Daily Practice · Higher
December 2022 - Higher 5-a-day
Every Higher sheet published in December 2022, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2022A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
- 2nd December 2022Work out (2 x 10^3) x (5 x 10^-3). Give your answer in standard form.
- 3rd December 2022A line has equation y = 2x + 1. Work out the gradient of any line perpendicular to it.
- 4th December 2022y is inversely proportional to x. When x = 2, y = 12. Work out y when x = 6.
- 5th December 2022ABCD is a cyclic quadrilateral. Angle ABC is 130°. Work out angle ADC.
- 6th December 202216 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 7th December 2022Four classes in order have frequencies 8, 4, 6, 4. Write down the cumulative frequency at the end of the third class.
- 8th December 2022Write the recurring decimal 0.5252... as a fraction in its simplest form.
- 9th December 2022For the curve y = -8/x, work out y when x = 1, and write down the equation of its vertical asymptote.
- 10th December 2022y is directly proportional to x^2. When x = 6, y = 180. Work out y when x = 2.
- 11th December 2022A, B and C are points on a circle with centre O. Angle AOC is 62°. Work out angle ABC, where B is on the major arc.
- 12th December 20226 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 13th December 202235 fish are marked and released. Later 72 are caught, of which 8 are marked. Estimate the population.
- 14th December 2022A bill is £360 including VAT at 20%. Work out the amount before VAT.
- 15th December 2022Expand and simplify (x + 2)(x - 2)(x + 3).
- 16th December 2022y is directly proportional to x. When x = 4, y = 44. Work out y when x = 9.
- 17th December 2022A cone has base radius 5 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
- 18th December 202222 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 19th December 2022A cumulative frequency graph is drawn for 40 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 20th December 2022A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 21st December 2022Make x the subject of y = 4x^2 - 2.
- 22nd December 2022A town's population is 8500 and grows by 6% each year. Work out the population after 3 years, to the nearest whole number.
- 23rd December 2022In triangle ABC, angle A is 66°, angle B is 83° and side a is 17 cm. Use the sine rule to work out side b, to 1 decimal place.
- 24th December 20223 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 25th December 2022A box plot has a minimum of 16 and a maximum of 38. Work out the range.
- 26th December 2022Work out (28 x 10^8) / (7 x 10^3). Give your answer in standard form.
- 27th December 2022Factorise x^2 - 100.
- 28th December 2022A block has volume 80 cm^3 and density 7.5 g/cm^3. Work out its mass.
- 29th December 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.
- 30th December 202211 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 31st December 2022A box plot has minimum 7, lower quartile 9, median 13, upper quartile 21 and maximum 29. Work out the interquartile range.