Daily Practice · Higher
October 2021 - Higher 5-a-day
Every Higher sheet published in October 2021, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' October 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2021A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 2nd October 2021Work out 49^(3/2).
- 3rd October 2021For the curve y = -1/x, work out y when x = 1, and write down the equation of its vertical asymptote.
- 4th October 2021A price rises by 15% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 5th October 2021A, B and C are points on a circle with centre O. Angle AOC is 158°. Work out angle ABC, where B is on the major arc.
- 6th October 20211 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 7th October 2021A histogram class is 20 units wide and contains 30 values. Work out the frequency density.
- 8th October 2021Write sqrt(48) in the form a sqrt(b), where b is as small as possible.
- 9th October 2021Expand and simplify (x - 4)(x - 2)(x - 1).
- 10th October 2021y is inversely proportional to x. When x = 9, y = 20. Work out y when x = 5.
- 11th October 2021A cone has base radius 3 cm and vertical height 12 cm. Work out its volume, leaving your answer in terms of pi.
- 12th October 202117 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 13th October 2021Four classes in order have frequencies 8, 10, 5, 6. Write down the cumulative frequency at the end of the third class.
- 14th October 2021A meal deal has 3 mains, 8 sides and 6 drinks. How many different meals are possible?
- 15th October 2021Make x the subject of y = 2x^2 - 10.
- 16th October 2021y is directly proportional to x^2. When x = 2, y = 28. Work out y when x = 9.
- 17th October 2021In triangle ABC, angle A is 50°, angle B is 95° and side a is 6 cm. Use the sine rule to work out side b, to 1 decimal place.
- 18th October 20213 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 19th October 202135 beetles are marked and released. Later 81 are caught, of which 9 are marked. Estimate the population.
- 20th October 2021A mass is 750 kg, correct to the nearest 10. Write down the upper bound.
- 21st October 2021Factorise x^2 - 36.
- 22nd October 2021y is directly proportional to x. When x = 5, y = 30. Work out y when x = 15.
- 23rd October 2021A right-angled triangle has sides 10 cm, 24 cm and 26 cm. Work out the angle opposite the 10 cm side, to 1 decimal place.
- 24th October 202121 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 25th October 2021A cumulative frequency graph is drawn for 128 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 26th October 2021Write 7^-3 as a fraction.
- 27th October 2021A region is defined by y <= -3x + 7. Should the boundary line be solid or dashed, and why?
- 28th October 2021A town's population is 28500 and grows by 5% each year. Work out the population after 4 years, to the nearest whole number.
- 29th October 2021The point (4, -3) is enlarged by scale factor -3 about the centre (4, -2). Write down the coordinates of the image.
- 30th October 20211 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 31st October 2021A box plot has a minimum of 6 and a maximum of 39. Work out the range.