Daily Practice · Higher
August 2022 - Higher 5-a-day
Every Higher sheet published in August 2022, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2022In triangle ABC, angle A is 74°, angle B is 60° and side a is 9 cm. Use the sine rule to work out side b, to 1 decimal place.
- 2nd August 20221 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd August 2022Four classes in order have frequencies 5, 4, 12, 11. Write down the cumulative frequency at the end of the third class.
- 4th August 2022A bill is £600 including VAT at 20%. Work out the amount before VAT.
- 5th August 2022Factorise x^2 - 9.
- 6th August 2022y is directly proportional to x^2. When x = 5, y = 50. Work out y when x = 6.
- 7th August 2022A right-angled triangle has sides 8 cm, 15 cm and 17 cm. Work out the angle opposite the 8 cm side, to 1 decimal place.
- 8th August 202229 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th August 202215 newts are marked and released. Later 18 are caught, of which 6 are marked. Estimate the population.
- 10th August 2022A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 11th August 2022A region is defined by y <= x + 3. Should the boundary line be solid or dashed, and why?
- 12th August 2022y is directly proportional to x. When x = 2, y = 14. Work out y when x = 13.
- 13th August 2022The point (2, 3) is enlarged by scale factor -3 about the centre (-3, -4). Write down the coordinates of the image.
- 14th August 20222 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th August 2022A cumulative frequency graph is drawn for 72 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 16th August 2022Work out (54 x 10^10) / (6 x 10^2). Give your answer in standard form.
- 17th August 2022Factorise x^2 - x - 56.
- 18th August 2022A town's population is 29000 and grows by 3% each year. Work out the population after 4 years, to the nearest whole number.
- 19th August 2022Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 72 cm^3. Work out the volume of the smaller.
- 20th August 202213 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st August 2022A box plot has a minimum of 20 and a maximum of 58. Work out the range.
- 22nd August 2022Write the recurring decimal 0.444... as a fraction in its simplest form.
- 23rd August 2022Work out the equation of the line parallel to y = -x + 4 that passes through (4, -12).
- 24th August 2022A block has volume 85 cm^3 and density 2.5 g/cm^3. Work out its mass.
- 25th August 2022A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 24 cm. Work out the other shorter side.
- 26th August 20221 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th August 2022A box plot has minimum 11, lower quartile 15, median 21, upper quartile 27 and maximum 32. Work out the interquartile range.
- 28th August 2022Work out 36^(3/2).
- 29th August 2022A line has equation y = -2x + 5. Work out the gradient of any line perpendicular to it.
- 30th August 2022x : y = 4 : 9. Write y in terms of x.
- 31st August 2022ABCD is a cyclic quadrilateral. Angle ABC is 123°. Work out angle ADC.