Daily Practice · Higher
August 2021 - Higher 5-a-day
Every Higher sheet published in August 2021, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 202110 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 August 2021A cumulative frequency graph is drawn for 176 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 3rd August 2021Write sqrt(75) in the form a sqrt(b), where b is as small as possible.
- 4th August 2021Work out the equation of the line parallel to y = 3x - 3 that passes through (4, 11).
- 5th August 2021A town's population is 5500 and grows by 4% each year. Work out the population after 6 years, to the nearest whole number.
- 6th August 2021A right-angled triangle has a hypotenuse of 10 cm and one shorter side of 6 cm. Work out the other shorter side.
- 7th August 20212 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 8th August 2021A box plot has a minimum of 16 and a maximum of 70. Work out the range.
- 9th August 2021A meal deal has 3 mains, 7 sides and 2 drinks. How many different meals are possible?
- 10th August 2021A line has equation y = -3x + 2. Work out the gradient of any line perpendicular to it.
- 11th August 2021A block has volume 160 cm^3 and density 11 g/cm^3. Work out its mass.
- 12th August 2021ABCD is a cyclic quadrilateral. Angle ABC is 119°. Work out angle ADC.
- 13th August 202121 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 14th August 2021A box plot has minimum 6, lower quartile 11, median 17, upper quartile 25 and maximum 32. Work out the interquartile range.
- 15th August 2021A mass is 23 kg, correct to the nearest whole number. Write down the upper bound.
- 16th August 2021For the curve y = -44/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 17th August 2021x : y = 7 : 9. Write y in terms of x.
- 18th August 2021A, B and C are points on a circle with centre O. Angle AOC is 152°. Work out angle ABC, where B is on the major arc.
- 19th August 20212 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 20th August 2021A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
- 21st August 2021Write 6^-3 as a fraction.
- 22nd August 2021Expand and simplify (x - 4)(x + 2)(x - 4).
- 23rd August 2021A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 24th August 2021A cone has base radius 4 cm and vertical height 6 cm. Work out its volume, leaving your answer in terms of pi.
- 25th August 202114 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 26th August 2021A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
- 27th August 2021Work out (4 x 10^3) x (4 x 10^-6). Give your answer in standard form.
- 28th August 2021Make x the subject of y = 2x^2 - 7.
- 29th August 2021y is inversely proportional to x. When x = 3, y = 12. Work out y when x = 12.
- 30th August 2021In triangle ABC, angle A is 55°, angle B is 90° and side a is 8 cm. Use the sine rule to work out side b, to 1 decimal place.
- 31st August 20215 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.