Daily Practice · Higher Plus

April 2016 - Higher Plus 5-a-day

Every Higher Plus sheet published in April 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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April 2016

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' April 2016 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in April 2016

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

  1. 1st April 2016Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
  2. 2nd April 2016Simplify (x^2 - 9x + 20)/(x - 5).
  3. 3rd April 2016A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
  4. 4th April 2016A cuboid measures 14 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  5. 5th April 2016A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  6. 6th April 2016A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
  7. 7th April 2016Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
  8. 8th April 2016In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
  9. 9th April 2016y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
  10. 10th April 2016A cuboid measures 10 cm by 4 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  11. 11th April 2016A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  12. 12th April 2016On 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?
  13. 13th April 2016A rectangle is 18 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
  14. 14th April 2016Make x the subject of 7x + 2 = y(x + 2).
  15. 15th April 2016y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
  16. 16th April 2016The 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.
  17. 17th April 2016A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
  18. 18th April 2016A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
  19. 19th April 2016Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
  20. 20th April 2016Write 5/(x - 2) + 4/(x + 1) as a single fraction.
  21. 21st April 2016y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 49.
  22. 22nd April 2016In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  23. 23rd April 2016The probability of winning a game is 1/4. A player expects 4 wins. How many games did they play?
  24. 24th April 2016On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  25. 25th April 2016A block has mass 200 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.
  26. 26th April 2016Solve 2x^2 + 3x - 20 = 0.
  27. 27th April 2016A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
  28. 28th April 2016In a vector proof you find that vector PQ = 6a - 2b and vector RS = 12a - 4b. What does this show about PQ and RS?
  29. 29th April 2016A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
  30. 30th April 2016A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?

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