Daily Practice · Higher
December 2013 - Higher 5-a-day
Every Higher sheet published in December 2013, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2013A bill is £792 including VAT at 20%. Work out the amount before VAT.
- 2nd December 2013Factorise x^2 - 81.
- 3rd December 2013x : y = 2 : 3. Write y in terms of x.
- 4th December 2013A right-angled triangle has sides 7 cm, 24 cm and 25 cm. Work out the angle opposite the 7 cm side, to 1 decimal place.
- 5th December 201330 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 6th December 2013A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 7th December 2013A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 8th December 2013A region is defined by y <= -5x - 6. Should the boundary line be solid or dashed, and why?
- 9th December 2013A price rises by 25% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 10th December 2013The point (6, 1) is enlarged by scale factor -2 about the centre (4, -2). Write down the coordinates of the image.
- 11th December 20135 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 12th December 2013A histogram class is 4 units wide and contains 12 values. Work out the frequency density.
- 13th December 2013Work out (32 x 10^11) / (8 x 10^4). Give your answer in standard form.
- 14th December 2013Factorise x^2 - x - 56.
- 15th December 2013y is inversely proportional to x. When x = 6, y = 20. Work out y when x = 5.
- 16th December 2013Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 2496 cm^3. Work out the volume of the smaller.
- 17th December 201324 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 18th December 2013Four classes in order have frequencies 8, 12, 6, 10. Write down the cumulative frequency at the end of the third class.
- 19th December 2013Write the recurring decimal 0.111... as a fraction in its simplest form.
- 20th December 2013Work out the equation of the line parallel to y = -x + 2 that passes through (1, -9).
- 21st December 2013y is directly proportional to x^2. When x = 6, y = 108. Work out y when x = 8.
- 22nd December 2013A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 16 cm. Work out the other shorter side.
- 23rd December 20132 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 24th December 201325 fish are marked and released. Later 108 are caught, of which 9 are marked. Estimate the population.
- 25th December 2013Work out 8^(2/3).
- 26th December 2013A line has equation y = -4x + 6. Work out the gradient of any line perpendicular to it.
- 27th December 2013y is directly proportional to x. When x = 4, y = 36. Work out y when x = 14.
- 28th December 2013ABCD is a cyclic quadrilateral. Angle ABC is 53°. Work out angle ADC.
- 29th December 201316 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 30th December 2013A cumulative frequency graph is drawn for 160 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 31st December 2013Write sqrt(75) in the form a sqrt(b), where b is as small as possible.