Daily Practice · Higher
December 2019 - Higher 5-a-day
Every Higher sheet published in December 2019, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2019For the curve y = 16/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 2nd December 2019A price rises by 10% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 3rd December 2019A, B and C are points on a circle with centre O. Angle AOC is 40°. Work out angle ABC, where B is on the major arc.
- 4th December 20193 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 5th December 2019A histogram class is 2 units wide and contains 8 values. Work out the frequency density.
- 6th December 2019Write the recurring decimal 0.555... as a fraction in its simplest form.
- 7th December 2019Expand and simplify (x + 3)(x + 2)(x - 4).
- 8th December 2019y is inversely proportional to x. When x = 2, y = 12. Work out y when x = 4.
- 9th December 2019A cone has base radius 4 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
- 10th December 201913 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 2019Four classes in order have frequencies 5, 4, 8, 12. Write down the cumulative frequency at the end of the third class.
- 12th December 2019Work out 16^(3/2).
- 13th December 2019Make x the subject of y = 5x^2 - 12.
- 14th December 2019y is directly proportional to x^2. When x = 5, y = 150. Work out y when x = 7.
- 15th December 2019In triangle ABC, angle A is 44°, angle B is 75° and side a is 7 cm. Use the sine rule to work out side b, to 1 decimal place.
- 16th December 20197 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 17th December 201920 newts are marked and released. Later 24 are caught, of which 6 are marked. Estimate the population.
- 18th December 2019Write sqrt(45) in the form a sqrt(b), where b is as small as possible.
- 19th December 2019Factorise x^2 - 36.
- 20th December 2019y is directly proportional to x. When x = 6, y = 30. Work out y when x = 7.
- 21st December 2019A right-angled triangle has sides 3 cm, 4 cm and 5 cm. Work out the angle opposite the 3 cm side, to 1 decimal place.
- 22nd December 201925 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 23rd December 2019A cumulative frequency graph is drawn for 176 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 24th December 2019A meal deal has 5 mains, 5 sides and 5 drinks. How many different meals are possible?
- 25th December 2019A region is defined by y <= -5x + 6. Should the boundary line be solid or dashed, and why?
- 26th December 2019A town's population is 24000 and grows by 6% each year. Work out the population after 5 years, to the nearest whole number.
- 27th December 2019The point (1, 2) is enlarged by scale factor -1 about the centre (-3, 0). Write down the coordinates of the image.
- 28th December 20192 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 29th December 2019A box plot has a minimum of 17 and a maximum of 52. Work out the range.
- 30th December 2019A mass is 10.1 kg, correct to 1 decimal place. Write down the lower bound.
- 31st December 2019Factorise x^2 + 4x - 32.