Daily Practice · Higher Plus

November 1954 5-a-day

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November 1954

30 sheets · 150 questions · Grades 8-9

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Every sheet in November 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 November 1954y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
  2. 2nd November 1954A cuboid measures 13 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  3. 3rd November 1954A bag holds 3 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  4. 4th November 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  5. 5th November 1954Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
  6. 6th November 1954Make x the subject of 3x + 4 = y(x + 4).
  7. 7th November 1954y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
  8. 8th November 1954The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
  9. 9th November 1954A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
  10. 10th November 1954A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
  11. 11th November 1954Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
  12. 12th November 1954Write 4/(x + 2) + 6/(x - 1) as a single fraction.
  13. 13th November 1954y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 9.
  14. 14th November 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.
  15. 15th November 1954The probability of winning a game is 1/5. A player expects 5 wins. How many games did they play?
  16. 16th November 1954On 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?
  17. 17th November 1954A rectangle is 4 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  18. 18th November 1954Solve 10x^2 - 13x + 4 = 0.
  19. 19th November 1954A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.
  20. 20th November 1954In a vector proof you find that vector PQ = 4a - b and vector RS = 16a - 4b. What does this show about PQ and RS?
  21. 21st November 1954A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  22. 22nd November 1954A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
  23. 23rd November 1954Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
  24. 24th November 1954f(x) = 2x - 4. Work out the inverse function f^-1(x).
  25. 25th November 1954y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
  26. 26th November 1954A cuboid measures 6 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  27. 27th November 1954A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  28. 28th November 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
  29. 29th November 1954A block has mass 680 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  30. 30th November 1954Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.

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