Daily Practice · Higher

December 1953 5-a-day

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December 1953

31 sheets · 155 questions · Grades 6-7

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Every sheet in December 1953

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 1953A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 16 cm. Work out the other shorter side.
  2. 2nd December 19534 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  3. 3rd December 1953A histogram class is 2 units wide and contains 5 values. Work out the frequency density.
  4. 4th December 1953A bill is £960 including VAT at 20%. Work out the amount before VAT.
  5. 5th December 1953A line has equation y = 3x + 7. Work out the gradient of any line perpendicular to it.
  6. 6th December 1953y is inversely proportional to x. When x = 2, y = 48. Work out y when x = 12.
  7. 7th December 1953ABCD is a cyclic quadrilateral. Angle ABC is 80°. Work out angle ADC.
  8. 8th December 195314 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  9. 9th December 1953Four classes in order have frequencies 6, 8, 6, 11. Write down the cumulative frequency at the end of the third class.
  10. 10th December 1953A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
  11. 11th December 1953For the curve y = 4/x, work out y when x = 4, and write down the equation of its vertical asymptote.
  12. 12th December 1953y is directly proportional to x^2. When x = 5, y = 200. Work out y when x = 2.
  13. 13th December 1953A, B and C are points on a circle with centre O. Angle AOC is 134°. Work out angle ABC, where B is on the major arc.
  14. 14th December 19536 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  15. 15th December 195325 newts are marked and released. Later 30 are caught, of which 3 are marked. Estimate the population.
  16. 16th December 1953Work out (30 x 10^12) / (6 x 10^5). Give your answer in standard form.
  17. 17th December 1953Expand and simplify (x + 1)(x + 3)(x - 1).
  18. 18th December 1953y is directly proportional to x. When x = 3, y = 36. Work out y when x = 2.
  19. 19th December 1953A cone has base radius 8 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
  20. 20th December 195311 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  21. 21st December 1953A cumulative frequency graph is drawn for 104 values. What cumulative frequency do you read across from to estimate the lower quartile?
  22. 22nd December 1953Write the recurring decimal 0.111... as a fraction in its simplest form.
  23. 23rd December 1953Make x the subject of y = 2x^2 - 5.
  24. 24th December 1953A town's population is 14000 and grows by 5% each year. Work out the population after 2 years, to the nearest whole number.
  25. 25th December 1953In triangle ABC, angle A is 70°, angle B is 59° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
  26. 26th December 19538 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  27. 27th December 1953A box plot has a minimum of 5 and a maximum of 58. Work out the range.
  28. 28th December 1953Work out 16^(3/2).
  29. 29th December 1953Factorise x^2 - 36.
  30. 30th December 1953A block has volume 85 cm^3 and density 2.5 g/cm^3. Work out its mass.
  31. 31st December 1953A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Work out the angle opposite the 6 cm side, to 1 decimal place.

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