Daily Practice · Higher
January 2020 - Higher 5-a-day
Every Higher sheet published in January 2020, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2020A block has volume 55 cm^3 and density 4 g/cm^3. Work out its mass.
- 2nd January 2020Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 304 cm^3. Work out the volume of the smaller.
- 3rd January 202013 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 4th January 2020A box plot has minimum 12, lower quartile 18, median 21, upper quartile 23 and maximum 30. Work out the interquartile range.
- 5th January 2020Write 9^-3 as a fraction.
- 6th January 2020Work out the equation of the line parallel to y = 5x + 6 that passes through (2, 11).
- 7th January 2020x : y = 5 : 8. Write y in terms of x.
- 8th January 2020A right-angled triangle has a hypotenuse of 25 cm and one shorter side of 24 cm. Work out the other shorter side.
- 9th January 20203 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 10th January 2020A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
- 11th January 2020Work out (9 x 10^3) x (3 x 10^5). Give your answer in standard form.
- 12th January 2020A line has equation y = 4x + 8. Work out the gradient of any line perpendicular to it.
- 13th January 2020A price rises by 15% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 14th January 2020ABCD is a cyclic quadrilateral. Angle ABC is 57°. Work out angle ADC.
- 15th January 202022 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 16th January 2020A histogram class is 10 units wide and contains 40 values. Work out the frequency density.
- 17th January 2020Write the recurring decimal 0.8787... as a fraction in its simplest form.
- 18th January 2020For the curve y = -36/x, work out y when x = -4, and write down the equation of its vertical asymptote.
- 19th January 2020y is inversely proportional to x. When x = 3, y = 30. Work out y when x = 10.
- 20th January 2020A, B and C are points on a circle with centre O. Angle AOC is 80°. Work out angle ABC, where B is on the major arc.
- 21st January 20202 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 22nd January 2020Four classes in order have frequencies 11, 4, 8, 6. Write down the cumulative frequency at the end of the third class.
- 23rd January 2020A bill is £912 including VAT at 20%. Work out the amount before VAT.
- 24th January 2020Expand and simplify (x + 5)(x + 2)(x - 3).
- 25th January 2020y is directly proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 26th January 2020A cone has base radius 3 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
- 27th January 202023 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 28th January 202015 beetles are marked and released. Later 96 are caught, of which 8 are marked. Estimate the population.
- 29th January 2020A code is 3 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 30th January 2020Make x the subject of y = 8x^2 - 4.
- 31st January 2020y is directly proportional to x. When x = 6, y = 18. Work out y when x = 8.