Daily Practice · Higher Plus

December 1994 - Higher Plus 5-a-day

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December 1994

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' December 1994 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 1994

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 1994y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
  2. 2nd December 1994A 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.
  3. 3rd December 1994A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  4. 4th December 1994On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
  5. 5th December 1994A block has mass 720 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  6. 6th December 1994f(x) = 5x - 6 and g(x) = 5x - 8. Work out fg(-2).
  7. 7th December 1994y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
  8. 8th December 1994The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
  9. 9th December 1994A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
  10. 10th December 1994A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
  11. 11th December 1994x = 186 and y = 126, each correct to the nearest whole number. Work out the upper bound of x - y.
  12. 12th December 1994The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
  13. 13th December 1994y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 9.
  14. 14th December 1994In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
  15. 15th December 1994The probability of winning a game is 7/8. A player expects 49 wins. How many games did they play?
  16. 16th December 1994On 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?
  17. 17th December 1994A car covers 390 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  18. 18th December 1994A quadratic sequence starts 12, 31, 60, 99. Work out the second difference, and the coefficient of n^2.
  19. 19th December 1994A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
  20. 20th December 1994In a vector proof you find that vector PQ = 3a - b and vector RS = 6a - 2b. What does this show about PQ and RS?
  21. 21st December 1994A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  22. 22nd December 1994A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
  23. 23rd December 1994Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
  24. 24th December 1994Solve x^2 + 2x - 8 > 0.
  25. 25th December 1994y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
  26. 26th December 1994A cuboid measures 5 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  27. 27th December 1994A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  28. 28th December 1994On 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?
  29. 29th December 1994Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
  30. 30th December 1994Write x^2 + 4x + 3 in the form (x + a)^2 + b.
  31. 31st December 1994y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.

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