Daily Practice · Higher Plus

April 2020 - Higher Plus 5-a-day

Every Higher Plus sheet published in April 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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April 2020

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' April 2020 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in April 2020

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 2020In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  2. 2nd April 2020The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
  3. 3rd April 2020On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
  4. 4th April 2020A car covers 550 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  5. 5th April 2020Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
  6. 6th April 2020A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
  7. 7th April 2020In a vector proof you find that vector PQ = 6a - 5b and vector RS = 24a - 20b. What does this show about PQ and RS?
  8. 8th April 2020A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
  9. 9th April 2020A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
  10. 10th April 2020Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
  11. 11th April 2020Use the iteration x(n+1) = cube root of (9x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
  12. 12th April 2020y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
  13. 13th April 2020A cuboid measures 5 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  14. 14th April 2020A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  15. 15th April 2020On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
  16. 16th April 2020Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
  17. 17th April 2020Work out the nth term of the quadratic sequence 2, 12, 28, 50, ...
  18. 18th April 2020y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
  19. 19th April 2020A cuboid measures 6 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  20. 20th April 2020A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  21. 21st April 2020A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
  22. 22nd April 2020A rectangle is 20 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
  23. 23rd April 2020The point (-4, -6) lies on y = f(x). Write down its image on y = -f(x).
  24. 24th April 2020y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
  25. 25th April 2020The 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.
  26. 26th April 2020A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
  27. 27th April 2020On 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?
  28. 28th April 2020Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
  29. 29th April 2020Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
  30. 30th April 2020A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.

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