Daily Practice · Higher
December 2025 - Higher 5-a-day
Every Higher sheet published in December 2025, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2025Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 184 cm^3. Work out the volume of the smaller.
- 2nd December 202516 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 3rd December 2025Four classes in order have frequencies 11, 4, 12, 12. Write down the cumulative frequency at the end of the third class.
- 4th December 2025Write sqrt(8) in the form a sqrt(b), where b is as small as possible.
- 5th December 2025Work out the equation of the line parallel to y = -x - 6 that passes through (2, 3).
- 6th December 2025y is directly proportional to x^2. When x = 4, y = 64. Work out y when x = 7.
- 7th December 2025A right-angled triangle has a hypotenuse of 41 cm and one shorter side of 9 cm. Work out the other shorter side.
- 8th December 20251 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 9th December 202510 fish are marked and released. Later 14 are caught, of which 2 are marked. Estimate the population.
- 10th December 2025A meal deal has 7 mains, 7 sides and 6 drinks. How many different meals are possible?
- 11th December 2025A line has equation y = 4x + 2. Work out the gradient of any line perpendicular to it.
- 12th December 2025y is directly proportional to x. When x = 9, y = 90. Work out y when x = 4.
- 13th December 2025ABCD is a cyclic quadrilateral. Angle ABC is 108°. Work out angle ADC.
- 14th December 202515 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 15th December 2025A cumulative frequency graph is drawn for 136 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 16th December 2025A mass is 23 kg, correct to the nearest whole number. Write down the lower bound.
- 17th December 2025For the curve y = -8/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 18th December 2025A town's population is 39500 and grows by 4% each year. Work out the population after 6 years, to the nearest whole number.
- 19th December 2025A, B and C are points on a circle with centre O. Angle AOC is 46°. Work out angle ABC, where B is on the major arc.
- 20th December 20254 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 21st December 2025A box plot has a minimum of 20 and a maximum of 60. Work out the range.
- 22nd December 2025Write 9^-2 as a fraction.
- 23rd December 2025Expand and simplify (x - 4)(x + 5)(x - 4).
- 24th December 2025A block has volume 95 cm^3 and density 3 g/cm^3. Work out its mass.
- 25th December 2025A cone has base radius 8 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
- 26th December 20259 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 27th December 2025A box plot has minimum 4, lower quartile 11, median 20, upper quartile 22 and maximum 26. Work out the interquartile range.
- 28th December 2025Work out (2 x 10^7) x (4 x 10^3). Give your answer in standard form.
- 29th December 2025Make x the subject of y = 5x^2 - 12.
- 30th December 2025x : y = 3 : 7. Write y in terms of x.
- 31st December 2025In triangle ABC, angle A is 40°, angle B is 40° and side a is 5 cm. Use the sine rule to work out side b, to 1 decimal place.