Daily Practice · Higher

September 2025 - Higher 5-a-day

Every Higher sheet published in September 2025, with answers. Grades 6-7 - Higher-tier method and manipulation.

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September 2025

30 sheets · 150 questions · Grades 6-7

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The batch download puts all 5 tiers' September 2025 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 2025

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

  1. 1st September 2025A price rises by 20% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
  2. 2nd September 2025A right-angled triangle has a hypotenuse of 5 cm and one shorter side of 4 cm. Work out the other shorter side.
  3. 3rd September 20257 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  4. 4th September 2025A histogram class is 10 units wide and contains 5 values. Work out the frequency density.
  5. 5th September 2025A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
  6. 6th September 2025A line has equation y = -4x + 3. Work out the gradient of any line perpendicular to it.
  7. 7th September 2025y is inversely proportional to x. When x = 8, y = 12. Work out y when x = 12.
  8. 8th September 2025ABCD is a cyclic quadrilateral. Angle ABC is 125°. Work out angle ADC.
  9. 9th September 202520 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  10. 10th September 2025Four classes in order have frequencies 6, 11, 10, 7. Write down the cumulative frequency at the end of the third class.
  11. 11th September 2025Work out (32 x 10^8) / (8 x 10^3). Give your answer in standard form.
  12. 12th September 2025For the curve y = 10/x, work out y when x = -2, and write down the equation of its vertical asymptote.
  13. 13th September 2025y is directly proportional to x^2. When x = 4, y = 96. Work out y when x = 7.
  14. 14th September 2025A, B and C are points on a circle with centre O. Angle AOC is 76°. Work out angle ABC, where B is on the major arc.
  15. 15th September 20253 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  16. 16th September 202560 fish are marked and released. Later 54 are caught, of which 6 are marked. Estimate the population.
  17. 17th September 2025Write the recurring decimal 0.222... as a fraction in its simplest form.
  18. 18th September 2025Expand and simplify (x + 5)(x + 4)(x - 5).
  19. 19th September 2025y is directly proportional to x. When x = 8, y = 24. Work out y when x = 9.
  20. 20th September 2025A cone has base radius 6 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
  21. 21st September 202515 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  22. 22nd September 2025A cumulative frequency graph is drawn for 64 values. What cumulative frequency do you read across from to estimate the lower quartile?
  23. 23rd September 2025Work out 27^(2/3).
  24. 24th September 2025Make x the subject of y = 3x^2 - 10.
  25. 25th September 2025A town's population is 26000 and grows by 4% each year. Work out the population after 4 years, to the nearest whole number.
  26. 26th September 2025In triangle ABC, angle A is 44°, angle B is 87° and side a is 15 cm. Use the sine rule to work out side b, to 1 decimal place.
  27. 27th September 20251 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  28. 28th September 2025A box plot has a minimum of 8 and a maximum of 54. Work out the range.
  29. 29th September 2025Write sqrt(8) in the form a sqrt(b), where b is as small as possible.
  30. 30th September 2025Factorise x^2 - 81.

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