Daily Practice · Higher
August 2019 - Higher 5-a-day
Every Higher sheet published in August 2019, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2019A histogram class is 5 units wide and contains 7.5 values. Work out the frequency density.
- 2nd August 2019Work out 125^(2/3).
- 3rd August 2019A region is defined by y < x - 9. Should the boundary line be solid or dashed, and why?
- 4th August 2019y is inversely proportional to x. When x = 7, y = 30. Work out y when x = 6.
- 5th August 2019The point (-3, -3) is enlarged by scale factor -3 about the centre (-4, 3). Write down the coordinates of the image.
- 6th August 20195 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 7th August 2019Four classes in order have frequencies 4, 9, 10, 12. Write down the cumulative frequency at the end of the third class.
- 8th August 2019Write sqrt(12) in the form a sqrt(b), where b is as small as possible.
- 9th August 2019Factorise x^2 - 25.
- 10th August 2019y is directly proportional to x^2. When x = 3, y = 81. Work out y when x = 8.
- 11th August 2019Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 459 cm^3. Work out the volume of the smaller.
- 12th August 201925 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 13th August 201935 beetles are marked and released. Later 84 are caught, of which 7 are marked. Estimate the population.
- 14th August 2019A meal deal has 6 mains, 5 sides and 4 drinks. How many different meals are possible?
- 15th August 2019Work out the equation of the line parallel to y = -5x + 7 that passes through (2, 1).
- 16th August 2019y is directly proportional to x. When x = 4, y = 16. Work out y when x = 10.
- 17th August 2019A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 12 cm. Work out the other shorter side.
- 18th August 20197 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 19th August 2019A cumulative frequency graph is drawn for 216 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 20th August 2019A mass is 56 kg, correct to the nearest whole number. Write down the lower bound.
- 21st August 2019A line has equation y = 2x + 2. Work out the gradient of any line perpendicular to it.
- 22nd August 2019A town's population is 16500 and grows by 5% each year. Work out the population after 2 years, to the nearest whole number.
- 23rd August 2019ABCD is a cyclic quadrilateral. Angle ABC is 95°. Work out angle ADC.
- 24th August 201925 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 25th August 2019A box plot has a minimum of 6 and a maximum of 58. Work out the range.
- 26th August 2019Write 3^-2 as a fraction.
- 27th August 2019For the curve y = -24/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 28th August 2019A block has volume 75 cm^3 and density 4 g/cm^3. Work out its mass.
- 29th August 2019A, B and C are points on a circle with centre O. Angle AOC is 80°. Work out angle ABC, where B is on the major arc.
- 30th August 20198 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 31st August 2019A box plot has minimum 13, lower quartile 19, median 28, upper quartile 37 and maximum 39. Work out the interquartile range.