Daily Practice · Higher Plus

April 2022 - Higher Plus 5-a-day

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

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April 2022

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' April 2022 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in April 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 April 2022Work out the nth term of the quadratic sequence 7, 13, 21, 31, ...
  2. 2nd April 2022y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
  3. 3rd April 2022A cuboid measures 12 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  4. 4th April 2022A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  5. 5th April 2022On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
  6. 6th April 2022A rectangle is 26 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
  7. 7th April 2022The point (1, 1) lies on y = f(x). Write down its image on y = -f(x).
  8. 8th April 2022y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
  9. 9th April 2022A cuboid measures 12 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  10. 10th April 2022A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  11. 11th April 2022A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
  12. 12th April 2022Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
  13. 13th April 2022Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
  14. 14th April 2022y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 49.
  15. 15th April 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.
  16. 16th April 2022A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
  17. 17th April 2022On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
  18. 18th April 2022A block has mass 340 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  19. 19th April 2022f(x) = 4x - 8 and g(x) = 2x + 2. Work out fg(0).
  20. 20th April 2022A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
  21. 21st April 2022In 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.
  22. 22nd April 2022The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
  23. 23rd April 2022A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
  24. 24th April 2022x = 80 and y = 50, each correct to the nearest whole number. Work out the upper bound of x - y.
  25. 25th April 2022The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  26. 26th April 2022y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
  27. 27th April 2022In a vector proof you find that vector PQ = a + 2b and vector RS = 2a + 4b. What does this show about PQ and RS?
  28. 28th April 2022A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
  29. 29th April 2022On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  30. 30th April 2022A car covers 720 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.

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