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.
Printing for a group?
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.
- 1st September 2025A price rises by 20% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 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.
- 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.
- 4th September 2025A histogram class is 10 units wide and contains 5 values. Work out the frequency density.
- 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?
- 6th September 2025A line has equation y = -4x + 3. Work out the gradient of any line perpendicular to it.
- 7th September 2025y is inversely proportional to x. When x = 8, y = 12. Work out y when x = 12.
- 8th September 2025ABCD is a cyclic quadrilateral. Angle ABC is 125°. Work out angle ADC.
- 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.
- 10th September 2025Four classes in order have frequencies 6, 11, 10, 7. Write down the cumulative frequency at the end of the third class.
- 11th September 2025Work out (32 x 10^8) / (8 x 10^3). Give your answer in standard form.
- 12th September 2025For the curve y = 10/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 13th September 2025y is directly proportional to x^2. When x = 4, y = 96. Work out y when x = 7.
- 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.
- 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.
- 16th September 202560 fish are marked and released. Later 54 are caught, of which 6 are marked. Estimate the population.
- 17th September 2025Write the recurring decimal 0.222... as a fraction in its simplest form.
- 18th September 2025Expand and simplify (x + 5)(x + 4)(x - 5).
- 19th September 2025y is directly proportional to x. When x = 8, y = 24. Work out y when x = 9.
- 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.
- 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.
- 22nd September 2025A cumulative frequency graph is drawn for 64 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 23rd September 2025Work out 27^(2/3).
- 24th September 2025Make x the subject of y = 3x^2 - 10.
- 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.
- 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.
- 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.
- 28th September 2025A box plot has a minimum of 8 and a maximum of 54. Work out the range.
- 29th September 2025Write sqrt(8) in the form a sqrt(b), where b is as small as possible.
- 30th September 2025Factorise x^2 - 81.