Daily Practice · Higher Plus

February 1955 5-a-day

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February 1955

28 sheets · 140 questions · Grades 8-9

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The batch download puts all 5 tiers' February 1955 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.

Every sheet in February 1955

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st February 1955A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  2. 2nd February 1955A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
  3. 3rd February 1955Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
  4. 4th February 1955Simplify (x^2 + 4x - 5)/(x + 5).
  5. 5th February 1955y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
  6. 6th February 1955The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
  7. 7th February 1955A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
  8. 8th February 1955On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
  9. 9th February 1955A rectangle is 18 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
  10. 10th February 1955In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 6 in terms of an integer n?
  11. 11th February 1955y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
  12. 12th February 1955In 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.
  13. 13th February 1955The probability of winning a game is 1/4. A player expects 28 wins. How many games did they play?
  14. 14th February 1955A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
  15. 15th February 1955Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
  16. 16th February 1955Make x the subject of 5x + 4 = y(x + 4).
  17. 17th February 1955y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 64.
  18. 18th February 1955In a vector proof you find that vector PQ = 3a - 5b and vector RS = 9a - 15b. What does this show about PQ and RS?
  19. 19th February 1955A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  20. 20th February 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  21. 21st February 1955A block has mass 650 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  22. 22nd February 1955Write 4/(x - 4) + 6/(x - 3) as a single fraction.
  23. 23rd February 1955A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
  24. 24th February 1955A cuboid measures 15 cm by 3 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  25. 25th February 1955A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  26. 26th February 1955A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
  27. 27th February 1955x = 166 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
  28. 28th February 1955Solve 12x^2 + 13x - 4 = 0.

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