Daily Practice · Higher
July 2026 - Higher 5-a-day
Every Higher sheet published in July 2026, with answers. Grades 6-7 - Higher-tier method and manipulation.
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The batch download puts all 5 tiers' July 2026 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2026
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2026Four classes in order have frequencies 3, 6, 4, 8. Write down the cumulative frequency at the end of the third class.
- 2nd July 2026A mass is 57 kg, correct to the nearest whole number. Write down the lower bound.
- 3rd July 2026Expand and simplify (x + 4)(x + 2)(x - 4).
- 4th July 2026y is directly proportional to x^2. When x = 4, y = 96. Work out y when x = 2.
- 5th July 2026A cone has base radius 2 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
- 6th July 202622 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 7th July 202615 voles are marked and released. Later 15 are caught, of which 3 are marked. Estimate the population.
- 8th July 2026Write 5^-2 as a fraction.
- 9th July 2026Make x the subject of y = 2x^2 - 9.
- 10th July 2026y is directly proportional to x. When x = 5, y = 15. Work out y when x = 6.
- 11th July 2026In triangle ABC, angle A is 36°, angle B is 93° and side a is 16 cm. Use the sine rule to work out side b, to 1 decimal place.
- 12th July 20262 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 13th July 2026A cumulative frequency graph is drawn for 92 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 14th July 2026Work out (8 x 10^4) x (9 x 10^-3). Give your answer in standard form.
- 15th July 2026Factorise x^2 - 144.
- 16th July 2026A town's population is 26500 and grows by 5% each year. Work out the population after 4 years, to the nearest whole number.
- 17th July 2026A right-angled triangle has sides 9 cm, 12 cm and 15 cm. Work out the angle opposite the 9 cm side, to 1 decimal place.
- 18th July 202621 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 19th July 2026A box plot has a minimum of 9 and a maximum of 66. Work out the range.
- 20th July 2026Write the recurring decimal 0.1313... as a fraction in its simplest form.
- 21st July 2026A region is defined by y < -x + 7. Should the boundary line be solid or dashed, and why?
- 22nd July 2026A block has volume 110 cm^3 and density 11 g/cm^3. Work out its mass.
- 23rd July 2026The point (-1, -3) is enlarged by scale factor -1 about the centre (-2, 2). Write down the coordinates of the image.
- 24th July 20263 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 25th July 2026A box plot has minimum 3, lower quartile 6, median 10, upper quartile 16 and maximum 21. Work out the interquartile range.
- 26th July 2026A bill is £48 including VAT at 20%. Work out the amount before VAT.
- 27th July 2026Factorise x^2 - 3x - 28.
- 28th July 2026x : y = 5 : 7. Write y in terms of x.
- 29th July 2026Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 128 cm^3. Work out the volume of the smaller.
- 30th July 202629 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 31st July 2026A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.