Daily Practice · Higher
August 2015 - Higher 5-a-day
Every Higher sheet published in August 2015, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2015y is directly proportional to x^2. When x = 4, y = 64. Work out y when x = 8.
- 2nd August 2015A, B and C are points on a circle with centre O. Angle AOC is 140°. Work out angle ABC, where B is on the major arc.
- 3rd August 20152 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 4th August 201515 voles are marked and released. Later 49 are caught, of which 7 are marked. Estimate the population.
- 5th August 2015Write the recurring decimal 0.444... as a fraction in its simplest form.
- 6th August 2015Expand and simplify (x + 5)(x - 3)(x - 2).
- 7th August 2015y is directly proportional to x. When x = 4, y = 20. Work out y when x = 15.
- 8th August 2015A cone has base radius 3 cm and vertical height 3 cm. Work out its volume, leaving your answer in terms of pi.
- 9th August 201518 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 10th August 2015A cumulative frequency graph is drawn for 48 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 11th August 2015Work out 100^(3/2).
- 12th August 2015Make x the subject of y = 9x^2 - 3.
- 13th August 2015A town's population is 40000 and grows by 5% each year. Work out the population after 3 years, to the nearest whole number.
- 14th August 2015In triangle ABC, angle A is 66°, angle B is 45° and side a is 11 cm. Use the sine rule to work out side b, to 1 decimal place.
- 15th August 20152 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 16th August 2015A box plot has a minimum of 5 and a maximum of 35. Work out the range.
- 17th August 2015Write sqrt(18) in the form a sqrt(b), where b is as small as possible.
- 18th August 2015Factorise x^2 - 4.
- 19th August 2015A block has volume 165 cm^3 and density 4 g/cm^3. Work out its mass.
- 20th August 2015A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Work out the angle opposite the 6 cm side, to 1 decimal place.
- 21st August 201525 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 22nd August 2015A box plot has minimum 14, lower quartile 20, median 27, upper quartile 33 and maximum 39. Work out the interquartile range.
- 23rd August 2015A meal deal has 4 mains, 9 sides and 4 drinks. How many different meals are possible?
- 24th August 2015A region is defined by y < 3x - 6. Should the boundary line be solid or dashed, and why?
- 25th August 2015x : y = 2 : 7. Write y in terms of x.
- 26th August 2015The point (2, 0) is enlarged by scale factor -2 about the centre (-1, 0). Write down the coordinates of the image.
- 27th August 20151 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 28th August 2015A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 29th August 2015A mass is 3.5 kg, correct to 1 decimal place. Write down the upper bound.
- 30th August 2015Factorise x^2 + 14x + 48.
- 31st August 2015A price rises by 15% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.