Daily Practice · Higher
October 2025 - Higher 5-a-day
Every Higher sheet published in October 2025, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' October 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2025A block has volume 120 cm^3 and density 2.5 g/cm^3. Work out its mass.
- 2nd October 2025A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Work out the angle opposite the 6 cm side, to 1 decimal place.
- 3rd October 202524 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 4th October 2025A box plot has minimum 15, lower quartile 25, median 27, upper quartile 34 and maximum 39. Work out the interquartile range.
- 5th October 2025A meal deal has 3 mains, 9 sides and 2 drinks. How many different meals are possible?
- 6th October 2025A region is defined by y <= -4x + 4. Should the boundary line be solid or dashed, and why?
- 7th October 2025x : y = 4 : 5. Write y in terms of x.
- 8th October 2025The point (-6, -6) is enlarged by scale factor -2 about the centre (-4, 1). Write down the coordinates of the image.
- 9th October 20256 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 10th October 2025A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 11th October 2025A mass is 69 kg, correct to the nearest whole number. Write down the lower bound.
- 12th October 2025Factorise x^2 - 4x - 45.
- 13th October 2025A price rises by 20% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 14th October 2025Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 1920 cm^3. Work out the volume of the smaller.
- 15th October 202525 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 16th October 2025A histogram class is 10 units wide and contains 5 values. Work out the frequency density.
- 17th October 2025Write 9^-2 as a fraction.
- 18th October 2025Work out the equation of the line parallel to y = -x - 7 that passes through (5, -2).
- 19th October 2025y is inversely proportional to x. When x = 3, y = 16. Work out y when x = 4.
- 20th October 2025A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 12 cm. Work out the other shorter side.
- 21st October 20251 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 22nd October 2025Four classes in order have frequencies 5, 11, 11, 9. Write down the cumulative frequency at the end of the third class.
- 23rd October 2025Work out (2 x 10^4) x (4 x 10^6). Give your answer in standard form.
- 24th October 2025A line has equation y = -5x + 5. Work out the gradient of any line perpendicular to it.
- 25th October 2025y is directly proportional to x^2. When x = 2, y = 16. Work out y when x = 7.
- 26th October 2025ABCD is a cyclic quadrilateral. Angle ABC is 54°. Work out angle ADC.
- 27th October 202527 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 28th October 202555 voles are marked and released. Later 21 are caught, of which 7 are marked. Estimate the population.
- 29th October 2025Write the recurring decimal 0.3838... as a fraction in its simplest form.
- 30th October 2025For the curve y = -12/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 31st October 2025y is directly proportional to x. When x = 8, y = 56. Work out y when x = 7.