Daily Practice · Higher

December 2018 - Higher 5-a-day

Every Higher sheet published in December 2018, with answers. Grades 6-7 - Higher-tier method and manipulation.

← Today's Higher sheet

December 2018

31 sheets · 155 questions · Grades 6-7

Printing for a group?

The batch download puts all 5 tiers' December 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in December 2018

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 2018y is directly proportional to x^2. When x = 3, y = 63. Work out y when x = 5.
  2. 2nd December 2018A right-angled triangle has sides 3 cm, 4 cm and 5 cm. Work out the angle opposite the 3 cm side, to 1 decimal place.
  3. 3rd December 201810 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  4. 4th December 201845 fish are marked and released. Later 21 are caught, of which 3 are marked. Estimate the population.
  5. 5th December 2018Write 5^-1 as a fraction.
  6. 6th December 2018A region is defined by y < -x - 7. Should the boundary line be solid or dashed, and why?
  7. 7th December 2018y is directly proportional to x. When x = 3, y = 27. Work out y when x = 7.
  8. 8th December 2018The point (6, 3) is enlarged by scale factor -1 about the centre (-4, -1). Write down the coordinates of the image.
  9. 9th December 20183 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  10. 10th December 2018A cumulative frequency graph is drawn for 148 values. What cumulative frequency do you read across from to estimate the lower quartile?
  11. 11th December 2018Work out (6 x 10^7) x (3 x 10^4). Give your answer in standard form.
  12. 12th December 2018Factorise x^2 + 18x + 81.
  13. 13th December 2018A town's population is 3000 and grows by 6% each year. Work out the population after 6 years, to the nearest whole number.
  14. 14th December 2018Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 513 cm^3. Work out the volume of the smaller.
  15. 15th December 201816 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  16. 16th December 2018A box plot has a minimum of 3 and a maximum of 57. Work out the range.
  17. 17th December 2018Write the recurring decimal 0.5454... as a fraction in its simplest form.
  18. 18th December 2018Work out the equation of the line parallel to y = -2x + 1 that passes through (4, -19).
  19. 19th December 2018A block has volume 35 cm^3 and density 4 g/cm^3. Work out its mass.
  20. 20th December 2018A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 12 cm. Work out the other shorter side.
  21. 21st December 20183 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  22. 22nd December 2018A box plot has minimum 10, lower quartile 14, median 19, upper quartile 21 and maximum 23. Work out the interquartile range.
  23. 23rd December 2018A bill is £528 including VAT at 20%. Work out the amount before VAT.
  24. 24th December 2018A line has equation y = 4x + 3. Work out the gradient of any line perpendicular to it.
  25. 25th December 2018x : y = 2 : 7. Write y in terms of x.
  26. 26th December 2018ABCD is a cyclic quadrilateral. Angle ABC is 89°. Work out angle ADC.
  27. 27th December 201820 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  28. 28th December 2018A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
  29. 29th December 2018A code is 3 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
  30. 30th December 2018For the curve y = -100/x, work out y when x = -10, and write down the equation of its vertical asymptote.
  31. 31st December 2018A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.

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