Daily Practice · Higher
December 2004 - Higher 5-a-day
Every Higher sheet published in December 2004, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2004 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2004A line has equation y = 3x + 1. Work out the gradient of any line perpendicular to it.
- 2nd December 2004A town's population is 24500 and grows by 5% each year. Work out the population after 4 years, to the nearest whole number.
- 3rd December 2004ABCD is a cyclic quadrilateral. Angle ABC is 85°. Work out angle ADC.
- 4th December 200421 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th December 2004A box plot has a minimum of 14 and a maximum of 28. Work out the range.
- 6th December 2004Write the recurring decimal 0.444... as a fraction in its simplest form.
- 7th December 2004For the curve y = 14/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 8th December 2004A block has volume 185 cm^3 and density 11 g/cm^3. Work out its mass.
- 9th December 2004A, B and C are points on a circle with centre O. Angle AOC is 86°. Work out angle ABC, where B is on the major arc.
- 10th December 20043 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th December 2004A box plot has minimum 11, lower quartile 16, median 23, upper quartile 33 and maximum 39. Work out the interquartile range.
- 12th December 2004Work out 125^(2/3).
- 13th December 2004Expand and simplify (x - 5)(x - 2)(x + 4).
- 14th December 2004x : y = 3 : 7. Write y in terms of x.
- 15th December 2004A cone has base radius 7 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
- 16th December 200424 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 17th December 2004A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 18th December 2004Write sqrt(48) in the form a sqrt(b), where b is as small as possible.
- 19th December 2004Make x the subject of y = 9x^2 - 2.
- 20th December 2004A price rises by 25% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 21st December 2004In triangle ABC, angle A is 56°, angle B is 77° and side a is 5 cm. Use the sine rule to work out side b, to 1 decimal place.
- 22nd December 20043 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd December 2004A histogram class is 10 units wide and contains 40 values. Work out the frequency density.
- 24th December 2004A meal deal has 8 mains, 6 sides and 4 drinks. How many different meals are possible?
- 25th December 2004Factorise x^2 - 81.
- 26th December 2004y is inversely proportional to x. When x = 7, y = 12. Work out y when x = 12.
- 27th December 2004A right-angled triangle has sides 20 cm, 21 cm and 29 cm. Work out the angle opposite the 20 cm side, to 1 decimal place.
- 28th December 20047 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th December 2004Four classes in order have frequencies 3, 6, 3, 4. Write down the cumulative frequency at the end of the third class.
- 30th December 2004A mass is 65 kg, correct to the nearest whole number. Write down the lower bound.
- 31st December 2004A region is defined by y <= -x - 4. Should the boundary line be solid or dashed, and why?