Daily Practice · Higher Plus

February 2022 - Higher Plus 5-a-day

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

← Today's Higher Plus sheet

February 2022

28 sheets · 140 questions · Grades 8-9

Printing for a group?

The batch download puts all 5 tiers' February 2022 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.

Every sheet in February 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 February 2022y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 9.
  2. 2nd February 2022A cuboid measures 7 cm by 13 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  3. 3rd February 2022A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  4. 4th February 2022On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  5. 5th February 2022A car covers 140 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  6. 6th February 2022Work out the coordinates of the turning point of y = x^2 + 6x + 1.
  7. 7th February 2022A train slows steadily from 37 m/s to rest in 4 seconds. Work out its deceleration.
  8. 8th February 2022A cuboid measures 8 cm by 8 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  9. 9th February 2022A bag holds 3 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  10. 10th February 2022A 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?
  11. 11th February 2022Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
  12. 12th February 2022Simplify (x^2 - 3x - 10)/(x - 5).
  13. 13th February 2022y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
  14. 14th February 2022The 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.
  15. 15th February 2022A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
  16. 16th February 2022On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  17. 17th February 2022Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
  18. 18th February 2022In an algebraic proof, how would you write an odd number in terms of an integer n?
  19. 19th February 2022y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
  20. 20th February 2022In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
  21. 21st February 2022The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
  22. 22nd February 2022A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
  23. 23rd February 2022A rectangle is 17 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
  24. 24th February 2022Make x the subject of 8x + 4 = y(x + 4).
  25. 25th February 2022y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 36.
  26. 26th February 2022In a vector proof you find that vector PQ = 6a - 6b and vector RS = 18a - 18b. What does this show about PQ and RS?
  27. 27th February 2022A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  28. 28th February 2022On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?

The same month at another level