Daily Practice · Higher
July 1986 5-a-day
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The batch download puts all 5 tiers' July 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 198655 fish are marked and released. Later 30 are caught, of which 3 are marked. Estimate the population.
- 2nd July 1986Write the recurring decimal 0.666... as a fraction in its simplest form.
- 3rd July 1986Work out the equation of the line parallel to y = 4x - 1 that passes through (5, 32).
- 4th July 1986y is directly proportional to x. When x = 2, y = 8. Work out y when x = 7.
- 5th July 1986A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 12 cm. Work out the other shorter side.
- 6th July 19865 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 7th July 1986A cumulative frequency graph is drawn for 80 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 8th July 1986Work out 25^(3/2).
- 9th July 1986A line has equation y = -3x + 5. Work out the gradient of any line perpendicular to it.
- 10th July 1986A town's population is 12500 and grows by 5% each year. Work out the population after 6 years, to the nearest whole number.
- 11th July 1986ABCD is a cyclic quadrilateral. Angle ABC is 78°. Work out angle ADC.
- 12th July 198610 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 13th July 1986A box plot has a minimum of 20 and a maximum of 70. Work out the range.
- 14th July 1986Write sqrt(75) in the form a sqrt(b), where b is as small as possible.
- 15th July 1986For the curve y = 100/x, work out y when x = -10, and write down the equation of its vertical asymptote.
- 16th July 1986A block has volume 145 cm^3 and density 8 g/cm^3. Work out its mass.
- 17th July 1986A, B and C are points on a circle with centre O. Angle AOC is 64°. Work out angle ABC, where B is on the major arc.
- 18th July 19863 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 19th July 1986A box plot has minimum 12, lower quartile 22, median 30, upper quartile 39 and maximum 43. Work out the interquartile range.
- 20th July 1986A meal deal has 6 mains, 3 sides and 5 drinks. How many different meals are possible?
- 21st July 1986Expand and simplify (x + 1)(x + 5)(x + 2).
- 22nd July 1986x : y = 3 : 8. Write y in terms of x.
- 23rd July 1986A cone has base radius 2 cm and vertical height 12 cm. Work out its volume, leaving your answer in terms of pi.
- 24th July 198630 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 25th July 1986A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 26th July 1986A mass is 380 kg, correct to the nearest 10. Write down the lower bound.
- 27th July 1986Make x the subject of y = 6x^2 - 6.
- 28th July 1986A price rises by 20% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 29th July 1986In triangle ABC, angle A is 53°, angle B is 63° and side a is 7 cm. Use the sine rule to work out side b, to 1 decimal place.
- 30th July 19864 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 31st July 1986A histogram class is 10 units wide and contains 25 values. Work out the frequency density.