Daily Practice · Higher Plus

January 1966 5-a-day

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January 1966

31 sheets · 155 questions · Grades 8-9

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Every sheet in January 1966

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

  1. 1st January 1966In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 5 in terms of an integer n?
  2. 2nd January 1966y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
  3. 3rd January 1966A cuboid measures 7 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  4. 4th January 1966A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  5. 5th January 1966On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  6. 6th January 1966Simplify sqrt(20) + sqrt(45), giving your answer in the form a sqrt(b).
  7. 7th January 1966Make x the subject of 6x + 4 = y(x + 4).
  8. 8th January 1966y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
  9. 9th January 1966The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
  10. 10th January 1966A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
  11. 11th January 1966A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
  12. 12th January 1966A rectangle is 17 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
  13. 13th January 1966Write 3/(x + 3) + 3/(x - 2) as a single fraction.
  14. 14th January 1966y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
  15. 15th January 1966In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  16. 16th January 1966The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
  17. 17th January 1966On 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?
  18. 18th January 1966Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
  19. 19th January 1966Solve 20x^2 + 29x + 6 = 0.
  20. 20th January 1966A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
  21. 21st January 1966In a vector proof you find that vector PQ = 4a - 5b and vector RS = 12a - 15b. What does this show about PQ and RS?
  22. 22nd January 1966A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
  23. 23rd January 1966A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
  24. 24th January 1966A block has mass 270 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.
  25. 25th January 1966f(x) = 8x - 7. Work out the inverse function f^-1(x).
  26. 26th January 1966y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
  27. 27th January 1966A cuboid measures 4 cm by 15 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  28. 28th January 1966A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  29. 29th January 1966On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  30. 30th January 1966x = 88 and y = 51, each correct to the nearest whole number. Work out the upper bound of x - y.
  31. 31st January 1966Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.

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