Daily Practice · Higher
December 2016 - Higher 5-a-day
Every Higher sheet published in December 2016, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 201617 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 2nd December 2016A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 3rd December 2016A mass is 310 kg, correct to the nearest 10. Write down the lower bound.
- 4th December 2016Make x the subject of y = 9x^2 - 4.
- 5th December 2016A price rises by 25% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 6th December 2016In triangle ABC, angle A is 39°, angle B is 60° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
- 7th December 20162 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 8th December 2016A histogram class is 2 units wide and contains 3 values. Work out the frequency density.
- 9th December 2016Write 7^-3 as a fraction.
- 10th December 2016Factorise x^2 - 25.
- 11th December 2016y is inversely proportional to x. When x = 6, y = 25. Work out y when x = 5.
- 12th December 2016A right-angled triangle has sides 8 cm, 15 cm and 17 cm. Work out the angle opposite the 8 cm side, to 1 decimal place.
- 13th December 201626 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 14th December 2016Four classes in order have frequencies 5, 3, 5, 7. Write down the cumulative frequency at the end of the third class.
- 15th December 2016Work out (7 x 10^4) x (4 x 10^-5). Give your answer in standard form.
- 16th December 2016A region is defined by y <= 2x + 1. Should the boundary line be solid or dashed, and why?
- 17th December 2016y is directly proportional to x^2. When x = 2, y = 24. Work out y when x = 9.
- 18th December 2016The point (2, 6) is enlarged by scale factor -1 about the centre (2, -2). Write down the coordinates of the image.
- 19th December 20161 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 20th December 201635 voles are marked and released. Later 32 are caught, of which 4 are marked. Estimate the population.
- 21st December 2016Write the recurring decimal 0.6868... as a fraction in its simplest form.
- 22nd December 2016Factorise x^2 + 2x + 1.
- 23rd December 2016y is directly proportional to x. When x = 9, y = 54. Work out y when x = 8.
- 24th December 2016Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 216 cm^3. Work out the volume of the smaller.
- 25th December 201623 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 26th December 2016A cumulative frequency graph is drawn for 140 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 27th December 2016A bill is £72 including VAT at 20%. Work out the amount before VAT.
- 28th December 2016Work out the equation of the line parallel to y = -x + 9 that passes through (6, -14).
- 29th December 2016A town's population is 25500 and grows by 5% each year. Work out the population after 5 years, to the nearest whole number.
- 30th December 2016A right-angled triangle has a hypotenuse of 17 cm and one shorter side of 8 cm. Work out the other shorter side.
- 31st December 20164 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.