Daily Practice · Higher

December 1961 5-a-day

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December 1961

31 sheets · 155 questions · Grades 6-7

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Every sheet in December 1961

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 1961Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 135 cm^3. Work out the volume of the smaller.
  2. 2nd December 196118 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  3. 3rd December 1961A box plot has a minimum of 18 and a maximum of 68. Work out the range.
  4. 4th December 1961Write the recurring decimal 0.888... as a fraction in its simplest form.
  5. 5th December 1961Work out the equation of the line parallel to y = -3x - 1 that passes through (2, -16).
  6. 6th December 1961A block has volume 20 cm^3 and density 3 g/cm^3. Work out its mass.
  7. 7th December 1961A right-angled triangle has a hypotenuse of 25 cm and one shorter side of 24 cm. Work out the other shorter side.
  8. 8th December 19611 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  9. 9th December 1961A box plot has minimum 14, lower quartile 23, median 31, upper quartile 36 and maximum 43. Work out the interquartile range.
  10. 10th December 1961Work out 8^(2/3).
  11. 11th December 1961A line has equation y = 2x + 2. Work out the gradient of any line perpendicular to it.
  12. 12th December 1961x : y = 3 : 5. Write y in terms of x.
  13. 13th December 1961ABCD is a cyclic quadrilateral. Angle ABC is 92°. Work out angle ADC.
  14. 14th December 196120 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  15. 15th December 1961A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
  16. 16th December 1961Write sqrt(12) in the form a sqrt(b), where b is as small as possible.
  17. 17th December 1961For the curve y = 18/x, work out y when x = 2, and write down the equation of its vertical asymptote.
  18. 18th December 1961A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
  19. 19th December 1961A, B and C are points on a circle with centre O. Angle AOC is 58°. Work out angle ABC, where B is on the major arc.
  20. 20th December 19611 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  21. 21st December 1961A histogram class is 4 units wide and contains 2 values. Work out the frequency density.
  22. 22nd December 1961A meal deal has 7 mains, 6 sides and 6 drinks. How many different meals are possible?
  23. 23rd December 1961Expand and simplify (x + 1)(x + 5)(x - 4).
  24. 24th December 1961y is inversely proportional to x. When x = 6, y = 10. Work out y when x = 5.
  25. 25th December 1961A cone has base radius 2 cm and vertical height 9 cm. Work out its volume, leaving your answer in terms of pi.
  26. 26th December 196118 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  27. 27th December 1961Four classes in order have frequencies 9, 4, 4, 7. Write down the cumulative frequency at the end of the third class.
  28. 28th December 1961A mass is 230 kg, correct to the nearest 10. Write down the lower bound.
  29. 29th December 1961Make x the subject of y = 7x^2 - 3.
  30. 30th December 1961y is directly proportional to x^2. When x = 4, y = 32. Work out y when x = 9.
  31. 31st December 1961In triangle ABC, angle A is 77°, angle B is 56° and side a is 5 cm. Use the sine rule to work out side b, to 1 decimal place.

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