Daily Practice · Higher
December 2015 - Higher 5-a-day
Every Higher sheet published in December 2015, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 20152 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 2nd December 2015Four classes in order have frequencies 5, 4, 9, 11. Write down the cumulative frequency at the end of the third class.
- 3rd December 2015A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 4th December 2015Factorise x^2 + 15x + 54.
- 5th December 2015y is directly proportional to x^2. When x = 4, y = 96. Work out y when x = 8.
- 6th December 2015Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 567 cm^3. Work out the volume of the smaller.
- 7th December 201519 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 8th December 201560 fish are marked and released. Later 48 are caught, of which 8 are marked. Estimate the population.
- 9th December 2015Work out (63 x 10^12) / (7 x 10^4). Give your answer in standard form.
- 10th December 2015Work out the equation of the line parallel to y = 3x - 2 that passes through (2, 15).
- 11th December 2015y is directly proportional to x. When x = 7, y = 49. Work out y when x = 12.
- 12th December 2015A right-angled triangle has a hypotenuse of 41 cm and one shorter side of 40 cm. Work out the other shorter side.
- 13th December 20153 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 14th December 2015A cumulative frequency graph is drawn for 104 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 15th December 2015Write the recurring decimal 0.111... as a fraction in its simplest form.
- 16th December 2015A line has equation y = 4x + 2. Work out the gradient of any line perpendicular to it.
- 17th December 2015A town's population is 12000 and grows by 5% each year. Work out the population after 5 years, to the nearest whole number.
- 18th December 2015ABCD is a cyclic quadrilateral. Angle ABC is 70°. Work out angle ADC.
- 19th December 201512 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 20th December 2015A box plot has a minimum of 4 and a maximum of 16. Work out the range.
- 21st December 2015Work out 49^(3/2).
- 22nd December 2015For the curve y = 120/x, work out y when x = -10, and write down the equation of its vertical asymptote.
- 23rd December 2015A block has volume 80 cm^3 and density 2.5 g/cm^3. Work out its mass.
- 24th December 2015A, B and C are points on a circle with centre O. Angle AOC is 146°. Work out angle ABC, where B is on the major arc.
- 25th December 20153 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 26th December 2015A box plot has minimum 2, lower quartile 10, median 12, upper quartile 18 and maximum 21. Work out the interquartile range.
- 27th December 2015Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
- 28th December 2015Expand and simplify (x + 4)(x + 2)(x + 1).
- 29th December 2015x : y = 4 : 9. Write y in terms of x.
- 30th December 2015A cone has base radius 9 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
- 31st December 201519 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.