Daily Practice · Higher Plus

March 1971 5-a-day

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March 1971

31 sheets · 155 questions · Grades 8-9

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Every sheet in March 1971

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 1971y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 36.
  2. 2nd March 1971A cuboid measures 11 cm by 7 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  3. 3rd March 1971A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  4. 4th March 1971On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  5. 5th March 1971Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
  6. 6th March 1971Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
  7. 7th March 1971A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
  8. 8th March 1971A cuboid measures 12 cm by 10 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  9. 9th March 1971A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  10. 10th March 1971A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
  11. 11th March 1971Simplify sqrt(50) + sqrt(8), giving your answer in the form a sqrt(b).
  12. 12th March 1971f(x) = 2x + 5 and g(x) = 2x - 5. Work out fg(1).
  13. 13th March 1971y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
  14. 14th March 1971The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
  15. 15th March 1971A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.
  16. 16th March 1971On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  17. 17th March 1971A rectangle is 5 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
  18. 18th March 1971The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
  19. 19th March 1971y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
  20. 20th March 1971In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  21. 21st March 1971The probability of winning a game is 3/5. A player expects 42 wins. How many games did they play?
  22. 22nd March 1971A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
  23. 23rd March 1971Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
  24. 24th March 1971A quadratic sequence starts 3, 6, 11, 18. Work out the second difference, and the coefficient of n^2.
  25. 25th March 1971y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 49.
  26. 26th March 1971In a vector proof you find that vector PQ = a - 6b and vector RS = 2a - 12b. What does this show about PQ and RS?
  27. 27th March 1971A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
  28. 28th March 1971On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  29. 29th March 1971A block has mass 230 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  30. 30th March 1971Solve x^2 + 3x + 2 > 0.
  31. 31st March 1971A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.

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