Daily Practice · Higher Plus

March 1954 5-a-day

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March 1954

31 sheets · 155 questions · Grades 8-9

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Every sheet in March 1954

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 1954A cuboid measures 14 cm by 10 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  2. 2nd March 1954A 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?
  3. 3rd March 1954A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
  4. 4th March 1954Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
  5. 5th March 1954The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
  6. 6th March 1954y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
  7. 7th March 1954A cuboid measures 10 cm by 9 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  8. 8th March 1954A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  9. 9th March 1954On 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?
  10. 10th March 1954A rectangle is 18 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
  11. 11th March 1954A quadratic sequence starts 7, 28, 59, 100. Work out the second difference, and the coefficient of n^2.
  12. 12th March 1954y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
  13. 13th March 1954The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
  14. 14th March 1954A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
  15. 15th March 1954A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
  16. 16th March 1954Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
  17. 17th March 1954Solve x^2 - 7x + 12 < 0.
  18. 18th March 1954y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 25.
  19. 19th March 1954In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
  20. 20th March 1954The probability of winning a game is 4/5. A player expects 24 wins. How many games did they play?
  21. 21st March 1954On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  22. 22nd March 1954A block has mass 520 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  23. 23rd March 1954Write x^2 - 6x - 7 in the form (x + a)^2 + b.
  24. 24th March 1954A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
  25. 25th March 1954In a vector proof you find that vector PQ = 5a - 4b and vector RS = 20a - 16b. What does this show about PQ and RS?
  26. 26th March 1954A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
  27. 27th March 1954A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
  28. 28th March 1954x = 88 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
  29. 29th March 1954Work out the coordinates of the turning point of y = x^2 - 6x + 3.
  30. 30th March 1954y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
  31. 31st March 1954A cuboid measures 4 cm by 15 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.

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