Daily Practice · Higher Plus

December 1974 5-a-day

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December 1974

31 sheets · 155 questions · Grades 8-9

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Every sheet in December 1974

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

  1. 1st December 1974On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
  2. 2nd December 1974A block has mass 520 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  3. 3rd December 1974Simplify (x^2 + 6x + 8)/(x + 2).
  4. 4th December 1974A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
  5. 5th December 1974In a vector proof you find that vector PQ = 4a - b and vector RS = 8a - 2b. What does this show about PQ and RS?
  6. 6th December 1974A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
  7. 7th December 1974A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
  8. 8th December 1974x = 146 and y = 69, each correct to the nearest whole number. Work out the upper bound of x - y.
  9. 9th December 1974In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
  10. 10th December 1974y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
  11. 11th December 1974A cuboid measures 9 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  12. 12th December 1974A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  13. 13th December 1974On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
  14. 14th December 1974A car covers 600 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  15. 15th December 1974Make x the subject of 7x + 5 = y(x + 5).
  16. 16th December 1974y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
  17. 17th December 1974A cuboid measures 13 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  18. 18th December 1974A bag holds 4 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  19. 19th December 1974A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
  20. 20th December 1974Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
  21. 21st December 1974Write 2/(x - 4) + 4/(x - 6) as a single fraction.
  22. 22nd December 1974y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 64.
  23. 23rd December 1974The 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.
  24. 24th December 1974A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
  25. 25th December 1974On 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?
  26. 26th December 1974Simplify sqrt(18) + sqrt(98), giving your answer in the form a sqrt(b).
  27. 27th December 1974Solve 4x^2 - 1 = 0.
  28. 28th December 1974A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
  29. 29th December 1974In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
  30. 30th December 1974The probability of winning a game is 9/10. A player expects 135 wins. How many games did they play?
  31. 31st December 1974A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?

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