Daily Practice · Higher
July 2023 - Higher 5-a-day
Every Higher sheet published in July 2023, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' July 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2023Make x the subject of y = 7x^2 - 10.
- 2nd July 2023y is inversely proportional to x. When x = 8, y = 18. Work out y when x = 6.
- 3rd July 2023In triangle ABC, angle A is 66°, angle B is 48° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
- 4th July 20237 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 5th July 2023Four classes in order have frequencies 8, 7, 10, 8. Write down the cumulative frequency at the end of the third class.
- 6th July 2023A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 7th July 2023Factorise x^2 - 36.
- 8th July 2023y is directly proportional to x^2. When x = 3, y = 18. Work out y when x = 2.
- 9th July 2023A right-angled triangle has sides 5 cm, 12 cm and 13 cm. Work out the angle opposite the 5 cm side, to 1 decimal place.
- 10th July 202330 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 11th July 202360 beetles are marked and released. Later 54 are caught, of which 6 are marked. Estimate the population.
- 12th July 2023Work out (18 x 10^9) / (6 x 10^3). Give your answer in standard form.
- 13th July 2023A region is defined by y <= -2x + 8. Should the boundary line be solid or dashed, and why?
- 14th July 2023y is directly proportional to x. When x = 4, y = 16. Work out y when x = 11.
- 15th July 2023The point (1, 4) is enlarged by scale factor -2 about the centre (-4, 2). Write down the coordinates of the image.
- 16th July 20231 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 17th July 2023A cumulative frequency graph is drawn for 228 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 18th July 2023Write the recurring decimal 0.888... as a fraction in its simplest form.
- 19th July 2023Factorise x^2 + x - 56.
- 20th July 2023A town's population is 34000 and grows by 4% each year. Work out the population after 6 years, to the nearest whole number.
- 21st July 2023Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 104 cm^3. Work out the volume of the smaller.
- 22nd July 202317 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 23rd July 2023A box plot has a minimum of 17 and a maximum of 40. Work out the range.
- 24th July 2023Work out 25^(3/2).
- 25th July 2023Work out the equation of the line parallel to y = -2x + 4 that passes through (3, 5).
- 26th July 2023A block has volume 170 cm^3 and density 8 g/cm^3. Work out its mass.
- 27th July 2023A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 21 cm. Work out the other shorter side.
- 28th July 20233 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 29th July 2023A box plot has minimum 15, lower quartile 23, median 33, upper quartile 40 and maximum 45. Work out the interquartile range.
- 30th July 2023Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
- 31st July 2023A line has equation y = 2x + 8. Work out the gradient of any line perpendicular to it.