Daily Practice · Higher
January 2022 - Higher 5-a-day
Every Higher sheet published in January 2022, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2022A line has equation y = 5x + 2. Work out the gradient of any line perpendicular to it.
- 2nd January 2022y is inversely proportional to x. When x = 8, y = 12. Work out y when x = 3.
- 3rd January 2022ABCD is a cyclic quadrilateral. Angle ABC is 89°. Work out angle ADC.
- 4th January 202219 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th January 2022Four classes in order have frequencies 5, 5, 6, 4. Write down the cumulative frequency at the end of the third class.
- 6th January 2022Work out (8 x 10^4) x (4 x 10^-2). Give your answer in standard form.
- 7th January 2022For the curve y = -100/x, work out y when x = 10, and write down the equation of its vertical asymptote.
- 8th January 2022y is directly proportional to x^2. When x = 4, y = 32. Work out y when x = 9.
- 9th January 2022A, B and C are points on a circle with centre O. Angle AOC is 100°. Work out angle ABC, where B is on the major arc.
- 10th January 20223 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th January 202250 beetles are marked and released. Later 81 are caught, of which 9 are marked. Estimate the population.
- 12th January 2022Write the recurring decimal 0.8282... as a fraction in its simplest form.
- 13th January 2022Expand and simplify (x - 2)(x - 3)(x + 2).
- 14th January 2022y is directly proportional to x. When x = 9, y = 18. Work out y when x = 7.
- 15th January 2022A cone has base radius 10 cm and vertical height 12 cm. Work out its volume, leaving your answer in terms of pi.
- 16th January 202222 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 17th January 2022A cumulative frequency graph is drawn for 80 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 18th January 2022A bill is £216 including VAT at 20%. Work out the amount before VAT.
- 19th January 2022Make x the subject of y = 6x^2 - 2.
- 20th January 2022A town's population is 32000 and grows by 8% each year. Work out the population after 4 years, to the nearest whole number.
- 21st January 2022In triangle ABC, angle A is 70°, angle B is 30° and side a is 9 cm. Use the sine rule to work out side b, to 1 decimal place.
- 22nd January 20222 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd January 2022A box plot has a minimum of 15 and a maximum of 25. Work out the range.
- 24th January 2022A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 25th January 2022Factorise x^2 - 4.
- 26th January 2022A block has volume 110 cm^3 and density 7.5 g/cm^3. Work out its mass.
- 27th January 2022A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Work out the angle opposite the 6 cm side, to 1 decimal place.
- 28th January 202220 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th January 2022A box plot has minimum 12, lower quartile 20, median 30, upper quartile 36 and maximum 41. Work out the interquartile range.
- 30th January 2022Work out (25 x 10^7) / (5 x 10^5). Give your answer in standard form.
- 31st January 2022A region is defined by y < -4x + 2. Should the boundary line be solid or dashed, and why?