Daily Practice · Higher
August 2025 - Higher 5-a-day
Every Higher sheet published in August 2025, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2025Expand and simplify (x - 2)(x - 5)(x + 3).
- 2nd August 2025y is directly proportional to x^2. When x = 4, y = 80. Work out y when x = 6.
- 3rd August 2025A cone has base radius 5 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 4th August 202521 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th August 202555 fish are marked and released. Later 90 are caught, of which 9 are marked. Estimate the population.
- 6th August 2025A mass is 13.8 kg, correct to 1 decimal place. Write down the upper bound.
- 7th August 2025Make x the subject of y = 6x^2 - 3.
- 8th August 2025y is directly proportional to x. When x = 2, y = 8. Work out y when x = 10.
- 9th August 2025In triangle ABC, angle A is 58°, angle B is 70° and side a is 15 cm. Use the sine rule to work out side b, to 1 decimal place.
- 10th August 20256 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th August 2025A cumulative frequency graph is drawn for 140 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 12th August 2025Write 7^-2 as a fraction.
- 13th August 2025Factorise x^2 - 100.
- 14th August 2025A town's population is 33000 and grows by 5% each year. Work out the population after 3 years, to the nearest whole number.
- 15th August 2025A right-angled triangle has sides 10 cm, 24 cm and 26 cm. Work out the angle opposite the 10 cm side, to 1 decimal place.
- 16th August 202529 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 17th August 2025A box plot has a minimum of 15 and a maximum of 61. Work out the range.
- 18th August 2025Work out (3 x 10^3) x (2 x 10^4). Give your answer in standard form.
- 19th August 2025A region is defined by y <= -4x + 5. Should the boundary line be solid or dashed, and why?
- 20th August 2025A block has volume 190 cm^3 and density 3 g/cm^3. Work out its mass.
- 21st August 2025The point (-6, 2) is enlarged by scale factor -2 about the centre (1, -2). Write down the coordinates of the image.
- 22nd August 20251 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd August 2025A box plot has minimum 9, lower quartile 19, median 21, upper quartile 23 and maximum 29. Work out the interquartile range.
- 24th August 2025Write the recurring decimal 0.7575... as a fraction in its simplest form.
- 25th August 2025Factorise x^2 - 9x + 14.
- 26th August 2025x : y = 2 : 5. Write y in terms of x.
- 27th August 2025Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 405 cm^3. Work out the volume of the smaller.
- 28th August 202526 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th August 2025A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 30th August 2025A bill is £672 including VAT at 20%. Work out the amount before VAT.
- 31st August 2025Work out the equation of the line parallel to y = -5x + 2 that passes through (3, -3).