Daily Practice · Higher Plus

March 2022 - Higher Plus 5-a-day

Every Higher Plus sheet published in March 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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March 2022

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' March 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in March 2022

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

  1. 1st March 2022Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
  2. 2nd March 2022Write 5/(x + 2) + 4/(x + 3) as a single fraction.
  3. 3rd March 2022A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
  4. 4th March 2022A cuboid measures 6 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  5. 5th March 2022A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  6. 6th March 2022A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
  7. 7th March 2022A block has mass 390 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  8. 8th March 2022Solve 9x^2 + 18x + 8 = 0.
  9. 9th March 2022y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
  10. 10th March 2022A cuboid measures 13 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  11. 11th March 2022A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  12. 12th March 2022On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  13. 13th March 2022x = 73 and y = 22, each correct to the nearest whole number. Work out the upper bound of x - y.
  14. 14th March 2022f(x) = 5x - 8. Work out the inverse function f^-1(x).
  15. 15th March 2022y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
  16. 16th March 2022The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
  17. 17th March 2022A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
  18. 18th March 2022A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
  19. 19th March 2022A car covers 560 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  20. 20th March 2022Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
  21. 21st March 2022y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 49.
  22. 22nd March 2022In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  23. 23rd March 2022The probability of winning a game is 1/10. A player expects 9 wins. How many games did they play?
  24. 24th March 2022On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
  25. 25th March 2022Rationalise the denominator of 24/sqrt(2), giving your answer in its simplest form.
  26. 26th March 2022Use the iteration x(n+1) = cube root of (7x(n) + 5) with x(0) = 4. Work out x(1) to 3 decimal places.
  27. 27th March 2022A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
  28. 28th March 2022In a vector proof you find that vector PQ = 6a + b and vector RS = 18a + 3b. What does this show about PQ and RS?
  29. 29th March 2022A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
  30. 30th March 2022A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
  31. 31st March 2022Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).

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