Daily Practice · Higher
December 2023 - Higher 5-a-day
Every Higher sheet published in December 2023, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 202324 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 2nd December 2023A box plot has minimum 10, lower quartile 18, median 25, upper quartile 30 and maximum 34. Work out the interquartile range.
- 3rd December 2023Work out 100^(3/2).
- 4th December 2023A region is defined by y <= -5x + 7. Should the boundary line be solid or dashed, and why?
- 5th December 2023x : y = 2 : 3. Write y in terms of x.
- 6th December 2023The point (5, -6) is enlarged by scale factor -1 about the centre (0, -1). Write down the coordinates of the image.
- 7th December 20233 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 8th December 2023A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
- 9th December 2023Write sqrt(72) in the form a sqrt(b), where b is as small as possible.
- 10th December 2023Factorise x^2 - 16x + 64.
- 11th December 2023A price rises by 25% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 12th December 2023Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 2048 cm^3. Work out the volume of the smaller.
- 13th December 202321 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 14th December 2023A histogram class is 10 units wide and contains 20 values. Work out the frequency density.
- 15th December 2023A meal deal has 6 mains, 5 sides and 3 drinks. How many different meals are possible?
- 16th December 2023Work out the equation of the line parallel to y = 2x - 6 that passes through (5, 17).
- 17th December 2023y is inversely proportional to x. When x = 3, y = 4. Work out y when x = 4.
- 18th December 2023A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 12 cm. Work out the other shorter side.
- 19th December 20233 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 20th December 2023Four classes in order have frequencies 10, 9, 4, 10. Write down the cumulative frequency at the end of the third class.
- 21st December 2023A mass is 790 kg, correct to the nearest 10. Write down the lower bound.
- 22nd December 2023A line has equation y = -3x + 7. Work out the gradient of any line perpendicular to it.
- 23rd December 2023y is directly proportional to x^2. When x = 6, y = 108. Work out y when x = 8.
- 24th December 2023ABCD is a cyclic quadrilateral. Angle ABC is 60°. Work out angle ADC.
- 25th December 202316 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 202355 fish are marked and released. Later 63 are caught, of which 9 are marked. Estimate the population.
- 27th December 2023Write 2^-3 as a fraction.
- 28th December 2023For the curve y = -9/x, work out y when x = 1, and write down the equation of its vertical asymptote.
- 29th December 2023y is directly proportional to x. When x = 6, y = 18. Work out y when x = 12.
- 30th December 2023A, B and C are points on a circle with centre O. Angle AOC is 72°. Work out angle ABC, where B is on the major arc.
- 31st December 20237 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.