Daily Practice · Higher
December 1991 - Higher 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 199120 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 2nd December 1991A cumulative frequency graph is drawn for 164 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 3rd December 1991Write the recurring decimal 0.444... as a fraction in its simplest form.
- 4th December 1991For the curve y = -20/x, work out y when x = -5, and write down the equation of its vertical asymptote.
- 5th December 1991A town's population is 22500 and grows by 4% each year. Work out the population after 3 years, to the nearest whole number.
- 6th December 1991A, B and C are points on a circle with centre O. Angle AOC is 176°. Work out angle ABC, where B is on the major arc.
- 7th December 19918 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 8th December 1991A box plot has a minimum of 5 and a maximum of 49. Work out the range.
- 9th December 1991Work out 125^(2/3).
- 10th December 1991Expand and simplify (x - 1)(x + 1)(x - 1).
- 11th December 1991A block has volume 75 cm^3 and density 4 g/cm^3. Work out its mass.
- 12th December 1991A cone has base radius 4 cm and vertical height 6 cm. Work out its volume, leaving your answer in terms of pi.
- 13th December 199115 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 14th December 1991A box plot has minimum 1, lower quartile 7, median 17, upper quartile 19 and maximum 22. Work out the interquartile range.
- 15th December 1991Write sqrt(27) in the form a sqrt(b), where b is as small as possible.
- 16th December 1991Make x the subject of y = 2x^2 - 3.
- 17th December 1991x : y = 5 : 9. Write y in terms of x.
- 18th December 1991In triangle ABC, angle A is 43°, angle B is 76° and side a is 17 cm. Use the sine rule to work out side b, to 1 decimal place.
- 19th December 19915 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 20th December 1991A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 21st December 1991A meal deal has 6 mains, 4 sides and 2 drinks. How many different meals are possible?
- 22nd December 1991Factorise x^2 - 100.
- 23rd December 1991A price rises by 20% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 24th December 1991A right-angled triangle has sides 12 cm, 16 cm and 20 cm. Work out the angle opposite the 12 cm side, to 1 decimal place.
- 25th December 199116 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 26th December 1991A histogram class is 5 units wide and contains 20 values. Work out the frequency density.
- 27th December 1991A mass is 160 kg, correct to the nearest 10. Write down the lower bound.
- 28th December 1991A region is defined by y <= 4x + 4. Should the boundary line be solid or dashed, and why?
- 29th December 1991y is inversely proportional to x. When x = 4, y = 12. Work out y when x = 6.
- 30th December 1991The point (6, -6) is enlarged by scale factor -3 about the centre (-3, -3). Write down the coordinates of the image.
- 31st December 19913 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.