Daily Practice · Higher Plus

September 1989 5-a-day

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September 1989

30 sheets · 150 questions · Grades 8-9

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Every sheet in September 1989

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

  1. 1st September 1989On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  2. 2nd September 1989A car covers 740 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  3. 3rd September 1989Solve x^2 + 11x + 24 < 0.
  4. 4th September 1989y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
  5. 5th September 1989The 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.
  6. 6th September 1989A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
  7. 7th September 1989A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
  8. 8th September 1989Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
  9. 9th September 1989Write x^2 - 4x + 7 in the form (x + a)^2 + b.
  10. 10th September 1989y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 36.
  11. 11th September 1989In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  12. 12th September 1989The probability of winning a game is 3/5. A player expects 9 wins. How many games did they play?
  13. 13th September 1989On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  14. 14th September 1989Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
  15. 15th September 1989Work out the coordinates of the turning point of y = x^2 - 12x - 9.
  16. 16th September 1989A train slows steadily from 26 m/s to rest in 4 seconds. Work out its deceleration.
  17. 17th September 1989In a vector proof you find that vector PQ = 5a + 3b and vector RS = 15a + 9b. What does this show about PQ and RS?
  18. 18th September 1989A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
  19. 19th September 1989A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
  20. 20th September 1989A rectangle is 9 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
  21. 21st September 1989Simplify (x^2 + 3x - 40)/(x - 5).
  22. 22nd September 1989y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
  23. 23rd September 1989A cuboid measures 13 cm by 14 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  24. 24th September 1989A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  25. 25th September 1989On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  26. 26th September 1989Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
  27. 27th September 1989In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
  28. 28th September 1989y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
  29. 29th September 1989A cuboid measures 7 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  30. 30th September 1989A bag holds 5 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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