Daily Practice · Higher

December 2019 - Higher 5-a-day

Every Higher sheet published in December 2019, with answers. Grades 6-7 - Higher-tier method and manipulation.

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December 2019

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' December 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 2019

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 2019For the curve y = 16/x, work out y when x = 4, and write down the equation of its vertical asymptote.
  2. 2nd December 2019A price rises by 10% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
  3. 3rd December 2019A, B and C are points on a circle with centre O. Angle AOC is 40°. Work out angle ABC, where B is on the major arc.
  4. 4th December 20193 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  5. 5th December 2019A histogram class is 2 units wide and contains 8 values. Work out the frequency density.
  6. 6th December 2019Write the recurring decimal 0.555... as a fraction in its simplest form.
  7. 7th December 2019Expand and simplify (x + 3)(x + 2)(x - 4).
  8. 8th December 2019y is inversely proportional to x. When x = 2, y = 12. Work out y when x = 4.
  9. 9th December 2019A cone has base radius 4 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
  10. 10th December 201913 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  11. 11th December 2019Four classes in order have frequencies 5, 4, 8, 12. Write down the cumulative frequency at the end of the third class.
  12. 12th December 2019Work out 16^(3/2).
  13. 13th December 2019Make x the subject of y = 5x^2 - 12.
  14. 14th December 2019y is directly proportional to x^2. When x = 5, y = 150. Work out y when x = 7.
  15. 15th December 2019In triangle ABC, angle A is 44°, angle B is 75° and side a is 7 cm. Use the sine rule to work out side b, to 1 decimal place.
  16. 16th December 20197 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  17. 17th December 201920 newts are marked and released. Later 24 are caught, of which 6 are marked. Estimate the population.
  18. 18th December 2019Write sqrt(45) in the form a sqrt(b), where b is as small as possible.
  19. 19th December 2019Factorise x^2 - 36.
  20. 20th December 2019y is directly proportional to x. When x = 6, y = 30. Work out y when x = 7.
  21. 21st December 2019A right-angled triangle has sides 3 cm, 4 cm and 5 cm. Work out the angle opposite the 3 cm side, to 1 decimal place.
  22. 22nd December 201925 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  23. 23rd December 2019A cumulative frequency graph is drawn for 176 values. What cumulative frequency do you read across from to estimate the lower quartile?
  24. 24th December 2019A meal deal has 5 mains, 5 sides and 5 drinks. How many different meals are possible?
  25. 25th December 2019A region is defined by y <= -5x + 6. Should the boundary line be solid or dashed, and why?
  26. 26th December 2019A town's population is 24000 and grows by 6% each year. Work out the population after 5 years, to the nearest whole number.
  27. 27th December 2019The point (1, 2) is enlarged by scale factor -1 about the centre (-3, 0). Write down the coordinates of the image.
  28. 28th December 20192 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  29. 29th December 2019A box plot has a minimum of 17 and a maximum of 52. Work out the range.
  30. 30th December 2019A mass is 10.1 kg, correct to 1 decimal place. Write down the lower bound.
  31. 31st December 2019Factorise x^2 + 4x - 32.

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