Daily Practice · Higher Plus

June 2015 - Higher Plus 5-a-day

Every Higher Plus sheet published in June 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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June 2015

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' June 2015 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in June 2015

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 2015Simplify (x^2 - 5x - 14)/(x - 7).
  2. 2nd June 2015y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
  3. 3rd June 2015In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
  4. 4th June 2015A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
  5. 5th June 2015On 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?
  6. 6th June 2015A car covers 480 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  7. 7th June 2015In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
  8. 8th June 2015y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
  9. 9th June 2015A cuboid measures 8 cm by 9 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  10. 10th June 2015A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  11. 11th June 2015A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
  12. 12th June 2015Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
  13. 13th June 2015Make x the subject of 3x + 6 = y(x + 6).
  14. 14th June 2015y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 25.
  15. 15th June 2015A cuboid measures 6 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  16. 16th June 2015A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  17. 17th June 2015On 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?
  18. 18th June 2015Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
  19. 19th June 2015Write 2/(x + 4) + 6/(x + 6) as a single fraction.
  20. 20th June 2015A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
  21. 21st June 2015The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
  22. 22nd June 2015A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
  23. 23rd June 2015A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
  24. 24th June 2015A rectangle is 6 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
  25. 25th June 2015Solve 3x^2 + 5x + 2 = 0.
  26. 26th June 2015y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
  27. 27th June 2015In 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.
  28. 28th June 2015The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
  29. 29th June 2015On a histogram, a 5-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 June 2015Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).

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