Daily Practice · Higher
December 2011 - Higher 5-a-day
Every Higher sheet published in December 2011, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2011Expand and simplify (x + 5)(x - 2)(x + 2).
- 2nd December 2011y is directly proportional to x. When x = 4, y = 28. Work out y when x = 5.
- 3rd December 2011A cone has base radius 2 cm and vertical height 3 cm. Work out its volume, leaving your answer in terms of pi.
- 4th December 201125 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th December 2011A cumulative frequency graph is drawn for 156 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 6th December 2011A bill is £912 including VAT at 20%. Work out the amount before VAT.
- 7th December 2011Make x the subject of y = 3x^2 - 7.
- 8th December 2011A town's population is 22500 and grows by 4% each year. Work out the population after 2 years, to the nearest whole number.
- 9th December 2011In triangle ABC, angle A is 30°, angle B is 39° and side a is 11 cm. Use the sine rule to work out side b, to 1 decimal place.
- 10th December 20113 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th December 2011A box plot has a minimum of 16 and a maximum of 58. Work out the range.
- 12th December 2011A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 13th December 2011Factorise x^2 - 100.
- 14th December 2011A block has volume 135 cm^3 and density 2.5 g/cm^3. Work out its mass.
- 15th December 2011A right-angled triangle has sides 12 cm, 16 cm and 20 cm. Work out the angle opposite the 12 cm side, to 1 decimal place.
- 16th December 201128 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 17th December 2011A box plot has minimum 13, lower quartile 18, median 24, upper quartile 31 and maximum 35. Work out the interquartile range.
- 18th December 2011Work out (30 x 10^9) / (6 x 10^2). Give your answer in standard form.
- 19th December 2011A region is defined by y < x + 9. Should the boundary line be solid or dashed, and why?
- 20th December 2011x : y = 3 : 5. Write y in terms of x.
- 21st December 2011The point (-5, 1) is enlarged by scale factor -1 about the centre (0, 4). Write down the coordinates of the image.
- 22nd December 20117 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd December 2011A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 24th December 2011Write the recurring decimal 0.555... as a fraction in its simplest form.
- 25th December 2011Factorise x^2 + 14x + 49.
- 26th December 2011A price rises by 15% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 27th December 2011Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 1026 cm^3. Work out the volume of the smaller.
- 28th December 201120 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th December 2011A histogram class is 20 units wide and contains 10 values. Work out the frequency density.
- 30th December 2011Work out 36^(3/2).
- 31st December 2011Work out the equation of the line parallel to y = 2x + 7 that passes through (6, 19).