Daily Practice · Higher
December 1998 - Higher 5-a-day
Every Higher sheet published in December 1998, with answers. Grades 6-7 - Higher-tier method and manipulation.
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The batch download puts all 5 tiers' December 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 199845 newts are marked and released. Later 80 are caught, of which 8 are marked. Estimate the population.
- 2nd December 1998A bill is £816 including VAT at 20%. Work out the amount before VAT.
- 3rd December 1998Make x the subject of y = 8x^2 - 4.
- 4th December 1998y is directly proportional to x. When x = 7, y = 84. Work out y when x = 9.
- 5th December 1998In triangle ABC, angle A is 31°, angle B is 44° and side a is 14 cm. Use the sine rule to work out side b, to 1 decimal place.
- 6th December 19982 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 7th December 1998A cumulative frequency graph is drawn for 120 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 8th December 1998A code is 3 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 9th December 1998Factorise x^2 - 100.
- 10th December 1998A town's population is 29500 and grows by 8% each year. Work out the population after 6 years, to the nearest whole number.
- 11th December 1998A right-angled triangle has sides 20 cm, 21 cm and 29 cm. Work out the angle opposite the 20 cm side, to 1 decimal place.
- 12th December 199811 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 December 1998A box plot has a minimum of 15 and a maximum of 57. Work out the range.
- 14th December 1998Work out (32 x 10^8) / (8 x 10^4). Give your answer in standard form.
- 15th December 1998A region is defined by y <= 3x + 6. Should the boundary line be solid or dashed, and why?
- 16th December 1998A block has volume 45 cm^3 and density 4 g/cm^3. Work out its mass.
- 17th December 1998The point (1, -1) is enlarged by scale factor -2 about the centre (0, -2). Write down the coordinates of the image.
- 18th December 19984 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 19th December 1998A box plot has minimum 12, lower quartile 21, median 24, upper quartile 33 and maximum 37. Work out the interquartile range.
- 20th December 1998Write the recurring decimal 0.777... as a fraction in its simplest form.
- 21st December 1998Factorise x^2 - x - 6.
- 22nd December 1998x : y = 3 : 4. Write y in terms of x.
- 23rd December 1998Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 280 cm^3. Work out the volume of the smaller.
- 24th December 199827 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 25th December 1998A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 26th December 1998Work out 36^(3/2).
- 27th December 1998Work out the equation of the line parallel to y = 5x - 2 that passes through (2, 4).
- 28th December 1998A price rises by 20% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 29th December 1998A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the other shorter side.
- 30th December 19987 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 31st December 1998A histogram class is 4 units wide and contains 16 values. Work out the frequency density.