Daily Practice · Higher Plus

January 2002 - Higher Plus 5-a-day

Every Higher Plus sheet published in January 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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January 2002

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' January 2002 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 2002

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 2002A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
  2. 2nd January 2002A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
  3. 3rd January 2002Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
  4. 4th January 2002Simplify (x^2 + 11x + 28)/(x + 7).
  5. 5th January 2002y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
  6. 6th January 2002In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  7. 7th January 2002The probability of winning a game is 1/5. A player expects 7 wins. How many games did they play?
  8. 8th January 2002On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  9. 9th January 2002A rectangle is 13 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
  10. 10th January 2002In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
  11. 11th January 2002y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
  12. 12th January 2002In a vector proof you find that vector PQ = 6a + 5b and vector RS = 12a + 10b. What does this show about PQ and RS?
  13. 13th January 2002A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
  14. 14th January 2002A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
  15. 15th January 2002Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
  16. 16th January 2002Make x the subject of 4x + 7 = y(x + 7).
  17. 17th January 2002y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 16.
  18. 18th January 2002A cuboid measures 3 cm by 13 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  19. 19th January 2002A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  20. 20th January 2002On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
  21. 21st January 2002A block has mass 300 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  22. 22nd January 2002Write 4/(x + 3) + 2/(x - 5) as a single fraction.
  23. 23rd January 2002A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
  24. 24th January 2002A cuboid measures 4 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  25. 25th January 2002A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  26. 26th January 2002A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
  27. 27th January 2002x = 189 and y = 169, each correct to the nearest whole number. Work out the upper bound of x - y.
  28. 28th January 2002Solve 4x^2 + 23x - 6 = 0.
  29. 29th January 2002y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
  30. 30th January 2002The 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.
  31. 31st January 2002A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.

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