Daily Practice · Higher

December 1987 5-a-day

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December 1987

31 sheets · 155 questions · Grades 6-7

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Every sheet in December 1987

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 1987A region is defined by y <= 3x + 5. Should the boundary line be solid or dashed, and why?
  2. 2nd December 1987A block has volume 40 cm^3 and density 3 g/cm^3. Work out its mass.
  3. 3rd December 1987The point (6, 3) is enlarged by scale factor -3 about the centre (0, -1). Write down the coordinates of the image.
  4. 4th December 19872 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  5. 5th December 1987A box plot has minimum 4, lower quartile 7, median 14, upper quartile 24 and maximum 28. Work out the interquartile range.
  6. 6th December 1987Work out (32 x 10^6) / (4 x 10^5). Give your answer in standard form.
  7. 7th December 1987Factorise x^2 + 11x + 30.
  8. 8th December 1987x : y = 2 : 3. Write y in terms of x.
  9. 9th December 1987Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 192 cm^3. Work out the volume of the smaller.
  10. 10th December 198715 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  11. 11th December 1987A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
  12. 12th December 1987Write the recurring decimal 0.444... as a fraction in its simplest form.
  13. 13th December 1987Work out the equation of the line parallel to y = 5x + 5 that passes through (6, 40).
  14. 14th December 1987A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
  15. 15th December 1987A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 10 cm. Work out the other shorter side.
  16. 16th December 19874 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 1987A histogram class is 4 units wide and contains 12 values. Work out the frequency density.
  18. 18th December 1987Work out 36^(3/2).
  19. 19th December 1987A line has equation y = -2x + 9. Work out the gradient of any line perpendicular to it.
  20. 20th December 1987y is inversely proportional to x. When x = 2, y = 15. Work out y when x = 3.
  21. 21st December 1987ABCD is a cyclic quadrilateral. Angle ABC is 104°. Work out angle ADC.
  22. 22nd December 198713 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  23. 23rd December 1987Four classes in order have frequencies 8, 4, 7, 7. Write down the cumulative frequency at the end of the third class.
  24. 24th December 1987Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
  25. 25th December 1987For the curve y = 8/x, work out y when x = 1, and write down the equation of its vertical asymptote.
  26. 26th December 1987y is directly proportional to x^2. When x = 2, y = 24. Work out y when x = 4.
  27. 27th December 1987A, B and C are points on a circle with centre O. Angle AOC is 40°. Work out angle ABC, where B is on the major arc.
  28. 28th December 19874 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  29. 29th December 198710 newts are marked and released. Later 48 are caught, of which 6 are marked. Estimate the population.
  30. 30th December 1987A meal deal has 6 mains, 4 sides and 5 drinks. How many different meals are possible?
  31. 31st December 1987Expand and simplify (x + 4)(x - 3)(x + 1).

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