Daily Practice · Higher
January 2026 - Higher 5-a-day
Every Higher sheet published in January 2026, with answers. Grades 6-7 - Higher-tier method and manipulation.
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The batch download puts all 5 tiers' January 2026 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2026
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 20261 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 2nd January 2026A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 3rd January 2026Write the recurring decimal 0.9696... as a fraction in its simplest form.
- 4th January 2026Factorise x^2 - 81.
- 5th January 2026A price rises by 15% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 6th January 2026A right-angled triangle has sides 12 cm, 16 cm and 20 cm. Work out the angle opposite the 12 cm side, to 1 decimal place.
- 7th January 202614 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 8th January 2026A histogram class is 5 units wide and contains 7.5 values. Work out the frequency density.
- 9th January 2026A bill is £528 including VAT at 20%. Work out the amount before VAT.
- 10th January 2026A region is defined by y < -x - 9. Should the boundary line be solid or dashed, and why?
- 11th January 2026y is inversely proportional to x. When x = 5, y = 36. Work out y when x = 6.
- 12th January 2026The point (-6, -5) is enlarged by scale factor -1 about the centre (-2, -2). Write down the coordinates of the image.
- 13th January 20262 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 14th January 2026Four classes in order have frequencies 7, 5, 4, 10. Write down the cumulative frequency at the end of the third class.
- 15th January 2026A code is 3 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 16th January 2026Factorise x^2 - 10x + 25.
- 17th January 2026y is directly proportional to x^2. When x = 5, y = 75. Work out y when x = 9.
- 18th January 2026Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 567 cm^3. Work out the volume of the smaller.
- 19th January 202618 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 20th January 202610 beetles are marked and released. Later 14 are caught, of which 2 are marked. Estimate the population.
- 21st January 2026Work out (36 x 10^12) / (4 x 10^3). Give your answer in standard form.
- 22nd January 2026Work out the equation of the line parallel to y = 2x + 1 that passes through (5, 14).
- 23rd January 2026y is directly proportional to x. When x = 6, y = 60. Work out y when x = 10.
- 24th January 2026A right-angled triangle has a hypotenuse of 5 cm and one shorter side of 3 cm. Work out the other shorter side.
- 25th January 20264 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 26th January 2026A cumulative frequency graph is drawn for 232 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 27th January 2026Write the recurring decimal 0.333... as a fraction in its simplest form.
- 28th January 2026A line has equation y = 5x + 9. Work out the gradient of any line perpendicular to it.
- 29th January 2026A town's population is 20000 and grows by 5% each year. Work out the population after 4 years, to the nearest whole number.
- 30th January 2026ABCD is a cyclic quadrilateral. Angle ABC is 87°. Work out angle ADC.
- 31st January 202622 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.