Daily Practice · Higher Plus

October 2014 - Higher Plus 5-a-day

Every Higher Plus sheet published in October 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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October 2014

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' October 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in October 2014

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

  1. 1st October 2014The probability of winning a game is 1/5. A player expects 5 wins. How many games did they play?
  2. 2nd October 2014A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
  3. 3rd October 2014Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
  4. 4th October 2014f(x) = 4x - 5 and g(x) = 6x + 4. Work out fg(6).
  5. 5th October 2014y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
  6. 6th October 2014In a vector proof you find that vector PQ = 4a + b and vector RS = 8a + 2b. What does this show about PQ and RS?
  7. 7th October 2014A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
  8. 8th October 2014On 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?
  9. 9th October 2014Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
  10. 10th October 2014The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
  11. 11th October 2014y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
  12. 12th October 2014A cuboid measures 12 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  13. 13th October 2014A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  14. 14th October 2014A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
  15. 15th October 2014A rectangle is 27 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
  16. 16th October 2014A quadratic sequence starts 2, 17, 40, 71. Work out the second difference, and the coefficient of n^2.
  17. 17th October 2014y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 25.
  18. 18th October 2014A cuboid measures 5 cm by 11 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  19. 19th October 2014A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  20. 20th October 2014On 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?
  21. 21st October 2014Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
  22. 22nd October 2014Solve x^2 + 9x + 18 < 0.
  23. 23rd October 2014A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
  24. 24th October 2014The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
  25. 25th October 2014A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
  26. 26th October 2014A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
  27. 27th October 2014A block has mass 540 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  28. 28th October 2014Write x^2 - 2x + 1 in the form (x + a)^2 + b.
  29. 29th October 2014y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
  30. 30th October 2014In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
  31. 31st October 2014The probability of winning a game is 1/5. A player expects 26 wins. How many games did they play?

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