Daily Practice · Higher
January 1987 5-a-day
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The batch download puts all 5 tiers' January 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1987The point (2, 3) is enlarged by scale factor -2 about the centre (0, 4). Write down the coordinates of the image.
- 2nd January 19876 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd January 1987A box plot has minimum 15, lower quartile 21, median 31, upper quartile 40 and maximum 50. Work out the interquartile range.
- 4th January 1987A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 5th January 1987Factorise x^2 - 12x + 35.
- 6th January 1987x : y = 4 : 5. Write y in terms of x.
- 7th January 1987Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 56 cm^3. Work out the volume of the smaller.
- 8th January 198715 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th January 1987A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 10th January 1987Work out (25 x 10^9) / (5 x 10^5). Give your answer in standard form.
- 11th January 1987Work out the equation of the line parallel to y = -4x + 9 that passes through (2, -4).
- 12th January 1987A price rises by 25% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 13th January 1987A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 9 cm. Work out the other shorter side.
- 14th January 19872 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th January 1987A histogram class is 20 units wide and contains 60 values. Work out the frequency density.
- 16th January 1987Write the recurring decimal 0.111... as a fraction in its simplest form.
- 17th January 1987A line has equation y = -5x + 4. Work out the gradient of any line perpendicular to it.
- 18th January 1987y is inversely proportional to x. When x = 7, y = 60. Work out y when x = 10.
- 19th January 1987ABCD is a cyclic quadrilateral. Angle ABC is 71°. Work out angle ADC.
- 20th January 198714 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st January 1987Four classes in order have frequencies 4, 6, 9, 6. Write down the cumulative frequency at the end of the third class.
- 22nd January 1987Work out 16^(3/2).
- 23rd January 1987For the curve y = -45/x, work out y when x = 5, and write down the equation of its vertical asymptote.
- 24th January 1987y is directly proportional to x^2. When x = 3, y = 45. Work out y when x = 6.
- 25th January 1987A, B and C are points on a circle with centre O. Angle AOC is 106°. Work out angle ABC, where B is on the major arc.
- 26th January 19872 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th January 198735 voles are marked and released. Later 30 are caught, of which 5 are marked. Estimate the population.
- 28th January 1987Write sqrt(48) in the form a sqrt(b), where b is as small as possible.
- 29th January 1987Expand and simplify (x - 3)(x + 3)(x - 4).
- 30th January 1987y is directly proportional to x. When x = 3, y = 9. Work out y when x = 12.
- 31st January 1987A cone has base radius 5 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.