Daily Practice · Higher
January 2013 - Higher 5-a-day
Every Higher sheet published in January 2013, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2013x : y = 4 : 7. Write y in terms of x.
- 2nd January 2013A right-angled triangle has sides 8 cm, 15 cm and 17 cm. Work out the angle opposite the 8 cm side, to 1 decimal place.
- 3rd January 201316 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 4th January 2013A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.
- 5th January 2013A bill is £216 including VAT at 20%. Work out the amount before VAT.
- 6th January 2013A region is defined by y < 2x - 3. Should the boundary line be solid or dashed, and why?
- 7th January 2013A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 8th January 2013The point (-4, 2) is enlarged by scale factor -1 about the centre (-4, -1). Write down the coordinates of the image.
- 9th January 20132 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 10th January 2013A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
- 11th January 2013A code is 3 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 12th January 2013Factorise x^2 + 2x - 24.
- 13th January 2013y is inversely proportional to x. When x = 4, y = 10. Work out y when x = 5.
- 14th January 2013Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 459 cm^3. Work out the volume of the smaller.
- 15th January 201318 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 16th January 2013Four classes in order have frequencies 9, 8, 8, 4. Write down the cumulative frequency at the end of the third class.
- 17th January 2013Work out (56 x 10^7) / (8 x 10^4). Give your answer in standard form.
- 18th January 2013Work out the equation of the line parallel to y = -4x - 5 that passes through (2, -2).
- 19th January 2013y is directly proportional to x^2. When x = 5, y = 100. Work out y when x = 6.
- 20th January 2013A right-angled triangle has a hypotenuse of 5 cm and one shorter side of 3 cm. Work out the other shorter side.
- 21st January 20136 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 22nd January 201345 voles are marked and released. Later 36 are caught, of which 3 are marked. Estimate the population.
- 23rd January 2013Write the recurring decimal 0.444... as a fraction in its simplest form.
- 24th January 2013A line has equation y = -2x + 7. Work out the gradient of any line perpendicular to it.
- 25th January 2013y is directly proportional to x. When x = 3, y = 30. Work out y when x = 14.
- 26th January 2013ABCD is a cyclic quadrilateral. Angle ABC is 105°. Work out angle ADC.
- 27th January 201315 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 28th January 2013A cumulative frequency graph is drawn for 196 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 29th January 2013Work out 36^(3/2).
- 30th January 2013For the curve y = 7/x, work out y when x = -1, and write down the equation of its vertical asymptote.
- 31st January 2013A town's population is 5000 and grows by 6% each year. Work out the population after 3 years, to the nearest whole number.