Daily Practice · Higher Plus

March 1965 5-a-day

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March 1965

31 sheets · 155 questions · Grades 8-9

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Every sheet in March 1965

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 1965In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
  2. 2nd March 1965y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
  3. 3rd March 1965A cuboid measures 7 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  4. 4th March 1965A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  5. 5th March 1965A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
  6. 6th March 1965A car covers 160 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  7. 7th March 1965Make x the subject of 5x + 2 = y(x + 2).
  8. 8th March 1965y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 9.
  9. 9th March 1965A cuboid measures 4 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  10. 10th March 1965A bag holds 6 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  11. 11th March 1965On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  12. 12th March 1965Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
  13. 13th March 1965Write 5/(x + 3) + 2/(x - 1) as a single fraction.
  14. 14th March 1965A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
  15. 15th March 1965The 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.
  16. 16th March 1965A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
  17. 17th March 1965A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
  18. 18th March 1965Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
  19. 19th March 1965Solve 9x^2 - 4 = 0.
  20. 20th March 1965y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
  21. 21st March 1965In 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.
  22. 22nd March 1965The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
  23. 23rd March 1965On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  24. 24th March 1965A rectangle is 21 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
  25. 25th March 1965f(x) = 6x - 4. Work out the inverse function f^-1(x).
  26. 26th March 1965y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
  27. 27th March 1965In a vector proof you find that vector PQ = a + 3b and vector RS = 2a + 6b. What does this show about PQ and RS?
  28. 28th March 1965A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  29. 29th March 1965A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
  30. 30th March 1965Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
  31. 31st March 1965Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.

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