Daily Practice · Higher
August 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 195725 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 2nd August 1957A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 3rd August 1957Write the recurring decimal 0.111... as a fraction in its simplest form.
- 4th August 1957Work out the equation of the line parallel to y = -4x + 8 that passes through (6, -25).
- 5th August 1957A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 6th August 1957A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 16 cm. Work out the other shorter side.
- 7th August 19572 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 8th August 1957A histogram class is 4 units wide and contains 2 values. Work out the frequency density.
- 9th August 1957Work out 8^(2/3).
- 10th August 1957A line has equation y = 3x + 7. Work out the gradient of any line perpendicular to it.
- 11th August 1957y is inversely proportional to x. When x = 4, y = 60. Work out y when x = 10.
- 12th August 1957ABCD is a cyclic quadrilateral. Angle ABC is 65°. Work out angle ADC.
- 13th August 19577 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 14th August 1957Four classes in order have frequencies 6, 12, 3, 11. Write down the cumulative frequency at the end of the third class.
- 15th August 1957Write sqrt(75) in the form a sqrt(b), where b is as small as possible.
- 16th August 1957For the curve y = -120/x, work out y when x = -10, and write down the equation of its vertical asymptote.
- 17th August 1957y is directly proportional to x^2. When x = 5, y = 75. Work out y when x = 9.
- 18th August 1957A, B and C are points on a circle with centre O. Angle AOC is 78°. Work out angle ABC, where B is on the major arc.
- 19th August 19574 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 20th August 195730 voles are marked and released. Later 96 are caught, of which 8 are marked. Estimate the population.
- 21st August 1957A meal deal has 4 mains, 4 sides and 4 drinks. How many different meals are possible?
- 22nd August 1957Expand and simplify (x - 5)(x - 1)(x - 1).
- 23rd August 1957y is directly proportional to x. When x = 8, y = 56. Work out y when x = 3.
- 24th August 1957A cone has base radius 3 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
- 25th August 195716 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 26th August 1957A cumulative frequency graph is drawn for 124 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 27th August 1957A mass is 43 kg, correct to the nearest whole number. Write down the lower bound.
- 28th August 1957Make x the subject of y = 7x^2 - 9.
- 29th August 1957A town's population is 13500 and grows by 4% each year. Work out the population after 3 years, to the nearest whole number.
- 30th August 1957In triangle ABC, angle A is 51°, angle B is 55° and side a is 12 cm. Use the sine rule to work out side b, to 1 decimal place.
- 31st August 19576 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.