Daily Practice · Higher
January 2005 - Higher 5-a-day
Every Higher sheet published in January 2005, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2005y is directly proportional to x^2. When x = 6, y = 324. Work out y when x = 3.
- 2nd January 2005The point (6, 5) is enlarged by scale factor -3 about the centre (3, 0). Write down the coordinates of the image.
- 3rd January 20053 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 4th January 200560 beetles are marked and released. Later 54 are caught, of which 9 are marked. Estimate the population.
- 5th January 2005Write 6^-3 as a fraction.
- 6th January 2005Factorise x^2 + 6x - 7.
- 7th January 2005y is directly proportional to x. When x = 3, y = 24. Work out y when x = 13.
- 8th January 2005Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 756 cm^3. Work out the volume of the smaller.
- 9th January 200512 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 10th January 2005A cumulative frequency graph is drawn for 144 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 11th January 2005Work out (7 x 10^6) x (9 x 10^-5). Give your answer in standard form.
- 12th January 2005Work out the equation of the line parallel to y = -5x + 4 that passes through (1, 3).
- 13th January 2005A town's population is 4500 and grows by 8% each year. Work out the population after 5 years, to the nearest whole number.
- 14th January 2005A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 10 cm. Work out the other shorter side.
- 15th January 20052 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 16th January 2005A box plot has a minimum of 9 and a maximum of 27. Work out the range.
- 17th January 2005Write the recurring decimal 0.2828... as a fraction in its simplest form.
- 18th January 2005A line has equation y = 5x + 3. Work out the gradient of any line perpendicular to it.
- 19th January 2005A block has volume 70 cm^3 and density 11 g/cm^3. Work out its mass.
- 20th January 2005ABCD is a cyclic quadrilateral. Angle ABC is 115°. Work out angle ADC.
- 21st January 200518 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 22nd January 2005A box plot has minimum 7, lower quartile 13, median 23, upper quartile 31 and maximum 33. Work out the interquartile range.
- 23rd January 2005A bill is £336 including VAT at 20%. Work out the amount before VAT.
- 24th January 2005For the curve y = 6/x, work out y when x = 2, and write down the equation of its vertical asymptote.
- 25th January 2005x : y = 2 : 9. Write y in terms of x.
- 26th January 2005A, B and C are points on a circle with centre O. Angle AOC is 114°. Work out angle ABC, where B is on the major arc.
- 27th January 20053 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 28th January 2005A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 29th January 2005A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 30th January 2005Expand and simplify (x + 2)(x + 3)(x - 2).
- 31st January 2005A price rises by 20% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.