Daily Practice · Higher

December 1970 5-a-day

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December 1970

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' December 1970 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 1970

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 1970x : y = 5 : 8. Write y in terms of x.
  2. 2nd December 1970A cone has base radius 9 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
  3. 3rd December 197018 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  4. 4th December 1970A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
  5. 5th December 1970A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
  6. 6th December 1970Make x the subject of y = 4x^2 - 11.
  7. 7th December 1970A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
  8. 8th December 1970In triangle ABC, angle A is 78°, angle B is 65° and side a is 12 cm. Use the sine rule to work out side b, to 1 decimal place.
  9. 9th December 19701 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  10. 10th December 1970A histogram class is 5 units wide and contains 10 values. Work out the frequency density.
  11. 11th December 1970Work out (30 x 10^11) / (5 x 10^5). Give your answer in standard form.
  12. 12th December 1970Factorise x^2 - 25.
  13. 13th December 1970y is inversely proportional to x. When x = 3, y = 48. Work out y when x = 12.
  14. 14th December 1970A 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.
  15. 15th December 197020 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  16. 16th December 1970Four classes in order have frequencies 12, 6, 3, 7. Write down the cumulative frequency at the end of the third class.
  17. 17th December 1970Write the recurring decimal 0.777... as a fraction in its simplest form.
  18. 18th December 1970A region is defined by y < 4x - 4. Should the boundary line be solid or dashed, and why?
  19. 19th December 1970y is directly proportional to x^2. When x = 2, y = 32. Work out y when x = 8.
  20. 20th December 1970The point (-1, 0) is enlarged by scale factor -1 about the centre (-3, -4). Write down the coordinates of the image.
  21. 21st December 19702 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  22. 22nd December 197025 fish are marked and released. Later 22 are caught, of which 2 are marked. Estimate the population.
  23. 23rd December 1970Work out 8^(2/3).
  24. 24th December 1970Factorise x^2 - x - 72.
  25. 25th December 1970y is directly proportional to x. When x = 6, y = 18. Work out y when x = 7.
  26. 26th December 1970Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 1408 cm^3. Work out the volume of the smaller.
  27. 27th December 197025 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  28. 28th December 1970A cumulative frequency graph is drawn for 164 values. What cumulative frequency do you read across from to estimate the lower quartile?
  29. 29th December 1970Write sqrt(32) in the form a sqrt(b), where b is as small as possible.
  30. 30th December 1970Work out the equation of the line parallel to y = -x - 2 that passes through (4, -14).
  31. 31st December 1970A town's population is 19000 and grows by 4% each year. Work out the population after 6 years, to the nearest whole number.

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