Daily Practice · Higher
July 2021 - Higher 5-a-day
Every Higher sheet published in July 2021, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' July 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2021A, B and C are points on a circle with centre O. Angle AOC is 154°. Work out angle ABC, where B is on the major arc.
- 2nd July 20217 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd July 2021A box plot has minimum 9, lower quartile 19, median 25, upper quartile 30 and maximum 36. Work out the interquartile range.
- 4th July 2021A bill is £168 including VAT at 20%. Work out the amount before VAT.
- 5th July 2021Expand and simplify (x - 2)(x - 1)(x - 1).
- 6th July 2021x : y = 5 : 7. Write y in terms of x.
- 7th July 2021A cone has base radius 10 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
- 8th July 202122 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th July 2021A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 10th July 2021A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 11th July 2021Make x the subject of y = 6x^2 - 9.
- 12th July 2021A price rises by 15% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 13th July 2021In triangle ABC, angle A is 43°, angle B is 80° and side a is 6 cm. Use the sine rule to work out side b, to 1 decimal place.
- 14th July 20215 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th July 2021A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
- 16th July 2021Work out (10 x 10^6) / (5 x 10^2). Give your answer in standard form.
- 17th July 2021Factorise x^2 - 9.
- 18th July 2021y is inversely proportional to x. When x = 6, y = 60. Work out y when x = 12.
- 19th July 2021A right-angled triangle has sides 20 cm, 21 cm and 29 cm. Work out the angle opposite the 20 cm side, to 1 decimal place.
- 20th July 202112 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st July 2021Four classes in order have frequencies 9, 12, 10, 9. Write down the cumulative frequency at the end of the third class.
- 22nd July 2021Write the recurring decimal 0.888... as a fraction in its simplest form.
- 23rd July 2021A region is defined by y < 3x + 2. Should the boundary line be solid or dashed, and why?
- 24th July 2021y is directly proportional to x^2. When x = 4, y = 128. Work out y when x = 3.
- 25th July 2021The point (6, 5) is enlarged by scale factor -3 about the centre (3, 1). Write down the coordinates of the image.
- 26th July 20214 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th July 202135 beetles are marked and released. Later 50 are caught, of which 5 are marked. Estimate the population.
- 28th July 2021Work out 49^(3/2).
- 29th July 2021Factorise x^2 - 4.
- 30th July 2021y is directly proportional to x. When x = 4, y = 48. Work out y when x = 2.
- 31st July 2021Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 304 cm^3. Work out the volume of the smaller.