Daily Practice · Higher
June 2023 - Higher 5-a-day
Every Higher sheet published in June 2023, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' June 2023 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2023Factorise x^2 + x - 20.
- 2nd June 2023y is directly proportional to x. When x = 5, y = 45. Work out y when x = 11.
- 3rd June 2023Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 486 cm^3. Work out the volume of the smaller.
- 4th June 202312 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th June 2023A cumulative frequency graph is drawn for 136 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 6th June 2023A mass is 63 kg, correct to the nearest whole number. Write down the lower bound.
- 7th June 2023Work out the equation of the line parallel to y = x + 3 that passes through (2, 6).
- 8th June 2023A town's population is 20000 and grows by 6% each year. Work out the population after 5 years, to the nearest whole number.
- 9th June 2023A right-angled triangle has a hypotenuse of 10 cm and one shorter side of 8 cm. Work out the other shorter side.
- 10th June 20232 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th June 2023A box plot has a minimum of 17 and a maximum of 29. Work out the range.
- 12th June 2023Write 9^-3 as a fraction.
- 13th June 2023A line has equation y = 2x + 5. Work out the gradient of any line perpendicular to it.
- 14th June 2023A block has volume 35 cm^3 and density 4 g/cm^3. Work out its mass.
- 15th June 2023ABCD is a cyclic quadrilateral. Angle ABC is 108°. Work out angle ADC.
- 16th June 202317 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 17th June 2023A box plot has minimum 9, lower quartile 18, median 22, upper quartile 31 and maximum 35. Work out the interquartile range.
- 18th June 2023Work out (8 x 10^3) x (5 x 10^2). Give your answer in standard form.
- 19th June 2023For the curve y = 2/x, work out y when x = 1, and write down the equation of its vertical asymptote.
- 20th June 2023x : y = 5 : 7. Write y in terms of x.
- 21st June 2023A, B and C are points on a circle with centre O. Angle AOC is 82°. Work out angle ABC, where B is on the major arc.
- 22nd June 20234 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd June 2023A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 24th June 2023Write the recurring decimal 0.7878... as a fraction in its simplest form.
- 25th June 2023Expand and simplify (x - 5)(x + 2)(x - 5).
- 26th June 2023A price rises by 15% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 27th June 2023A cone has base radius 5 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
- 28th June 202315 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th June 2023A histogram class is 20 units wide and contains 80 values. Work out the frequency density.
- 30th June 2023A bill is £288 including VAT at 20%. Work out the amount before VAT.