Daily Practice · Higher

December 1986 5-a-day

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December 1986

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' December 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 1986

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 1986A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
  2. 2nd December 1986ABCD is a cyclic quadrilateral. Angle ABC is 114°. Work out angle ADC.
  3. 3rd December 198619 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  4. 4th December 1986A histogram class is 20 units wide and contains 40 values. Work out the frequency density.
  5. 5th December 1986A mass is 80 kg, correct to the nearest 10. Write down the lower bound.
  6. 6th December 1986For the curve y = -4/x, work out y when x = 4, and write down the equation of its vertical asymptote.
  7. 7th December 1986y is inversely proportional to x. When x = 6, y = 12. Work out y when x = 2.
  8. 8th December 1986A, B and C are points on a circle with centre O. Angle AOC is 60°. Work out angle ABC, where B is on the major arc.
  9. 9th December 19868 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  10. 10th December 1986Four classes in order have frequencies 5, 6, 8, 8. Write down the cumulative frequency at the end of the third class.
  11. 11th December 1986Write 9^-2 as a fraction.
  12. 12th December 1986Expand and simplify (x + 2)(x - 1)(x + 4).
  13. 13th December 1986y is directly proportional to x^2. When x = 3, y = 36. Work out y when x = 7.
  14. 14th December 1986A cone has base radius 6 cm and vertical height 12 cm. Work out its volume, leaving your answer in terms of pi.
  15. 15th December 198625 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  16. 16th December 198650 voles are marked and released. Later 24 are caught, of which 8 are marked. Estimate the population.
  17. 17th December 1986Work out (7 x 10^4) x (2 x 10^5). Give your answer in standard form.
  18. 18th December 1986Make x the subject of y = 7x^2 - 8.
  19. 19th December 1986y is directly proportional to x. When x = 3, y = 15. Work out y when x = 7.
  20. 20th December 1986In triangle ABC, angle A is 30°, angle B is 62° and side a is 13 cm. Use the sine rule to work out side b, to 1 decimal place.
  21. 21st December 19867 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  22. 22nd December 1986A cumulative frequency graph is drawn for 80 values. What cumulative frequency do you read across from to estimate the lower quartile?
  23. 23rd December 1986Write the recurring decimal 0.1616... as a fraction in its simplest form.
  24. 24th December 1986Factorise x^2 - 4.
  25. 25th December 1986A town's population is 31000 and grows by 8% each year. Work out the population after 2 years, to the nearest whole number.
  26. 26th December 1986A right-angled triangle has sides 5 cm, 12 cm and 13 cm. Work out the angle opposite the 5 cm side, to 1 decimal place.
  27. 27th December 198619 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  28. 28th December 1986A box plot has a minimum of 8 and a maximum of 63. Work out the range.
  29. 29th December 1986A bill is £600 including VAT at 20%. Work out the amount before VAT.
  30. 30th December 1986A region is defined by y < -3x - 5. Should the boundary line be solid or dashed, and why?
  31. 31st December 1986A block has volume 140 cm^3 and density 7.5 g/cm^3. Work out its mass.

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