Daily Practice · Higher Plus

December 1996 - Higher Plus 5-a-day

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December 1996

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' December 1996 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 1996

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 1996A quadratic sequence starts 8, 13, 24, 41. Work out the second difference, and the coefficient of n^2.
  2. 2nd December 1996y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 64.
  3. 3rd December 1996In 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.
  4. 4th December 1996The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
  5. 5th December 1996On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  6. 6th December 1996Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
  7. 7th December 1996Solve x^2 + 12x + 35 > 0.
  8. 8th December 1996A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
  9. 9th December 1996In a vector proof you find that vector PQ = 4a - 2b and vector RS = 20a - 10b. What does this show about PQ and RS?
  10. 10th December 1996A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  11. 11th December 1996A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
  12. 12th December 1996Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
  13. 13th December 1996Write x^2 - 4x + 7 in the form (x + a)^2 + b.
  14. 14th December 1996y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
  15. 15th December 1996A cuboid measures 5 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  16. 16th December 1996A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  17. 17th December 1996On 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?
  18. 18th December 1996A rectangle is 18 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
  19. 19th December 1996Work out the coordinates of the turning point of y = x^2 + 12x - 14.
  20. 20th December 1996y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
  21. 21st December 1996A cuboid measures 6 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  22. 22nd December 1996A bag holds 5 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  23. 23rd December 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
  24. 24th December 1996Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).
  25. 25th December 1996Simplify (x^2 - 15x + 56)/(x - 8).
  26. 26th December 1996y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 36.
  27. 27th December 1996The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
  28. 28th December 1996A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
  29. 29th December 1996On 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 1996A block has mass 200 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  31. 31st December 1996In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?

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