Daily Practice · Higher Plus

July 1996 - Higher Plus 5-a-day

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July 1996

31 sheets · 155 questions · Grades 8-9

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Every sheet in July 1996

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

  1. 1st July 1996A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
  2. 2nd July 1996On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
  3. 3rd July 1996A rectangle is 9 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
  4. 4th July 1996f(x) = 5x - 11. Work out the inverse function f^-1(x).
  5. 5th July 1996y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
  6. 6th July 1996In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  7. 7th July 1996The probability of winning a game is 7/8. A player expects 63 wins. How many games did they play?
  8. 8th July 1996A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
  9. 9th July 1996Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
  10. 10th July 1996Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
  11. 11th July 1996y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.
  12. 12th July 1996In a vector proof you find that vector PQ = 6a + 5b and vector RS = 12a + 10b. What does this show about PQ and RS?
  13. 13th July 1996A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
  14. 14th July 1996On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
  15. 15th July 1996A block has mass 420 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.
  16. 16th July 1996Use the iteration x(n+1) = cube root of (2x(n) + 9) with x(0) = 4. Work out x(1) to 3 decimal places.
  17. 17th July 1996A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
  18. 18th July 1996A cuboid measures 6 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  19. 19th July 1996A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  20. 20th July 1996A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
  21. 21st July 1996x = 42 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
  22. 22nd July 1996Work out the nth term of the quadratic sequence 3, 5, 9, 15, ...
  23. 23rd July 1996y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
  24. 24th July 1996A cuboid measures 6 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  25. 25th July 1996A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  26. 26th July 1996On 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?
  27. 27th July 1996A car covers 710 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.
  28. 28th July 1996The point (4, -6) lies on y = f(x). Write down its image on y = f(x) + 1.
  29. 29th July 1996y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
  30. 30th July 1996The 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.
  31. 31st July 1996A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.

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