Daily Practice · Higher

July 1991 - Higher 5-a-day

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July 1991

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' July 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in July 1991

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st July 1991Work out the equation of the line parallel to y = 5x - 3 that passes through (5, 15).
  2. 2nd July 1991x : y = 2 : 7. Write y in terms of x.
  3. 3rd July 1991A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the other shorter side.
  4. 4th July 19912 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  5. 5th July 1991A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
  6. 6th July 1991A bill is £144 including VAT at 20%. Work out the amount before VAT.
  7. 7th July 1991A line has equation y = -2x + 5. Work out the gradient of any line perpendicular to it.
  8. 8th July 1991A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
  9. 9th July 1991ABCD is a cyclic quadrilateral. Angle ABC is 84°. Work out angle ADC.
  10. 10th July 199121 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  11. 11th July 1991A histogram class is 10 units wide and contains 30 values. Work out the frequency density.
  12. 12th July 1991A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
  13. 13th July 1991For the curve y = -3/x, work out y when x = -1, and write down the equation of its vertical asymptote.
  14. 14th July 1991y is inversely proportional to x. When x = 5, y = 4. Work out y when x = 2.
  15. 15th July 1991A, B and C are points on a circle with centre O. Angle AOC is 162°. Work out angle ABC, where B is on the major arc.
  16. 16th July 19912 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  17. 17th July 1991Four classes in order have frequencies 7, 3, 5, 9. Write down the cumulative frequency at the end of the third class.
  18. 18th July 1991Work out (30 x 10^9) / (5 x 10^4). Give your answer in standard form.
  19. 19th July 1991Expand and simplify (x - 5)(x - 5)(x - 5).
  20. 20th July 1991y is directly proportional to x^2. When x = 6, y = 180. Work out y when x = 2.
  21. 21st July 1991A cone has base radius 2 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
  22. 22nd July 199120 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  23. 23rd July 199110 fish are marked and released. Later 28 are caught, of which 7 are marked. Estimate the population.
  24. 24th July 1991Write the recurring decimal 0.777... as a fraction in its simplest form.
  25. 25th July 1991Make x the subject of y = 3x^2 - 2.
  26. 26th July 1991y is directly proportional to x. When x = 8, y = 48. Work out y when x = 5.
  27. 27th July 1991In triangle ABC, angle A is 45°, angle B is 38° and side a is 20 cm. Use the sine rule to work out side b, to 1 decimal place.
  28. 28th July 19912 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  29. 29th July 1991A cumulative frequency graph is drawn for 236 values. What cumulative frequency do you read across from to estimate the lower quartile?
  30. 30th July 1991Work out 81^(3/2).
  31. 31st July 1991Factorise x^2 - 121.

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