Daily Practice · Higher Plus

March 1975 5-a-day

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March 1975

31 sheets · 155 questions · Grades 8-9

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Every sheet in March 1975

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 1975A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
  2. 2nd March 1975x = 110 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
  3. 3rd March 1975Write x^2 - 14x + 5 in the form (x + a)^2 + b.
  4. 4th March 1975y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 25.
  5. 5th March 1975In a vector proof you find that vector PQ = 3a - 3b and vector RS = 9a - 9b. What does this show about PQ and RS?
  6. 6th March 1975A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  7. 7th March 1975On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  8. 8th March 1975A car covers 340 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  9. 9th March 1975Work out the coordinates of the turning point of y = x^2 - 16x - 9.
  10. 10th March 1975A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
  11. 11th March 1975A cuboid measures 12 cm by 11 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  12. 12th March 1975A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  13. 13th March 1975A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
  14. 14th March 1975Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
  15. 15th March 1975Simplify (x^2 - 2x - 15)/(x + 3).
  16. 16th March 1975y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
  17. 17th March 1975A cuboid measures 12 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  18. 18th March 1975A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  19. 19th March 1975On 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?
  20. 20th March 1975Simplify sqrt(80) + sqrt(245), giving your answer in the form a sqrt(b).
  21. 21st March 1975In an algebraic proof, how would you write an odd number in terms of an integer n?
  22. 22nd March 1975y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
  23. 23rd March 1975The 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.
  24. 24th March 1975A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
  25. 25th March 1975A 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?
  26. 26th March 1975A rectangle is 27 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  27. 27th March 1975Make x the subject of 6x + 6 = y(x + 6).
  28. 28th March 1975y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 25.
  29. 29th March 1975In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
  30. 30th March 1975The probability of winning a game is 1/10. A player expects 10 wins. How many games did they play?
  31. 31st March 1975On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

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