Daily Practice · Higher
August 1987 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1987A box plot has minimum 2, lower quartile 4, median 12, upper quartile 18 and maximum 25. Work out the interquartile range.
- 2nd August 1987Write the recurring decimal 0.444... as a fraction in its simplest form.
- 3rd August 1987For the curve y = -14/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 4th August 1987x : y = 3 : 7. Write y in terms of x.
- 5th August 1987A, B and C are points on a circle with centre O. Angle AOC is 114°. Work out angle ABC, where B is on the major arc.
- 6th August 19873 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 7th August 1987A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 8th August 1987Work out 8^(2/3).
- 9th August 1987Expand and simplify (x + 4)(x + 5)(x - 5).
- 10th August 1987A price rises by 20% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 11th August 1987A cone has base radius 10 cm and vertical height 9 cm. Work out its volume, leaving your answer in terms of pi.
- 12th August 198718 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 1987A histogram class is 2 units wide and contains 5 values. Work out the frequency density.
- 14th August 1987Write sqrt(75) in the form a sqrt(b), where b is as small as possible.
- 15th August 1987Make x the subject of y = 8x^2 - 7.
- 16th August 1987y is inversely proportional to x. When x = 3, y = 40. Work out y when x = 10.
- 17th August 1987In triangle ABC, angle A is 37°, angle B is 92° and side a is 19 cm. Use the sine rule to work out side b, to 1 decimal place.
- 18th August 19871 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 19th August 1987Four classes in order have frequencies 7, 12, 5, 3. Write down the cumulative frequency at the end of the third class.
- 20th August 1987A meal deal has 6 mains, 4 sides and 4 drinks. How many different meals are possible?
- 21st August 1987Factorise x^2 - 49.
- 22nd August 1987y is directly proportional to x^2. When x = 2, y = 32. Work out y when x = 9.
- 23rd August 1987A right-angled triangle has sides 10 cm, 24 cm and 26 cm. Work out the angle opposite the 10 cm side, to 1 decimal place.
- 24th August 198722 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 25th August 198760 voles are marked and released. Later 20 are caught, of which 2 are marked. Estimate the population.
- 26th August 1987A mass is 60 kg, correct to the nearest 10. Write down the lower bound.
- 27th August 1987A region is defined by y < -3x - 5. Should the boundary line be solid or dashed, and why?
- 28th August 1987y is directly proportional to x. When x = 9, y = 54. Work out y when x = 7.
- 29th August 1987The point (-5, -3) is enlarged by scale factor -1 about the centre (-3, 2). Write down the coordinates of the image.
- 30th August 19873 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 31st August 1987A cumulative frequency graph is drawn for 220 values. What cumulative frequency do you read across from to estimate the lower quartile?