Daily Practice · Higher
June 2025 - Higher 5-a-day
Every Higher sheet published in June 2025, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' June 2025 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2025A mass is 7.2 kg, correct to 1 decimal place. Write down the lower bound.
- 2nd June 2025A line has equation y = 5x + 2. Work out the gradient of any line perpendicular to it.
- 3rd June 2025x : y = 4 : 9. Write y in terms of x.
- 4th June 2025ABCD is a cyclic quadrilateral. Angle ABC is 60°. Work out angle ADC.
- 5th June 202519 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 6th June 2025A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 7th June 2025Write 7^-1 as a fraction.
- 8th June 2025For the curve y = 12/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 9th June 2025A price rises by 10% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 10th June 2025A, B and C are points on a circle with centre O. Angle AOC is 94°. Work out angle ABC, where B is on the major arc.
- 11th June 20253 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 12th June 2025A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
- 13th June 2025Work out (4 x 10^4) x (7 x 10^5). Give your answer in standard form.
- 14th June 2025Expand and simplify (x - 2)(x - 4)(x + 1).
- 15th June 2025y is inversely proportional to x. When x = 6, y = 16. Work out y when x = 4.
- 16th June 2025A cone has base radius 10 cm and vertical height 6 cm. Work out its volume, leaving your answer in terms of pi.
- 17th June 202514 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 18th June 2025Four classes in order have frequencies 10, 12, 9, 11. Write down the cumulative frequency at the end of the third class.
- 19th June 2025Write the recurring decimal 0.8080... as a fraction in its simplest form.
- 20th June 2025Make x the subject of y = 6x^2 - 6.
- 21st June 2025y is directly proportional to x^2. When x = 5, y = 50. Work out y when x = 9.
- 22nd June 2025In triangle ABC, angle A is 41°, angle B is 36° and side a is 6 cm. Use the sine rule to work out side b, to 1 decimal place.
- 23rd June 20255 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 24th June 202520 fish are marked and released. Later 56 are caught, of which 8 are marked. Estimate the population.
- 25th June 2025A bill is £264 including VAT at 20%. Work out the amount before VAT.
- 26th June 2025Factorise x^2 - 25.
- 27th June 2025y is directly proportional to x. When x = 3, y = 18. Work out y when x = 6.
- 28th June 2025A right-angled triangle has sides 3 cm, 4 cm and 5 cm. Work out the angle opposite the 3 cm side, to 1 decimal place.
- 29th June 202522 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 30th June 2025A cumulative frequency graph is drawn for 136 values. What cumulative frequency do you read across from to estimate the lower quartile?