Daily Practice · Higher Plus

September 1956 5-a-day

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September 1956

30 sheets · 150 questions · Grades 8-9

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Every sheet in September 1956

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 1956A car covers 520 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  2. 2nd September 1956f(x) = 5x + 8 and g(x) = 2x + 6. Work out fg(3).
  3. 3rd September 1956y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
  4. 4th September 1956In 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.
  5. 5th September 1956The probability of winning a game is 4/5. A player expects 20 wins. How many games did they play?
  6. 6th September 1956On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
  7. 7th September 1956Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
  8. 8th September 1956The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
  9. 9th September 1956y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
  10. 10th September 1956In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
  11. 11th September 1956A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  12. 12th September 1956A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
  13. 13th September 1956Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
  14. 14th September 1956A quadratic sequence starts 10, 16, 26, 40. Work out the second difference, and the coefficient of n^2.
  15. 15th September 1956y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 16.
  16. 16th September 1956A cuboid measures 13 cm by 12 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  17. 17th September 1956A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  18. 18th September 1956On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
  19. 19th September 1956A rectangle is 10 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
  20. 20th September 1956Solve x^2 - 9 > 0.
  21. 21st September 1956A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
  22. 22nd September 1956A cuboid measures 4 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  23. 23rd September 1956A bag holds 7 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  24. 24th September 1956A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
  25. 25th September 1956Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
  26. 26th September 1956Write x^2 - 4x - 8 in the form (x + a)^2 + b.
  27. 27th September 1956y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
  28. 28th September 1956The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
  29. 29th September 1956A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
  30. 30th September 1956On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?

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