Daily Practice · Higher
December 2003 - Higher 5-a-day
Every Higher sheet published in December 2003, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2003Make x the subject of y = 5x^2 - 8.
- 2nd December 2003x : y = 3 : 7. Write y in terms of x.
- 3rd December 2003In triangle ABC, angle A is 62°, angle B is 75° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
- 4th December 20031 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 5th December 2003A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 6th December 2003Write 7^-1 as a fraction.
- 7th December 2003Factorise x^2 - 121.
- 8th December 2003A price rises by 25% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 9th December 2003A right-angled triangle has sides 9 cm, 12 cm and 15 cm. Work out the angle opposite the 9 cm side, to 1 decimal place.
- 10th December 200317 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 11th December 2003A histogram class is 4 units wide and contains 6 values. Work out the frequency density.
- 12th December 2003Work out (2 x 10^6) x (8 x 10^-4). Give your answer in standard form.
- 13th December 2003A region is defined by y <= 3x + 8. Should the boundary line be solid or dashed, and why?
- 14th December 2003y is inversely proportional to x. When x = 9, y = 8. Work out y when x = 2.
- 15th December 2003The point (4, 1) is enlarged by scale factor -3 about the centre (4, -3). Write down the coordinates of the image.
- 16th December 20032 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 17th December 2003Four classes in order have frequencies 8, 3, 11, 4. Write down the cumulative frequency at the end of the third class.
- 18th December 2003Write the recurring decimal 0.9292... as a fraction in its simplest form.
- 19th December 2003Factorise x^2 + 10x + 24.
- 20th December 2003y is directly proportional to x^2. When x = 3, y = 45. Work out y when x = 9.
- 21st December 2003Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 540 cm^3. Work out the volume of the smaller.
- 22nd December 200323 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 23rd December 200335 voles are marked and released. Later 40 are caught, of which 5 are marked. Estimate the population.
- 24th December 2003A bill is £504 including VAT at 20%. Work out the amount before VAT.
- 25th December 2003Work out the equation of the line parallel to y = 4x - 1 that passes through (1, 0).
- 26th December 2003y is directly proportional to x. When x = 4, y = 8. Work out y when x = 3.
- 27th December 2003A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 9 cm. Work out the other shorter side.
- 28th December 20031 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 29th December 2003A cumulative frequency graph is drawn for 96 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 30th December 2003A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 31st December 2003A line has equation y = -4x + 2. Work out the gradient of any line perpendicular to it.