Daily Practice · Higher

December 2015 - Higher 5-a-day

Every Higher sheet published in December 2015, with answers. Grades 6-7 - Higher-tier method and manipulation.

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December 2015

31 sheets · 155 questions · Grades 6-7

Printing for a group?

The batch download puts all 5 tiers' December 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 2015

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 20152 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  2. 2nd December 2015Four classes in order have frequencies 5, 4, 9, 11. Write down the cumulative frequency at the end of the third class.
  3. 3rd December 2015A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
  4. 4th December 2015Factorise x^2 + 15x + 54.
  5. 5th December 2015y is directly proportional to x^2. When x = 4, y = 96. Work out y when x = 8.
  6. 6th December 2015Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 567 cm^3. Work out the volume of the smaller.
  7. 7th December 201519 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  8. 8th December 201560 fish are marked and released. Later 48 are caught, of which 8 are marked. Estimate the population.
  9. 9th December 2015Work out (63 x 10^12) / (7 x 10^4). Give your answer in standard form.
  10. 10th December 2015Work out the equation of the line parallel to y = 3x - 2 that passes through (2, 15).
  11. 11th December 2015y is directly proportional to x. When x = 7, y = 49. Work out y when x = 12.
  12. 12th December 2015A right-angled triangle has a hypotenuse of 41 cm and one shorter side of 40 cm. Work out the other shorter side.
  13. 13th December 20153 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  14. 14th December 2015A cumulative frequency graph is drawn for 104 values. What cumulative frequency do you read across from to estimate the lower quartile?
  15. 15th December 2015Write the recurring decimal 0.111... as a fraction in its simplest form.
  16. 16th December 2015A line has equation y = 4x + 2. Work out the gradient of any line perpendicular to it.
  17. 17th December 2015A town's population is 12000 and grows by 5% each year. Work out the population after 5 years, to the nearest whole number.
  18. 18th December 2015ABCD is a cyclic quadrilateral. Angle ABC is 70°. Work out angle ADC.
  19. 19th December 201512 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  20. 20th December 2015A box plot has a minimum of 4 and a maximum of 16. Work out the range.
  21. 21st December 2015Work out 49^(3/2).
  22. 22nd December 2015For the curve y = 120/x, work out y when x = -10, and write down the equation of its vertical asymptote.
  23. 23rd December 2015A block has volume 80 cm^3 and density 2.5 g/cm^3. Work out its mass.
  24. 24th December 2015A, B and C are points on a circle with centre O. Angle AOC is 146°. Work out angle ABC, where B is on the major arc.
  25. 25th December 20153 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  26. 26th December 2015A box plot has minimum 2, lower quartile 10, median 12, upper quartile 18 and maximum 21. Work out the interquartile range.
  27. 27th December 2015Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
  28. 28th December 2015Expand and simplify (x + 4)(x + 2)(x + 1).
  29. 29th December 2015x : y = 4 : 9. Write y in terms of x.
  30. 30th December 2015A cone has base radius 9 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
  31. 31st December 201519 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.

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