Daily Practice · Higher Plus

June 2001 - Higher Plus 5-a-day

Every Higher Plus sheet published in June 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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June 2001

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' June 2001 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in June 2001

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

  1. 1st June 2001Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
  2. 2nd June 2001Write x^2 + 4x + 10 in the form (x + a)^2 + b.
  3. 3rd June 2001y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
  4. 4th June 2001The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
  5. 5th June 2001A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
  6. 6th June 2001On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
  7. 7th June 2001Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
  8. 8th June 2001Work out the coordinates of the turning point of y = x^2 - 16x - 1.
  9. 9th June 2001y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
  10. 10th June 2001In 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.
  11. 11th June 2001The probability of winning a game is 7/8. A player expects 49 wins. How many games did they play?
  12. 12th June 2001A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
  13. 13th June 2001A rectangle is 12 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
  14. 14th June 2001Simplify (x^2 + 5x - 24)/(x - 3).
  15. 15th June 2001y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 49.
  16. 16th June 2001In a vector proof you find that vector PQ = 6a + 4b and vector RS = 12a + 8b. What does this show about PQ and RS?
  17. 17th June 2001A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  18. 18th June 2001On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  19. 19th June 2001Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
  20. 20th June 2001In an algebraic proof, how would you write an even number in terms of an integer n?
  21. 21st June 2001A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
  22. 22nd June 2001A cuboid measures 9 cm by 4 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  23. 23rd June 2001A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  24. 24th June 2001A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
  25. 25th June 2001A block has mass 450 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  26. 26th June 2001Make x the subject of 5x + 4 = y(x + 4).
  27. 27th June 2001y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
  28. 28th June 2001A cuboid measures 11 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  29. 29th June 2001A bag holds 6 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  30. 30th June 2001On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

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