Daily Practice · Higher
June 2022 - Higher 5-a-day
Every Higher sheet published in June 2022, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' June 2022 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2022A block has volume 40 cm^3 and density 4 g/cm^3. Work out its mass.
- 2nd June 2022A, B and C are points on a circle with centre O. Angle AOC is 92°. Work out angle ABC, where B is on the major arc.
- 3rd June 20221 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 4th June 2022A box plot has minimum 5, lower quartile 8, median 15, upper quartile 24 and maximum 27. Work out the interquartile range.
- 5th June 2022A code is 3 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 6th June 2022Expand and simplify (x + 2)(x + 1)(x - 1).
- 7th June 2022x : y = 2 : 9. Write y in terms of x.
- 8th June 2022A cone has base radius 4 cm and vertical height 3 cm. Work out its volume, leaving your answer in terms of pi.
- 9th June 202224 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 10th June 2022A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 11th June 2022Work out (14 x 10^6) / (7 x 10^5). Give your answer in standard form.
- 12th June 2022Make x the subject of y = 3x^2 - 5.
- 13th June 2022A price rises by 10% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 14th June 2022In triangle ABC, angle A is 75°, angle B is 74° and side a is 13 cm. Use the sine rule to work out side b, to 1 decimal place.
- 15th June 20222 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 16th June 2022A histogram class is 5 units wide and contains 12.5 values. Work out the frequency density.
- 17th June 2022Write the recurring decimal 0.666... as a fraction in its simplest form.
- 18th June 2022Factorise x^2 - 16.
- 19th June 2022y is inversely proportional to x. When x = 2, y = 60. Work out y when x = 10.
- 20th June 2022A 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.
- 21st June 202229 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 22nd June 2022Four classes in order have frequencies 5, 7, 6, 3. Write down the cumulative frequency at the end of the third class.
- 23rd June 2022Work out 216^(2/3).
- 24th June 2022A region is defined by y <= -2x + 6. Should the boundary line be solid or dashed, and why?
- 25th June 2022y is directly proportional to x^2. When x = 4, y = 112. Work out y when x = 7.
- 26th June 2022The point (5, 4) is enlarged by scale factor -3 about the centre (4, -1). Write down the coordinates of the image.
- 27th June 20223 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 28th June 202260 fish are marked and released. Later 54 are caught, of which 6 are marked. Estimate the population.
- 29th June 2022Write sqrt(18) in the form a sqrt(b), where b is as small as possible.
- 30th June 2022Factorise x^2 + 13x + 40.