Daily Practice · Higher Plus

March 1961 5-a-day

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March 1961

31 sheets · 155 questions · Grades 8-9

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Every sheet in March 1961

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

  1. 1st March 1961A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  2. 2nd March 1961A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
  3. 3rd March 1961Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
  4. 4th March 1961A quadratic sequence starts -5, 3, 19, 43. Work out the second difference, and the coefficient of n^2.
  5. 5th March 1961y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 4.
  6. 6th March 1961The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
  7. 7th March 1961A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
  8. 8th March 1961On 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?
  9. 9th March 1961Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
  10. 10th March 1961Solve x^2 - 8x > 0.
  11. 11th March 1961A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
  12. 12th March 1961In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  13. 13th March 1961The probability of winning a game is 3/4. A player expects 90 wins. How many games did they play?
  14. 14th March 1961A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
  15. 15th March 1961A rectangle is 30 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
  16. 16th March 1961Write x^2 + 2x - 10 in the form (x + a)^2 + b.
  17. 17th March 1961y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
  18. 18th March 1961In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
  19. 19th March 1961A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
  20. 20th March 1961On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
  21. 21st March 1961Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
  22. 22nd March 1961Work out the coordinates of the turning point of y = x^2 + 8x - 11.
  23. 23rd March 1961y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
  24. 24th March 1961A cuboid measures 11 cm by 14 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  25. 25th March 1961A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  26. 26th March 1961A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
  27. 27th March 1961A block has mass 810 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  28. 28th March 1961Simplify (x^2 - 8x + 15)/(x - 3).
  29. 29th March 1961y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 36.
  30. 30th March 1961A cuboid measures 9 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  31. 31st March 1961A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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