Daily Practice · Higher

December 1957 5-a-day

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December 1957

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' December 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 1957

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 1957A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
  2. 2nd December 1957Make x the subject of y = 4x^2 - 10.
  3. 3rd December 1957x : y = 2 : 3. Write y in terms of x.
  4. 4th December 1957In triangle ABC, angle A is 61°, angle B is 85° and side a is 9 cm. Use the sine rule to work out side b, to 1 decimal place.
  5. 5th December 19575 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  6. 6th December 1957A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
  7. 7th December 1957Work out (54 x 10^7) / (9 x 10^4). Give your answer in standard form.
  8. 8th December 1957Factorise x^2 - 81.
  9. 9th December 1957A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
  10. 10th December 1957A right-angled triangle has sides 12 cm, 16 cm and 20 cm. Work out the angle opposite the 12 cm side, to 1 decimal place.
  11. 11th December 195726 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  12. 12th December 1957A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
  13. 13th December 1957Write the recurring decimal 0.666... as a fraction in its simplest form.
  14. 14th December 1957A region is defined by y <= x + 3. Should the boundary line be solid or dashed, and why?
  15. 15th December 1957y is inversely proportional to x. When x = 5, y = 36. Work out y when x = 12.
  16. 16th December 1957The point (-2, 6) is enlarged by scale factor -1 about the centre (3, 1). Write down the coordinates of the image.
  17. 17th December 19571 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  18. 18th December 1957Four classes in order have frequencies 3, 10, 7, 4. Write down the cumulative frequency at the end of the third class.
  19. 19th December 1957Work out 25^(3/2).
  20. 20th December 1957Factorise x^2 - 8x + 7.
  21. 21st December 1957y is directly proportional to x^2. When x = 3, y = 54. Work out y when x = 9.
  22. 22nd December 1957Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 296 cm^3. Work out the volume of the smaller.
  23. 23rd December 195715 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  24. 24th December 195755 newts are marked and released. Later 50 are caught, of which 5 are marked. Estimate the population.
  25. 25th December 1957Write sqrt(50) in the form a sqrt(b), where b is as small as possible.
  26. 26th December 1957Work out the equation of the line parallel to y = -x - 6 that passes through (5, -8).
  27. 27th December 1957y is directly proportional to x. When x = 8, y = 88. Work out y when x = 3.
  28. 28th December 1957A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Work out the other shorter side.
  29. 29th December 19572 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  30. 30th December 1957A cumulative frequency graph is drawn for 156 values. What cumulative frequency do you read across from to estimate the lower quartile?
  31. 31st December 1957A meal deal has 9 mains, 4 sides and 3 drinks. How many different meals are possible?

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