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.

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December 2020

31 sheets · 155 questions · Grades 6-7

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.

  1. 1st December 2020Factorise x^2 - 12x + 32.
  2. 2nd December 2020A block has volume 40 cm^3 and density 3 g/cm^3. Work out its mass.
  3. 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.
  4. 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.
  5. 5th December 2020A box plot has minimum 13, lower quartile 23, median 25, upper quartile 29 and maximum 39. Work out the interquartile range.
  6. 6th December 2020Work out (8 x 10^3) x (2 x 10^-6). Give your answer in standard form.
  7. 7th December 2020Work out the equation of the line parallel to y = -2x + 4 that passes through (3, 3).
  8. 8th December 2020x : y = 5 : 9. Write y in terms of x.
  9. 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.
  10. 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.
  11. 11th December 2020A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
  12. 12th December 2020Write the recurring decimal 0.9898... as a fraction in its simplest form.
  13. 13th December 2020A line has equation y = 3x + 2. Work out the gradient of any line perpendicular to it.
  14. 14th December 2020A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
  15. 15th December 2020ABCD is a cyclic quadrilateral. Angle ABC is 55°. Work out angle ADC.
  16. 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.
  17. 17th December 2020A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
  18. 18th December 2020A bill is £72 including VAT at 20%. Work out the amount before VAT.
  19. 19th December 2020For the curve y = 25/x, work out y when x = 5, and write down the equation of its vertical asymptote.
  20. 20th December 2020y is inversely proportional to x. When x = 4, y = 5. Work out y when x = 5.
  21. 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.
  22. 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.
  23. 23rd December 2020Four classes in order have frequencies 7, 11, 6, 12. Write down the cumulative frequency at the end of the third class.
  24. 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?
  25. 25th December 2020Expand and simplify (x - 4)(x + 5)(x - 2).
  26. 26th December 2020y is directly proportional to x^2. When x = 2, y = 8. Work out y when x = 9.
  27. 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.
  28. 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.
  29. 29th December 202060 beetles are marked and released. Later 16 are caught, of which 2 are marked. Estimate the population.
  30. 30th December 2020Work out (42 x 10^7) / (7 x 10^4). Give your answer in standard form.
  31. 31st December 2020Make x the subject of y = 2x^2 - 5.

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