Daily Practice · Higher
December 2024 - Higher 5-a-day
Every Higher sheet published in December 2024, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 20242 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 2nd December 2024A cumulative frequency graph is drawn for 232 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 3rd December 2024Write the recurring decimal 0.6262... as a fraction in its simplest form.
- 4th December 2024Expand and simplify (x - 5)(x + 1)(x + 1).
- 5th December 2024A town's population is 23500 and grows by 6% each year. Work out the population after 2 years, to the nearest whole number.
- 6th December 2024A cone has base radius 10 cm and vertical height 6 cm. Work out its volume, leaving your answer in terms of pi.
- 7th December 202422 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 8th December 2024A box plot has a minimum of 15 and a maximum of 25. Work out the range.
- 9th December 2024A bill is £672 including VAT at 20%. Work out the amount before VAT.
- 10th December 2024Make x the subject of y = 7x^2 - 6.
- 11th December 2024A block has volume 85 cm^3 and density 8 g/cm^3. Work out its mass.
- 12th December 2024In triangle ABC, angle A is 52°, angle B is 88° and side a is 16 cm. Use the sine rule to work out side b, to 1 decimal place.
- 13th December 20244 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 14th December 2024A box plot has minimum 7, lower quartile 14, median 20, upper quartile 26 and maximum 36. Work out the interquartile range.
- 15th December 2024A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 16th December 2024Factorise x^2 - 121.
- 17th December 2024x : y = 4 : 7. Write y in terms of x.
- 18th December 2024A 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.
- 19th December 202415 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 20th December 2024A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 21st December 2024Work out (15 x 10^10) / (5 x 10^3). Give your answer in standard form.
- 22nd December 2024A region is defined by y <= -x - 1. Should the boundary line be solid or dashed, and why?
- 23rd December 2024A price rises by 20% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 24th December 2024The point (-6, 2) is enlarged by scale factor -3 about the centre (3, 4). Write down the coordinates of the image.
- 25th December 20246 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 26th December 2024A histogram class is 2 units wide and contains 8 values. Work out the frequency density.
- 27th December 2024Write the recurring decimal 0.111... as a fraction in its simplest form.
- 28th December 2024Factorise x^2 - 10x + 16.
- 29th December 2024y is inversely proportional to x. When x = 3, y = 24. Work out y when x = 4.
- 30th December 2024Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 1026 cm^3. Work out the volume of the smaller.
- 31st December 202424 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.