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.

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December 2022

31 sheets · 155 questions · Grades 6-7

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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.

  1. 1st December 2022A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
  2. 2nd December 2022Work out (2 x 10^3) x (5 x 10^-3). Give your answer in standard form.
  3. 3rd December 2022A line has equation y = 2x + 1. Work out the gradient of any line perpendicular to it.
  4. 4th December 2022y is inversely proportional to x. When x = 2, y = 12. Work out y when x = 6.
  5. 5th December 2022ABCD is a cyclic quadrilateral. Angle ABC is 130°. Work out angle ADC.
  6. 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.
  7. 7th December 2022Four classes in order have frequencies 8, 4, 6, 4. Write down the cumulative frequency at the end of the third class.
  8. 8th December 2022Write the recurring decimal 0.5252... as a fraction in its simplest form.
  9. 9th December 2022For the curve y = -8/x, work out y when x = 1, and write down the equation of its vertical asymptote.
  10. 10th December 2022y is directly proportional to x^2. When x = 6, y = 180. Work out y when x = 2.
  11. 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.
  12. 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.
  13. 13th December 202235 fish are marked and released. Later 72 are caught, of which 8 are marked. Estimate the population.
  14. 14th December 2022A bill is £360 including VAT at 20%. Work out the amount before VAT.
  15. 15th December 2022Expand and simplify (x + 2)(x - 2)(x + 3).
  16. 16th December 2022y is directly proportional to x. When x = 4, y = 44. Work out y when x = 9.
  17. 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.
  18. 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.
  19. 19th December 2022A cumulative frequency graph is drawn for 40 values. What cumulative frequency do you read across from to estimate the lower quartile?
  20. 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?
  21. 21st December 2022Make x the subject of y = 4x^2 - 2.
  22. 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.
  23. 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.
  24. 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.
  25. 25th December 2022A box plot has a minimum of 16 and a maximum of 38. Work out the range.
  26. 26th December 2022Work out (28 x 10^8) / (7 x 10^3). Give your answer in standard form.
  27. 27th December 2022Factorise x^2 - 100.
  28. 28th December 2022A block has volume 80 cm^3 and density 7.5 g/cm^3. Work out its mass.
  29. 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.
  30. 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.
  31. 31st December 2022A box plot has minimum 7, lower quartile 9, median 13, upper quartile 21 and maximum 29. Work out the interquartile range.

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