Daily Practice · Higher
August 1972 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1972 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 197210 beetles are marked and released. Later 12 are caught, of which 2 are marked. Estimate the population.
- 2nd August 1972Write the recurring decimal 0.666... as a fraction in its simplest form.
- 3rd August 1972A line has equation y = -2x + 1. Work out the gradient of any line perpendicular to it.
- 4th August 1972y is directly proportional to x. When x = 6, y = 24. Work out y when x = 9.
- 5th August 1972ABCD is a cyclic quadrilateral. Angle ABC is 66°. Work out angle ADC.
- 6th August 197212 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 7th August 1972A cumulative frequency graph is drawn for 156 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 8th August 1972Work out 125^(2/3).
- 9th August 1972For the curve y = 10/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 10th August 1972A town's population is 16000 and grows by 4% each year. Work out the population after 6 years, to the nearest whole number.
- 11th August 1972A, B and C are points on a circle with centre O. Angle AOC is 62°. Work out angle ABC, where B is on the major arc.
- 12th August 19722 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 13th August 1972A box plot has a minimum of 18 and a maximum of 67. Work out the range.
- 14th August 1972Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
- 15th August 1972Expand and simplify (x + 5)(x + 2)(x + 1).
- 16th August 1972A block has volume 155 cm^3 and density 11 g/cm^3. Work out its mass.
- 17th August 1972A cone has base radius 6 cm and vertical height 12 cm. Work out its volume, leaving your answer in terms of pi.
- 18th August 197226 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 19th August 1972A box plot has minimum 15, lower quartile 18, median 22, upper quartile 29 and maximum 32. Work out the interquartile range.
- 20th August 1972A meal deal has 3 mains, 9 sides and 3 drinks. How many different meals are possible?
- 21st August 1972Make x the subject of y = 4x^2 - 10.
- 22nd August 1972x : y = 3 : 7. Write y in terms of x.
- 23rd August 1972In triangle ABC, angle A is 77°, angle B is 68° and side a is 17 cm. Use the sine rule to work out side b, to 1 decimal place.
- 24th August 19721 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 25th August 1972A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 26th August 1972A mass is 22.3 kg, correct to 1 decimal place. Write down the upper bound.
- 27th August 1972Factorise x^2 - 121.
- 28th August 1972A price rises by 25% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 29th August 1972A right-angled triangle has sides 7 cm, 24 cm and 25 cm. Work out the angle opposite the 7 cm side, to 1 decimal place.
- 30th August 197224 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 31st August 1972A histogram class is 20 units wide and contains 50 values. Work out the frequency density.