 23rd June 1984On 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?
  24. 24th June 1984x = 97 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
  25. 25th June 1984Solve 2x^2 - 15x + 25 = 0.
  26. 26th June 1984y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
  27. 27th June 1984A cuboid measures 10 cm by 9 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  28. 28th June 1984A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  29. 29th June 1984A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
  30. 30th June 1984A car covers 810 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

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