Daily Practice · Higher Plus

November 1961 5-a-day

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November 1961

30 sheets · 150 questions · Grades 8-9

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Every sheet in November 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 November 1961The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
  2. 2nd November 1961A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
  3. 3rd November 1961On 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?
  4. 4th November 1961A car covers 830 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  5. 5th November 1961Write 4/(x - 6) + 5/(x - 4) as a single fraction.
  6. 6th November 1961A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
  7. 7th November 1961In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  8. 8th November 1961The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
  9. 9th November 1961A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
  10. 10th November 1961Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
  11. 11th November 1961Solve 6x^2 - 11x + 3 = 0.
  12. 12th November 1961y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
  13. 13th November 1961In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
  14. 14th November 1961A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  15. 15th November 1961On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  16. 16th November 1961Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
  17. 17th November 1961f(x) = 4x - 8. Work out the inverse function f^-1(x).
  18. 18th November 1961y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
  19. 19th November 1961A cuboid measures 6 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  20. 20th November 1961A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  21. 21st November 1961A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
  22. 22nd November 1961A rectangle is 17 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
  23. 23rd November 1961Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
  24. 24th November 1961y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
  25. 25th November 1961A cuboid measures 14 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  26. 26th November 1961A bag holds 3 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  27. 27th November 1961On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
  28. 28th November 1961Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
  29. 29th November 1961Use the iteration x(n+1) = cube root of (11x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
  30. 30th November 1961A train slows steadily from 14 m/s to rest in 5 seconds. Work out its deceleration.

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