Daily Practice · Higher Plus

February 1954 5-a-day

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February 1954

28 sheets · 140 questions · Grades 8-9

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Every sheet in February 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 February 1954On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  2. 2nd February 1954Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
  3. 3rd February 1954Use the iteration x(n+1) = cube root of (8x(n) + 4) with x(0) = 5. Work out x(1) to 3 decimal places.
  4. 4th February 1954A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
  5. 5th February 1954A cuboid measures 12 cm by 13 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  6. 6th February 1954A bag holds 6 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  7. 7th February 1954A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
  8. 8th February 1954A block has mass 570 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  9. 9th February 1954Work out the nth term of the quadratic sequence 6, 18, 36, 60, ...
  10. 10th February 1954y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
  11. 11th February 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.
  12. 12th February 1954A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
  13. 13th February 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  14. 14th February 1954x = 48 and y = 28, each correct to the nearest whole number. Work out the upper bound of x - y.
  15. 15th February 1954The point (4, 0) lies on y = f(x). Write down its image on y = f(x + 1).
  16. 16th February 1954y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
  17. 17th February 1954In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  18. 18th February 1954The probability of winning a game is 4/5. A player expects 48 wins. How many games did they play?
  19. 19th February 1954A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
  20. 20th February 1954A car covers 100 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  21. 21st February 1954Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
  22. 22nd February 1954y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 49.
  23. 23rd February 1954In a vector proof you find that vector PQ = a + 6b and vector RS = 3a + 18b. What does this show about PQ and RS?
  24. 24th February 1954A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
  25. 25th February 1954On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
  26. 26th February 1954Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
  27. 27th February 1954f(x) = 6x + 5 and g(x) = 5x - 9. Work out fg(2).
  28. 28th February 1954A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.

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