Daily Practice · Higher
August 1990 5-a-day
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The batch download puts all 5 tiers' August 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1990A right-angled triangle has a hypotenuse of 25 cm and one shorter side of 7 cm. Work out the other shorter side.
- 2nd August 19902 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd August 1990A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 4th August 1990Write the recurring decimal 0.6868... as a fraction in its simplest form.
- 5th August 1990A line has equation y = 5x + 8. Work out the gradient of any line perpendicular to it.
- 6th August 1990A price rises by 25% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 7th August 1990ABCD is a cyclic quadrilateral. Angle ABC is 92°. Work out angle ADC.
- 8th August 199019 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th August 1990A histogram class is 10 units wide and contains 5 values. Work out the frequency density.
- 10th August 1990A bill is £936 including VAT at 20%. Work out the amount before VAT.
- 11th August 1990For the curve y = 12/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 12th August 1990y is inversely proportional to x. When x = 6, y = 12. Work out y when x = 12.
- 13th August 1990A, B and C are points on a circle with centre O. Angle AOC is 94°. Work out angle ABC, where B is on the major arc.
- 14th August 19903 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th August 1990Four classes in order have frequencies 7, 7, 12, 5. Write down the cumulative frequency at the end of the third class.
- 16th August 1990A code is 3 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 17th August 1990Expand and simplify (x + 2)(x - 5)(x - 1).
- 18th August 1990y is directly proportional to x^2. When x = 5, y = 75. Work out y when x = 2.
- 19th August 1990A cone has base radius 7 cm and vertical height 3 cm. Work out its volume, leaving your answer in terms of pi.
- 20th August 199010 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st August 199015 fish are marked and released. Later 28 are caught, of which 7 are marked. Estimate the population.
- 22nd August 1990Work out (9 x 10^8) / (3 x 10^5). Give your answer in standard form.
- 23rd August 1990Make x the subject of y = 5x^2 - 9.
- 24th August 1990y is directly proportional to x. When x = 2, y = 6. Work out y when x = 10.
- 25th August 1990In triangle ABC, angle A is 36°, angle B is 59° and side a is 17 cm. Use the sine rule to work out side b, to 1 decimal place.
- 26th August 19904 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th August 1990A cumulative frequency graph is drawn for 164 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 28th August 1990Write the recurring decimal 0.222... as a fraction in its simplest form.
- 29th August 1990Factorise x^2 - 144.
- 30th August 1990A town's population is 15500 and grows by 8% each year. Work out the population after 3 years, to the nearest whole number.
- 31st August 1990A 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.