Daily Practice · Higher
October 2023 - Higher 5-a-day
Every Higher sheet published in October 2023, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' October 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2023A cone has base radius 5 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
- 2nd October 202313 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 3rd October 202320 beetles are marked and released. Later 33 are caught, of which 3 are marked. Estimate the population.
- 4th October 2023Write sqrt(32) in the form a sqrt(b), where b is as small as possible.
- 5th October 2023Make x the subject of y = 8x^2 - 2.
- 6th October 2023y is directly proportional to x. When x = 5, y = 50. Work out y when x = 10.
- 7th October 2023In triangle ABC, angle A is 70°, angle B is 34° and side a is 8 cm. Use the sine rule to work out side b, to 1 decimal place.
- 8th October 20231 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 9th October 2023A cumulative frequency graph is drawn for 68 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 10th October 2023A meal deal has 4 mains, 3 sides and 2 drinks. How many different meals are possible?
- 11th October 2023Factorise x^2 - 144.
- 12th October 2023A town's population is 9000 and grows by 5% each year. Work out the population after 3 years, to the nearest whole number.
- 13th October 2023A right-angled triangle has sides 9 cm, 12 cm and 15 cm. Work out the angle opposite the 9 cm side, to 1 decimal place.
- 14th October 202316 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 15th October 2023A box plot has a minimum of 15 and a maximum of 47. Work out the range.
- 16th October 2023A mass is 260 kg, correct to the nearest 10. Write down the lower bound.
- 17th October 2023A region is defined by y < -5x + 9. Should the boundary line be solid or dashed, and why?
- 18th October 2023A block has volume 25 cm^3 and density 4 g/cm^3. Work out its mass.
- 19th October 2023The point (-5, 1) is enlarged by scale factor -1 about the centre (-2, 3). Write down the coordinates of the image.
- 20th October 20231 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 21st October 2023A box plot has minimum 13, lower quartile 22, median 27, upper quartile 33 and maximum 37. Work out the interquartile range.
- 22nd October 2023Write 8^-1 as a fraction.
- 23rd October 2023Factorise x^2 + 4x + 4.
- 24th October 2023x : y = 5 : 9. Write y in terms of x.
- 25th October 2023Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 1856 cm^3. Work out the volume of the smaller.
- 26th October 202323 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 27th October 2023A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 28th October 2023Work out (4 x 10^5) x (7 x 10^-2). Give your answer in standard form.
- 29th October 2023Work out the equation of the line parallel to y = -5x - 2 that passes through (1, -1).
- 30th October 2023A price rises by 10% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 31st October 2023A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the other shorter side.