Daily Practice · Higher
December 1997 - Higher 5-a-day
Every Higher sheet published in December 1997, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1997Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
- 2nd December 1997Factorise x^2 - 9.
- 3rd December 1997A block has volume 190 cm^3 and density 2.5 g/cm^3. Work out its mass.
- 4th December 1997Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 189 cm^3. Work out the volume of the smaller.
- 5th December 199724 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 6th December 1997A box plot has minimum 3, lower quartile 10, median 17, upper quartile 26 and maximum 34. Work out the interquartile range.
- 7th December 1997A meal deal has 6 mains, 8 sides and 5 drinks. How many different meals are possible?
- 8th December 1997Work out the equation of the line parallel to y = x - 7 that passes through (1, 2).
- 9th December 1997x : y = 7 : 9. Write y in terms of x.
- 10th December 1997A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 12 cm. Work out the other shorter side.
- 11th December 19975 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 12th December 1997A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 13th December 1997A mass is 15 kg, correct to the nearest whole number. Write down the lower bound.
- 14th December 1997A line has equation y = -3x + 7. Work out the gradient of any line perpendicular to it.
- 15th December 1997A price rises by 25% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 16th December 1997ABCD is a cyclic quadrilateral. Angle ABC is 89°. Work out angle ADC.
- 17th December 199719 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 18th December 1997A histogram class is 2 units wide and contains 5 values. Work out the frequency density.
- 19th December 1997Write 3^-2 as a fraction.
- 20th December 1997For the curve y = -45/x, work out y when x = 5, and write down the equation of its vertical asymptote.
- 21st December 1997y is inversely proportional to x. When x = 2, y = 15. Work out y when x = 5.
- 22nd December 1997A, B and C are points on a circle with centre O. Angle AOC is 108°. Work out angle ABC, where B is on the major arc.
- 23rd December 19972 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 24th December 1997Four classes in order have frequencies 6, 10, 7, 5. Write down the cumulative frequency at the end of the third class.
- 25th December 1997Work out (7 x 10^4) x (2 x 10^5). Give your answer in standard form.
- 26th December 1997Expand and simplify (x - 4)(x - 2)(x - 4).
- 27th December 1997y is directly proportional to x^2. When x = 2, y = 24. Work out y when x = 6.
- 28th December 1997A cone has base radius 2 cm and vertical height 6 cm. Work out its volume, leaving your answer in terms of pi.
- 29th December 199727 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 30th December 199710 beetles are marked and released. Later 16 are caught, of which 4 are marked. Estimate the population.
- 31st December 1997Write the recurring decimal 0.2020... as a fraction in its simplest form.