Daily Practice · Higher Plus

December 1980 5-a-day

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December 1980

31 sheets · 155 questions · Grades 8-9

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Every sheet in December 1980

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 1980Work out the nth term of the quadratic sequence -9, -8, -3, 6, ...
  2. 2nd December 1980y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
  3. 3rd December 1980In a vector proof you find that vector PQ = 5a - 2b and vector RS = 15a - 6b. What does this show about PQ and RS?
  4. 4th December 1980A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
  5. 5th December 1980On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  6. 6th December 1980A car covers 380 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  7. 7th December 1980The point (-5, 6) lies on y = f(x). Write down its image on y = -f(x).
  8. 8th December 1980y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
  9. 9th December 1980A cuboid measures 6 cm by 7 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  10. 10th December 1980A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  11. 11th December 1980A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
  12. 12th December 1980Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
  13. 13th December 1980Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
  14. 14th December 1980y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 9.
  15. 15th December 1980A cuboid measures 4 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  16. 16th December 1980A bag holds 7 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  17. 17th December 1980On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  18. 18th December 1980Simplify sqrt(48) + sqrt(147), giving your answer in the form a sqrt(b).
  19. 19th December 1980f(x) = 6x + 2 and g(x) = 2x + 7. Work out fg(1).
  20. 20th December 1980A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
  21. 21st December 1980The 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.
  22. 22nd December 1980A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
  23. 23rd December 1980A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
  24. 24th December 1980A rectangle is 20 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  25. 25th December 1980The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
  26. 26th December 1980y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
  27. 27th December 1980In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
  28. 28th December 1980The probability of winning a game is 4/5. A player expects 52 wins. How many games did they play?
  29. 29th December 1980On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  30. 30th December 1980Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
  31. 31st December 1980A quadratic sequence starts 11, 23, 45, 77. Work out the second difference, and the coefficient of n^2.

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