Daily Practice · Higher
July 2016 - Higher 5-a-day
Every Higher sheet published in July 2016, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' July 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2016For the curve y = 40/x, work out y when x = -5, and write down the equation of its vertical asymptote.
- 2nd July 2016y is directly proportional to x^2. When x = 3, y = 18. Work out y when x = 8.
- 3rd July 2016A, B and C are points on a circle with centre O. Angle AOC is 136°. Work out angle ABC, where B is on the major arc.
- 4th July 20161 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 5th July 201610 beetles are marked and released. Later 36 are caught, of which 4 are marked. Estimate the population.
- 6th July 2016Work out 125^(2/3).
- 7th July 2016Expand and simplify (x + 2)(x + 1)(x - 2).
- 8th July 2016y is directly proportional to x. When x = 7, y = 35. Work out y when x = 13.
- 9th July 2016A cone has base radius 2 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 10th July 201617 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 11th July 2016A cumulative frequency graph is drawn for 136 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 12th July 2016Write sqrt(12) in the form a sqrt(b), where b is as small as possible.
- 13th July 2016Make x the subject of y = 9x^2 - 4.
- 14th July 2016A town's population is 5500 and grows by 4% each year. Work out the population after 5 years, to the nearest whole number.
- 15th July 2016In triangle ABC, angle A is 46°, angle B is 86° and side a is 19 cm. Use the sine rule to work out side b, to 1 decimal place.
- 16th July 20163 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 17th July 2016A box plot has a minimum of 12 and a maximum of 52. Work out the range.
- 18th July 2016A meal deal has 4 mains, 3 sides and 5 drinks. How many different meals are possible?
- 19th July 2016Factorise x^2 - 100.
- 20th July 2016A block has volume 45 cm^3 and density 8 g/cm^3. Work out its mass.
- 21st July 2016A 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.
- 22nd July 201616 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 23rd July 2016A box plot has minimum 6, lower quartile 16, median 23, upper quartile 26 and maximum 30. Work out the interquartile range.
- 24th July 2016A mass is 25.4 kg, correct to 1 decimal place. Write down the upper bound.
- 25th July 2016A region is defined by y <= -3x - 7. Should the boundary line be solid or dashed, and why?
- 26th July 2016x : y = 3 : 5. Write y in terms of x.
- 27th July 2016The point (5, 6) is enlarged by scale factor -2 about the centre (1, 0). Write down the coordinates of the image.
- 28th July 20163 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 29th July 2016A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 30th July 2016Write 8^-2 as a fraction.
- 31st July 2016Factorise x^2 - 4x + 3.