Daily Practice · Higher
July 1991 - Higher 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1991Work out the equation of the line parallel to y = 5x - 3 that passes through (5, 15).
- 2nd July 1991x : y = 2 : 7. Write y in terms of x.
- 3rd July 1991A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the other shorter side.
- 4th July 19912 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 5th July 1991A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
- 6th July 1991A bill is £144 including VAT at 20%. Work out the amount before VAT.
- 7th July 1991A line has equation y = -2x + 5. Work out the gradient of any line perpendicular to it.
- 8th July 1991A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 9th July 1991ABCD is a cyclic quadrilateral. Angle ABC is 84°. Work out angle ADC.
- 10th July 199121 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 11th July 1991A histogram class is 10 units wide and contains 30 values. Work out the frequency density.
- 12th July 1991A code is 3 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 13th July 1991For the curve y = -3/x, work out y when x = -1, and write down the equation of its vertical asymptote.
- 14th July 1991y is inversely proportional to x. When x = 5, y = 4. Work out y when x = 2.
- 15th July 1991A, B and C are points on a circle with centre O. Angle AOC is 162°. Work out angle ABC, where B is on the major arc.
- 16th July 19912 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 17th July 1991Four classes in order have frequencies 7, 3, 5, 9. Write down the cumulative frequency at the end of the third class.
- 18th July 1991Work out (30 x 10^9) / (5 x 10^4). Give your answer in standard form.
- 19th July 1991Expand and simplify (x - 5)(x - 5)(x - 5).
- 20th July 1991y is directly proportional to x^2. When x = 6, y = 180. Work out y when x = 2.
- 21st July 1991A cone has base radius 2 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
- 22nd July 199120 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 23rd July 199110 fish are marked and released. Later 28 are caught, of which 7 are marked. Estimate the population.
- 24th July 1991Write the recurring decimal 0.777... as a fraction in its simplest form.
- 25th July 1991Make x the subject of y = 3x^2 - 2.
- 26th July 1991y is directly proportional to x. When x = 8, y = 48. Work out y when x = 5.
- 27th July 1991In triangle ABC, angle A is 45°, angle B is 38° and side a is 20 cm. Use the sine rule to work out side b, to 1 decimal place.
- 28th July 19912 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 29th July 1991A cumulative frequency graph is drawn for 236 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 30th July 1991Work out 81^(3/2).
- 31st July 1991Factorise x^2 - 121.