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January 1987 5-a-day

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January 1987

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' January 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 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 January 1987The point (2, 3) is enlarged by scale factor -2 about the centre (0, 4). Write down the coordinates of the image.
  2. 2nd January 19876 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  3. 3rd January 1987A box plot has minimum 15, lower quartile 21, median 31, upper quartile 40 and maximum 50. Work out the interquartile range.
  4. 4th January 1987A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
  5. 5th January 1987Factorise x^2 - 12x + 35.
  6. 6th January 1987x : y = 4 : 5. Write y in terms of x.
  7. 7th January 1987Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 56 cm^3. Work out the volume of the smaller.
  8. 8th January 198715 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  9. 9th January 1987A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
  10. 10th January 1987Work out (25 x 10^9) / (5 x 10^5). Give your answer in standard form.
  11. 11th January 1987Work out the equation of the line parallel to y = -4x + 9 that passes through (2, -4).
  12. 12th January 1987A price rises by 25% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
  13. 13th January 1987A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 9 cm. Work out the other shorter side.
  14. 14th January 19872 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  15. 15th January 1987A histogram class is 20 units wide and contains 60 values. Work out the frequency density.
  16. 16th January 1987Write the recurring decimal 0.111... as a fraction in its simplest form.
  17. 17th January 1987A line has equation y = -5x + 4. Work out the gradient of any line perpendicular to it.
  18. 18th January 1987y is inversely proportional to x. When x = 7, y = 60. Work out y when x = 10.
  19. 19th January 1987ABCD is a cyclic quadrilateral. Angle ABC is 71°. Work out angle ADC.
  20. 20th January 198714 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  21. 21st January 1987Four classes in order have frequencies 4, 6, 9, 6. Write down the cumulative frequency at the end of the third class.
  22. 22nd January 1987Work out 16^(3/2).
  23. 23rd January 1987For the curve y = -45/x, work out y when x = 5, and write down the equation of its vertical asymptote.
  24. 24th January 1987y is directly proportional to x^2. When x = 3, y = 45. Work out y when x = 6.
  25. 25th January 1987A, B and C are points on a circle with centre O. Angle AOC is 106°. Work out angle ABC, where B is on the major arc.
  26. 26th January 19872 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  27. 27th January 198735 voles are marked and released. Later 30 are caught, of which 5 are marked. Estimate the population.
  28. 28th January 1987Write sqrt(48) in the form a sqrt(b), where b is as small as possible.
  29. 29th January 1987Expand and simplify (x - 3)(x + 3)(x - 4).
  30. 30th January 1987y is directly proportional to x. When x = 3, y = 9. Work out y when x = 12.
  31. 31st January 1987A cone has base radius 5 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.

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