Daily Practice · Higher
January 2003 - Higher 5-a-day
Every Higher sheet published in January 2003, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2003In triangle ABC, angle A is 63°, angle B is 49° and side a is 19 cm. Use the sine rule to work out side b, to 1 decimal place.
- 2nd January 20031 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd January 2003A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 4th January 2003A mass is 420 kg, correct to the nearest 10. Write down the upper bound.
- 5th January 2003Factorise x^2 - 4.
- 6th January 2003A price rises by 10% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 7th January 2003A 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.
- 8th January 200324 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th January 2003A histogram class is 4 units wide and contains 2 values. Work out the frequency density.
- 10th January 2003Write 7^-1 as a fraction.
- 11th January 2003A region is defined by y <= -5x - 7. Should the boundary line be solid or dashed, and why?
- 12th January 2003y is inversely proportional to x. When x = 7, y = 5. Work out y when x = 5.
- 13th January 2003The point (4, -4) is enlarged by scale factor -3 about the centre (-2, 3). Write down the coordinates of the image.
- 14th January 20035 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th January 2003Four classes in order have frequencies 9, 10, 11, 8. Write down the cumulative frequency at the end of the third class.
- 16th January 2003Work out (4 x 10^5) x (2 x 10^-4). Give your answer in standard form.
- 17th January 2003Factorise x^2 - 18x + 81.
- 18th January 2003y is directly proportional to x^2. When x = 5, y = 100. Work out y when x = 7.
- 19th January 2003Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 128 cm^3. Work out the volume of the smaller.
- 20th January 200322 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st January 200350 voles are marked and released. Later 36 are caught, of which 9 are marked. Estimate the population.
- 22nd January 2003Write the recurring decimal 0.6161... as a fraction in its simplest form.
- 23rd January 2003Work out the equation of the line parallel to y = -5x + 4 that passes through (5, -13).
- 24th January 2003y is directly proportional to x. When x = 6, y = 18. Work out y when x = 9.
- 25th January 2003A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 9 cm. Work out the other shorter side.
- 26th January 20032 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th January 2003A cumulative frequency graph is drawn for 64 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 28th January 2003A bill is £408 including VAT at 20%. Work out the amount before VAT.
- 29th January 2003A line has equation y = -4x + 6. Work out the gradient of any line perpendicular to it.
- 30th January 2003A town's population is 15500 and grows by 4% each year. Work out the population after 4 years, to the nearest whole number.
- 31st January 2003ABCD is a cyclic quadrilateral. Angle ABC is 56°. Work out angle ADC.