Daily Practice · Higher Plus

June 1977 5-a-day

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June 1977

30 sheets · 150 questions · Grades 8-9

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Every sheet in June 1977

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 1977A rectangle is 24 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  2. 2nd June 1977Work out the coordinates of the turning point of y = x^2 - 2x + 13.
  3. 3rd June 1977A train slows steadily from 31 m/s to rest in 4 seconds. Work out its deceleration.
  4. 4th June 1977A cuboid measures 10 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  5. 5th June 1977A bag holds 4 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  6. 6th June 1977A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
  7. 7th June 1977Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
  8. 8th June 1977Simplify (x^2 - 5x - 24)/(x + 3).
  9. 9th June 1977y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
  10. 10th June 1977The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
  11. 11th June 1977A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
  12. 12th June 1977On 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?
  13. 13th June 1977A block has mass 380 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  14. 14th June 1977In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
  15. 15th June 1977y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
  16. 16th June 1977In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  17. 17th June 1977The probability of winning a game is 3/4. A player expects 54 wins. How many games did they play?
  18. 18th June 1977A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
  19. 19th June 1977x = 79 and y = 52, each correct to the nearest whole number. Work out the upper bound of x - y.
  20. 20th June 1977Make x the subject of 6x + 6 = y(x + 6).
  21. 21st June 1977y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 4.
  22. 22nd June 1977In a vector proof you find that vector PQ = 3a + 6b and vector RS = 9a + 18b. What does this show about PQ and RS?
  23. 23rd June 1977A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
  24. 24th June 1977On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  25. 25th June 1977A car covers 220 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  26. 26th June 1977Write 7/(x + 5) + 4/(x - 5) as a single fraction.
  27. 27th June 1977A train slows steadily from 18 m/s to rest in 4 seconds. Work out its deceleration.
  28. 28th June 1977A cuboid measures 11 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  29. 29th June 1977A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  30. 30th June 1977A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?

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