Daily Practice · Higher
July 2019 - Higher 5-a-day
Every Higher sheet published in July 2019, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' July 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 20191 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 2nd July 201920 fish are marked and released. Later 48 are caught, of which 8 are marked. Estimate the population.
- 3rd July 2019Write the recurring decimal 0.8080... as a fraction in its simplest form.
- 4th July 2019A line has equation y = 2x + 1. Work out the gradient of any line perpendicular to it.
- 5th July 2019y is directly proportional to x. When x = 6, y = 12. Work out y when x = 7.
- 6th July 2019ABCD is a cyclic quadrilateral. Angle ABC is 121°. Work out angle ADC.
- 7th July 201922 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 8th July 2019A cumulative frequency graph is drawn for 236 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 9th July 2019A bill is £840 including VAT at 20%. Work out the amount before VAT.
- 10th July 2019For the curve y = -12/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 11th July 2019A town's population is 38500 and grows by 4% each year. Work out the population after 5 years, to the nearest whole number.
- 12th July 2019A, B and C are points on a circle with centre O. Angle AOC is 42°. Work out angle ABC, where B is on the major arc.
- 13th July 20193 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 14th July 2019A box plot has a minimum of 16 and a maximum of 44. Work out the range.
- 15th July 2019A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 16th July 2019Expand and simplify (x + 3)(x - 5)(x + 5).
- 17th July 2019A block has volume 50 cm^3 and density 11 g/cm^3. Work out its mass.
- 18th July 2019A cone has base radius 10 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
- 19th July 201928 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 20th July 2019A box plot has minimum 5, lower quartile 9, median 16, upper quartile 22 and maximum 27. Work out the interquartile range.
- 21st July 2019Work out (24 x 10^11) / (8 x 10^3). Give your answer in standard form.
- 22nd July 2019Make x the subject of y = 2x^2 - 9.
- 23rd July 2019x : y = 5 : 9. Write y in terms of x.
- 24th July 2019In triangle ABC, angle A is 43°, angle B is 81° and side a is 19 cm. Use the sine rule to work out side b, to 1 decimal place.
- 25th July 20192 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 26th July 2019A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 27th July 2019Write the recurring decimal 0.333... as a fraction in its simplest form.
- 28th July 2019Factorise x^2 - 81.
- 29th July 2019A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 30th July 2019A right-angled triangle has sides 3 cm, 4 cm and 5 cm. Work out the angle opposite the 3 cm side, to 1 decimal place.
- 31st July 201913 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.