Daily Practice · Higher
July 2025 - Higher 5-a-day
Every Higher sheet published in July 2025, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' July 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2025A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 2nd July 2025A region is defined by y < 4x + 8. Should the boundary line be solid or dashed, and why?
- 3rd July 2025A town's population is 35500 and grows by 5% each year. Work out the population after 2 years, to the nearest whole number.
- 4th July 2025The point (-6, 1) is enlarged by scale factor -1 about the centre (-2, 3). Write down the coordinates of the image.
- 5th July 20255 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 6th July 2025A box plot has a minimum of 4 and a maximum of 38. Work out the range.
- 7th July 2025Work out (8 x 10^12) / (4 x 10^4). Give your answer in standard form.
- 8th July 2025Factorise x^2 + 4x - 21.
- 9th July 2025A block has volume 175 cm^3 and density 7.5 g/cm^3. Work out its mass.
- 10th July 2025Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 513 cm^3. Work out the volume of the smaller.
- 11th July 202515 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 12th July 2025A box plot has minimum 11, lower quartile 15, median 24, upper quartile 30 and maximum 36. Work out the interquartile range.
- 13th July 2025Write the recurring decimal 0.333... as a fraction in its simplest form.
- 14th July 2025Work out the equation of the line parallel to y = -3x + 8 that passes through (3, 2).
- 15th July 2025x : y = 5 : 7. Write y in terms of x.
- 16th July 2025A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 16 cm. Work out the other shorter side.
- 17th July 20252 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 18th July 2025A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 19th July 2025Work out 16^(3/2).
- 20th July 2025A line has equation y = 5x + 1. Work out the gradient of any line perpendicular to it.
- 21st July 2025A price rises by 20% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 22nd July 2025ABCD is a cyclic quadrilateral. Angle ABC is 122°. Work out angle ADC.
- 23rd July 202522 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 24th July 2025A histogram class is 2 units wide and contains 3 values. Work out the frequency density.
- 25th July 2025Write sqrt(32) in the form a sqrt(b), where b is as small as possible.
- 26th July 2025For the curve y = 6/x, work out y when x = 1, and write down the equation of its vertical asymptote.
- 27th July 2025y is inversely proportional to x. When x = 5, y = 24. Work out y when x = 6.
- 28th July 2025A, B and C are points on a circle with centre O. Angle AOC is 72°. Work out angle ABC, where B is on the major arc.
- 29th July 20255 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 30th July 2025Four classes in order have frequencies 10, 3, 9, 3. Write down the cumulative frequency at the end of the third class.
- 31st July 2025A meal deal has 9 mains, 6 sides and 2 drinks. How many different meals are possible?