Daily Practice · Higher
December 1987 5-a-day
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The batch download puts all 5 tiers' December 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1987A region is defined by y <= 3x + 5. Should the boundary line be solid or dashed, and why?
- 2nd December 1987A block has volume 40 cm^3 and density 3 g/cm^3. Work out its mass.
- 3rd December 1987The point (6, 3) is enlarged by scale factor -3 about the centre (0, -1). Write down the coordinates of the image.
- 4th December 19872 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 5th December 1987A box plot has minimum 4, lower quartile 7, median 14, upper quartile 24 and maximum 28. Work out the interquartile range.
- 6th December 1987Work out (32 x 10^6) / (4 x 10^5). Give your answer in standard form.
- 7th December 1987Factorise x^2 + 11x + 30.
- 8th December 1987x : y = 2 : 3. Write y in terms of x.
- 9th December 1987Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 192 cm^3. Work out the volume of the smaller.
- 10th December 198715 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 11th December 1987A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
- 12th December 1987Write the recurring decimal 0.444... as a fraction in its simplest form.
- 13th December 1987Work out the equation of the line parallel to y = 5x + 5 that passes through (6, 40).
- 14th December 1987A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 15th December 1987A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 10 cm. Work out the other shorter side.
- 16th December 19874 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 17th December 1987A histogram class is 4 units wide and contains 12 values. Work out the frequency density.
- 18th December 1987Work out 36^(3/2).
- 19th December 1987A line has equation y = -2x + 9. Work out the gradient of any line perpendicular to it.
- 20th December 1987y is inversely proportional to x. When x = 2, y = 15. Work out y when x = 3.
- 21st December 1987ABCD is a cyclic quadrilateral. Angle ABC is 104°. Work out angle ADC.
- 22nd December 198713 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 23rd December 1987Four classes in order have frequencies 8, 4, 7, 7. Write down the cumulative frequency at the end of the third class.
- 24th December 1987Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
- 25th December 1987For the curve y = 8/x, work out y when x = 1, and write down the equation of its vertical asymptote.
- 26th December 1987y is directly proportional to x^2. When x = 2, y = 24. Work out y when x = 4.
- 27th December 1987A, B and C are points on a circle with centre O. Angle AOC is 40°. Work out angle ABC, where B is on the major arc.
- 28th December 19874 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 29th December 198710 newts are marked and released. Later 48 are caught, of which 6 are marked. Estimate the population.
- 30th December 1987A meal deal has 6 mains, 4 sides and 5 drinks. How many different meals are possible?
- 31st December 1987Expand and simplify (x + 4)(x - 3)(x + 1).