Daily Practice · Higher
December 2020 - Higher 5-a-day
Every Higher sheet published in December 2020, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2020Factorise x^2 - 12x + 32.
- 2nd December 2020A block has volume 40 cm^3 and density 3 g/cm^3. Work out its mass.
- 3rd December 2020Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 152 cm^3. Work out the volume of the smaller.
- 4th December 202019 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th December 2020A box plot has minimum 13, lower quartile 23, median 25, upper quartile 29 and maximum 39. Work out the interquartile range.
- 6th December 2020Work out (8 x 10^3) x (2 x 10^-6). Give your answer in standard form.
- 7th December 2020Work out the equation of the line parallel to y = -2x + 4 that passes through (3, 3).
- 8th December 2020x : y = 5 : 9. Write y in terms of x.
- 9th December 2020A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 24 cm. Work out the other shorter side.
- 10th December 20207 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th December 2020A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
- 12th December 2020Write the recurring decimal 0.9898... as a fraction in its simplest form.
- 13th December 2020A line has equation y = 3x + 2. Work out the gradient of any line perpendicular to it.
- 14th December 2020A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 15th December 2020ABCD is a cyclic quadrilateral. Angle ABC is 55°. Work out angle ADC.
- 16th December 202014 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 17th December 2020A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
- 18th December 2020A bill is £72 including VAT at 20%. Work out the amount before VAT.
- 19th December 2020For the curve y = 25/x, work out y when x = 5, and write down the equation of its vertical asymptote.
- 20th December 2020y is inversely proportional to x. When x = 4, y = 5. Work out y when x = 5.
- 21st December 2020A, B and C are points on a circle with centre O. Angle AOC is 152°. Work out angle ABC, where B is on the major arc.
- 22nd December 20203 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd December 2020Four classes in order have frequencies 7, 11, 6, 12. Write down the cumulative frequency at the end of the third class.
- 24th December 2020A code is 3 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 25th December 2020Expand and simplify (x - 4)(x + 5)(x - 2).
- 26th December 2020y is directly proportional to x^2. When x = 2, y = 8. Work out y when x = 9.
- 27th December 2020A cone has base radius 4 cm and vertical height 6 cm. Work out its volume, leaving your answer in terms of pi.
- 28th December 202025 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th December 202060 beetles are marked and released. Later 16 are caught, of which 2 are marked. Estimate the population.
- 30th December 2020Work out (42 x 10^7) / (7 x 10^4). Give your answer in standard form.
- 31st December 2020Make x the subject of y = 2x^2 - 5.