Daily Practice · Higher

January 1990 5-a-day

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January 1990

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' January 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 1990

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 1990Factorise x^2 - 144.
  2. 2nd January 1990x : y = 2 : 3. Write y in terms of x.
  3. 3rd January 1990A 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.
  4. 4th January 199015 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  5. 5th January 1990A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
  6. 6th January 1990Write 9^-2 as a fraction.
  7. 7th January 1990A region is defined by y < 2x - 8. Should the boundary line be solid or dashed, and why?
  8. 8th January 1990A price rises by 20% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
  9. 9th January 1990The point (3, -6) is enlarged by scale factor -3 about the centre (-1, -3). Write down the coordinates of the image.
  10. 10th January 19901 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  11. 11th January 1990A histogram class is 2 units wide and contains 5 values. Work out the frequency density.
  12. 12th January 1990Work out (7 x 10^3) x (3 x 10^2). Give your answer in standard form.
  13. 13th January 1990Factorise x^2 + 5x - 6.
  14. 14th January 1990y is inversely proportional to x. When x = 3, y = 4. Work out y when x = 2.
  15. 15th January 1990Two 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.
  16. 16th January 199019 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  17. 17th January 1990Four classes in order have frequencies 10, 9, 7, 12. Write down the cumulative frequency at the end of the third class.
  18. 18th January 1990Write the recurring decimal 0.6161... as a fraction in its simplest form.
  19. 19th January 1990Work out the equation of the line parallel to y = -3x - 4 that passes through (2, -13).
  20. 20th January 1990y is directly proportional to x^2. When x = 3, y = 27. Work out y when x = 7.
  21. 21st January 1990A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Work out the other shorter side.
  22. 22nd January 19902 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  23. 23rd January 199055 beetles are marked and released. Later 63 are caught, of which 7 are marked. Estimate the population.
  24. 24th January 1990A bill is £240 including VAT at 20%. Work out the amount before VAT.
  25. 25th January 1990A line has equation y = -4x + 7. Work out the gradient of any line perpendicular to it.
  26. 26th January 1990y is directly proportional to x. When x = 3, y = 27. Work out y when x = 5.
  27. 27th January 1990ABCD is a cyclic quadrilateral. Angle ABC is 120°. Work out angle ADC.
  28. 28th January 199012 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  29. 29th January 1990A cumulative frequency graph is drawn for 132 values. What cumulative frequency do you read across from to estimate the lower quartile?
  30. 30th January 1990A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
  31. 31st January 1990For the curve y = 10/x, work out y when x = -1, and write down the equation of its vertical asymptote.

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