Daily Practice · Higher

January 2005 - Higher 5-a-day

Every Higher sheet published in January 2005, with answers. Grades 6-7 - Higher-tier method and manipulation.

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January 2005

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' January 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 2005

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 2005y is directly proportional to x^2. When x = 6, y = 324. Work out y when x = 3.
  2. 2nd January 2005The point (6, 5) is enlarged by scale factor -3 about the centre (3, 0). Write down the coordinates of the image.
  3. 3rd January 20053 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  4. 4th January 200560 beetles are marked and released. Later 54 are caught, of which 9 are marked. Estimate the population.
  5. 5th January 2005Write 6^-3 as a fraction.
  6. 6th January 2005Factorise x^2 + 6x - 7.
  7. 7th January 2005y is directly proportional to x. When x = 3, y = 24. Work out y when x = 13.
  8. 8th January 2005Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 756 cm^3. Work out the volume of the smaller.
  9. 9th January 200512 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  10. 10th January 2005A cumulative frequency graph is drawn for 144 values. What cumulative frequency do you read across from to estimate the lower quartile?
  11. 11th January 2005Work out (7 x 10^6) x (9 x 10^-5). Give your answer in standard form.
  12. 12th January 2005Work out the equation of the line parallel to y = -5x + 4 that passes through (1, 3).
  13. 13th January 2005A town's population is 4500 and grows by 8% each year. Work out the population after 5 years, to the nearest whole number.
  14. 14th January 2005A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 10 cm. Work out the other shorter side.
  15. 15th January 20052 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  16. 16th January 2005A box plot has a minimum of 9 and a maximum of 27. Work out the range.
  17. 17th January 2005Write the recurring decimal 0.2828... as a fraction in its simplest form.
  18. 18th January 2005A line has equation y = 5x + 3. Work out the gradient of any line perpendicular to it.
  19. 19th January 2005A block has volume 70 cm^3 and density 11 g/cm^3. Work out its mass.
  20. 20th January 2005ABCD is a cyclic quadrilateral. Angle ABC is 115°. Work out angle ADC.
  21. 21st January 200518 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  22. 22nd January 2005A box plot has minimum 7, lower quartile 13, median 23, upper quartile 31 and maximum 33. Work out the interquartile range.
  23. 23rd January 2005A bill is £336 including VAT at 20%. Work out the amount before VAT.
  24. 24th January 2005For the curve y = 6/x, work out y when x = 2, and write down the equation of its vertical asymptote.
  25. 25th January 2005x : y = 2 : 9. Write y in terms of x.
  26. 26th January 2005A, B and C are points on a circle with centre O. Angle AOC is 114°. Work out angle ABC, where B is on the major arc.
  27. 27th January 20053 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  28. 28th January 2005A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
  29. 29th January 2005A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
  30. 30th January 2005Expand and simplify (x + 2)(x + 3)(x - 2).
  31. 31st January 2005A price rises by 20% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.

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