Daily Practice · Higher
December 2005 - Higher 5-a-day
Every Higher sheet published in December 2005, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2005Write 6^-3 as a fraction.
- 2nd December 2005A region is defined by y <= -3x + 9. Should the boundary line be solid or dashed, and why?
- 3rd December 2005y is directly proportional to x^2. When x = 6, y = 72. Work out y when x = 7.
- 4th December 2005The point (-4, -3) is enlarged by scale factor -2 about the centre (-1, -3). Write down the coordinates of the image.
- 5th December 20058 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 6th December 200545 voles are marked and released. Later 72 are caught, of which 8 are marked. Estimate the population.
- 7th December 2005Work out (7 x 10^7) x (6 x 10^6). Give your answer in standard form.
- 8th December 2005Factorise x^2 + 3x - 40.
- 9th December 2005y is directly proportional to x. When x = 9, y = 99. Work out y when x = 13.
- 10th December 2005Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 1280 cm^3. Work out the volume of the smaller.
- 11th December 200530 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 12th December 2005A cumulative frequency graph is drawn for 212 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 13th December 2005Write the recurring decimal 0.8181... as a fraction in its simplest form.
- 14th December 2005Work out the equation of the line parallel to y = 4x - 8 that passes through (4, 4).
- 15th December 2005A town's population is 22000 and grows by 5% each year. Work out the population after 6 years, to the nearest whole number.
- 16th December 2005A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 12 cm. Work out the other shorter side.
- 17th December 20056 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 18th December 2005A box plot has a minimum of 15 and a maximum of 39. Work out the range.
- 19th December 2005A bill is £384 including VAT at 20%. Work out the amount before VAT.
- 20th December 2005A line has equation y = 5x + 5. Work out the gradient of any line perpendicular to it.
- 21st December 2005A block has volume 135 cm^3 and density 2.5 g/cm^3. Work out its mass.
- 22nd December 2005ABCD is a cyclic quadrilateral. Angle ABC is 100°. Work out angle ADC.
- 23rd December 200519 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 24th December 2005A box plot has minimum 2, lower quartile 4, median 6, upper quartile 12 and maximum 18. Work out the interquartile range.
- 25th December 2005A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 26th December 2005For the curve y = 70/x, work out y when x = -10, and write down the equation of its vertical asymptote.
- 27th December 2005x : y = 5 : 7. Write y in terms of x.
- 28th December 2005A, B and C are points on a circle with centre O. Angle AOC is 176°. Work out angle ABC, where B is on the major arc.
- 29th December 20052 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 30th December 2005A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 31st December 2005Work out (16 x 10^9) / (2 x 10^2). Give your answer in standard form.