Daily Practice · Higher
August 2023 - Higher 5-a-day
Every Higher sheet published in August 2023, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2023x : y = 5 : 8. Write y in terms of x.
- 2nd August 2023ABCD is a cyclic quadrilateral. Angle ABC is 124°. Work out angle ADC.
- 3rd August 202314 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 4th August 2023A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 5th August 2023A meal deal has 5 mains, 6 sides and 4 drinks. How many different meals are possible?
- 6th August 2023For the curve y = -50/x, work out y when x = -5, and write down the equation of its vertical asymptote.
- 7th August 2023A price rises by 25% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 8th August 2023A, B and C are points on a circle with centre O. Angle AOC is 126°. Work out angle ABC, where B is on the major arc.
- 9th August 20231 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 10th August 2023A histogram class is 5 units wide and contains 15 values. Work out the frequency density.
- 11th August 2023A mass is 380 kg, correct to the nearest 10. Write down the upper bound.
- 12th August 2023Expand and simplify (x - 5)(x + 5)(x + 5).
- 13th August 2023y is inversely proportional to x. When x = 2, y = 10. Work out y when x = 10.
- 14th August 2023A cone has base radius 7 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 15th August 202316 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 16th August 2023Four classes in order have frequencies 8, 6, 4, 10. Write down the cumulative frequency at the end of the third class.
- 17th August 2023Write 4^-2 as a fraction.
- 18th August 2023Make x the subject of y = 3x^2 - 5.
- 19th August 2023y is directly proportional to x^2. When x = 5, y = 125. Work out y when x = 4.
- 20th August 2023In triangle ABC, angle A is 44°, angle B is 31° and side a is 6 cm. Use the sine rule to work out side b, to 1 decimal place.
- 21st August 20233 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 22nd August 202325 voles are marked and released. Later 16 are caught, of which 4 are marked. Estimate the population.
- 23rd August 2023Work out (9 x 10^3) x (6 x 10^-3). Give your answer in standard form.
- 24th August 2023Factorise x^2 - 4.
- 25th August 2023y is directly proportional to x. When x = 9, y = 108. Work out y when x = 11.
- 26th August 2023A right-angled triangle has sides 7 cm, 24 cm and 25 cm. Work out the angle opposite the 7 cm side, to 1 decimal place.
- 27th August 202315 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 28th August 2023A cumulative frequency graph is drawn for 140 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 29th August 2023Write the recurring decimal 0.4040... as a fraction in its simplest form.
- 30th August 2023A region is defined by y <= 2x + 7. Should the boundary line be solid or dashed, and why?
- 31st August 2023A town's population is 35000 and grows by 5% each year. Work out the population after 3 years, to the nearest whole number.