Daily Practice · Higher

December 2003 - Higher 5-a-day

Every Higher sheet published in December 2003, with answers. Grades 6-7 - Higher-tier method and manipulation.

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December 2003

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' December 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 2003

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 2003Make x the subject of y = 5x^2 - 8.
  2. 2nd December 2003x : y = 3 : 7. Write y in terms of x.
  3. 3rd December 2003In triangle ABC, angle A is 62°, angle B is 75° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
  4. 4th December 20031 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  5. 5th December 2003A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
  6. 6th December 2003Write 7^-1 as a fraction.
  7. 7th December 2003Factorise x^2 - 121.
  8. 8th December 2003A price rises by 25% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
  9. 9th December 2003A right-angled triangle has sides 9 cm, 12 cm and 15 cm. Work out the angle opposite the 9 cm side, to 1 decimal place.
  10. 10th December 200317 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 2003A histogram class is 4 units wide and contains 6 values. Work out the frequency density.
  12. 12th December 2003Work out (2 x 10^6) x (8 x 10^-4). Give your answer in standard form.
  13. 13th December 2003A region is defined by y <= 3x + 8. Should the boundary line be solid or dashed, and why?
  14. 14th December 2003y is inversely proportional to x. When x = 9, y = 8. Work out y when x = 2.
  15. 15th December 2003The point (4, 1) is enlarged by scale factor -3 about the centre (4, -3). Write down the coordinates of the image.
  16. 16th December 20032 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  17. 17th December 2003Four classes in order have frequencies 8, 3, 11, 4. Write down the cumulative frequency at the end of the third class.
  18. 18th December 2003Write the recurring decimal 0.9292... as a fraction in its simplest form.
  19. 19th December 2003Factorise x^2 + 10x + 24.
  20. 20th December 2003y is directly proportional to x^2. When x = 3, y = 45. Work out y when x = 9.
  21. 21st December 2003Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 540 cm^3. Work out the volume of the smaller.
  22. 22nd December 200323 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  23. 23rd December 200335 voles are marked and released. Later 40 are caught, of which 5 are marked. Estimate the population.
  24. 24th December 2003A bill is £504 including VAT at 20%. Work out the amount before VAT.
  25. 25th December 2003Work out the equation of the line parallel to y = 4x - 1 that passes through (1, 0).
  26. 26th December 2003y is directly proportional to x. When x = 4, y = 8. Work out y when x = 3.
  27. 27th December 2003A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 9 cm. Work out the other shorter side.
  28. 28th December 20031 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  29. 29th December 2003A cumulative frequency graph is drawn for 96 values. What cumulative frequency do you read across from to estimate the lower quartile?
  30. 30th December 2003A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
  31. 31st December 2003A line has equation y = -4x + 2. Work out the gradient of any line perpendicular to it.

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