Daily Practice · Higher
December 2009 - Higher 5-a-day
Every Higher sheet published in December 2009, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2009ABCD is a cyclic quadrilateral. Angle ABC is 93°. Work out angle ADC.
- 2nd December 200921 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 3rd December 2009A histogram class is 20 units wide and contains 50 values. Work out the frequency density.
- 4th December 2009Write the recurring decimal 0.5454... as a fraction in its simplest form.
- 5th December 2009For the curve y = 40/x, work out y when x = -5, and write down the equation of its vertical asymptote.
- 6th December 2009y is inversely proportional to x. When x = 3, y = 60. Work out y when x = 10.
- 7th December 2009A, B and C are points on a circle with centre O. Angle AOC is 48°. Work out angle ABC, where B is on the major arc.
- 8th December 20091 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 9th December 2009Four classes in order have frequencies 4, 6, 7, 4. Write down the cumulative frequency at the end of the third class.
- 10th December 2009A bill is £360 including VAT at 20%. Work out the amount before VAT.
- 11th December 2009Expand and simplify (x + 5)(x + 3)(x + 2).
- 12th December 2009y is directly proportional to x^2. When x = 5, y = 150. Work out y when x = 7.
- 13th December 2009A cone has base radius 8 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 14th December 200919 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 15th December 200960 beetles are marked and released. Later 40 are caught, of which 4 are marked. Estimate the population.
- 16th December 2009A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 17th December 2009Make x the subject of y = 6x^2 - 12.
- 18th December 2009y is directly proportional to x. When x = 7, y = 49. Work out y when x = 2.
- 19th December 2009In triangle ABC, angle A is 62°, angle B is 42° and side a is 7 cm. Use the sine rule to work out side b, to 1 decimal place.
- 20th December 20093 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 21st December 2009A cumulative frequency graph is drawn for 116 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 22nd December 2009Work out (28 x 10^11) / (7 x 10^2). Give your answer in standard form.
- 23rd December 2009Factorise x^2 - 100.
- 24th December 2009A town's population is 15000 and grows by 4% each year. Work out the population after 2 years, to the nearest whole number.
- 25th December 2009A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Work out the angle opposite the 6 cm side, to 1 decimal place.
- 26th December 200924 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 27th December 2009A box plot has a minimum of 8 and a maximum of 61. Work out the range.
- 28th December 2009Write the recurring decimal 0.111... as a fraction in its simplest form.
- 29th December 2009A region is defined by y < -4x - 5. Should the boundary line be solid or dashed, and why?
- 30th December 2009A block has volume 180 cm^3 and density 11 g/cm^3. Work out its mass.
- 31st December 2009The point (-3, 6) is enlarged by scale factor -1 about the centre (4, 4). Write down the coordinates of the image.