Daily Practice · Higher
December 2021 - Higher 5-a-day
Every Higher sheet published in December 2021, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2021Write the recurring decimal 0.444... as a fraction in its simplest form.
- 2nd December 2021Make x the subject of y = 2x^2 - 11.
- 3rd December 2021y is directly proportional to x. When x = 4, y = 12. Work out y when x = 14.
- 4th December 2021In triangle ABC, angle A is 62°, angle B is 46° and side a is 11 cm. Use the sine rule to work out side b, to 1 decimal place.
- 5th December 20212 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 6th December 2021A cumulative frequency graph is drawn for 148 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 7th December 2021Work out 25^(3/2).
- 8th December 2021Factorise x^2 - 36.
- 9th December 2021A town's population is 4500 and grows by 8% each year. Work out the population after 6 years, to the nearest whole number.
- 10th December 2021A 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.
- 11th December 202114 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 12th December 2021A box plot has a minimum of 19 and a maximum of 58. Work out the range.
- 13th December 2021Write sqrt(18) in the form a sqrt(b), where b is as small as possible.
- 14th December 2021A region is defined by y < -x - 2. Should the boundary line be solid or dashed, and why?
- 15th December 2021A block has volume 70 cm^3 and density 7.5 g/cm^3. Work out its mass.
- 16th December 2021The point (3, 0) is enlarged by scale factor -2 about the centre (3, -4). Write down the coordinates of the image.
- 17th December 20213 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 18th December 2021A box plot has minimum 12, lower quartile 20, median 27, upper quartile 33 and maximum 37. Work out the interquartile range.
- 19th December 2021A meal deal has 7 mains, 9 sides and 3 drinks. How many different meals are possible?
- 20th December 2021Factorise x^2 - 9x + 20.
- 21st December 2021x : y = 4 : 5. Write y in terms of x.
- 22nd December 2021Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 264 cm^3. Work out the volume of the smaller.
- 23rd December 202123 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 24th December 2021A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 25th December 2021A mass is 24 kg, correct to the nearest whole number. Write down the upper bound.
- 26th December 2021Work out the equation of the line parallel to y = 4x - 3 that passes through (2, 4).
- 27th December 2021A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 28th December 2021A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Work out the other shorter side.
- 29th December 20216 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 30th December 2021A histogram class is 5 units wide and contains 2.5 values. Work out the frequency density.
- 31st December 2021Write 4^-3 as a fraction.