Daily Practice · Higher
December 1985 5-a-day
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The batch download puts all 5 tiers' December 1985 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1985In triangle ABC, angle A is 51°, angle B is 63° and side a is 20 cm. Use the sine rule to work out side b, to 1 decimal place.
- 2nd December 19854 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd December 198515 fish are marked and released. Later 28 are caught, of which 4 are marked. Estimate the population.
- 4th December 1985A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 5th December 1985Factorise x^2 - 16.
- 6th December 1985y is directly proportional to x. When x = 5, y = 45. Work out y when x = 13.
- 7th December 1985A right-angled triangle has sides 5 cm, 12 cm and 13 cm. Work out the angle opposite the 5 cm side, to 1 decimal place.
- 8th December 198519 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th December 1985A cumulative frequency graph is drawn for 104 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 10th December 1985Work out (35 x 10^7) / (5 x 10^3). Give your answer in standard form.
- 11th December 1985A region is defined by y <= 5x - 2. Should the boundary line be solid or dashed, and why?
- 12th December 1985A town's population is 17000 and grows by 5% each year. Work out the population after 4 years, to the nearest whole number.
- 13th December 1985The point (-5, -2) is enlarged by scale factor -2 about the centre (4, 2). Write down the coordinates of the image.
- 14th December 19855 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th December 1985A box plot has a minimum of 2 and a maximum of 16. Work out the range.
- 16th December 1985Write the recurring decimal 0.444... as a fraction in its simplest form.
- 17th December 1985Factorise x^2 + 2x - 35.
- 18th December 1985A block has volume 150 cm^3 and density 4 g/cm^3. Work out its mass.
- 19th December 1985Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 891 cm^3. Work out the volume of the smaller.
- 20th December 198521 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st December 1985A box plot has minimum 4, lower quartile 7, median 17, upper quartile 27 and maximum 37. Work out the interquartile range.
- 22nd December 1985Work out 27^(2/3).
- 23rd December 1985Work out the equation of the line parallel to y = x - 5 that passes through (6, -5).
- 24th December 1985x : y = 5 : 6. Write y in terms of x.
- 25th December 1985A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 21 cm. Work out the other shorter side.
- 26th December 19852 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th December 1985A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 28th December 1985Write sqrt(32) in the form a sqrt(b), where b is as small as possible.
- 29th December 1985A line has equation y = -2x + 7. Work out the gradient of any line perpendicular to it.
- 30th December 1985A price rises by 10% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 31st December 1985ABCD is a cyclic quadrilateral. Angle ABC is 87°. Work out angle ADC.