Daily Practice · Higher
December 2018 - Higher 5-a-day
Every Higher sheet published in December 2018, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2018y is directly proportional to x^2. When x = 3, y = 63. Work out y when x = 5.
- 2nd December 2018A right-angled triangle has sides 3 cm, 4 cm and 5 cm. Work out the angle opposite the 3 cm side, to 1 decimal place.
- 3rd December 201810 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 4th December 201845 fish are marked and released. Later 21 are caught, of which 3 are marked. Estimate the population.
- 5th December 2018Write 5^-1 as a fraction.
- 6th December 2018A region is defined by y < -x - 7. Should the boundary line be solid or dashed, and why?
- 7th December 2018y is directly proportional to x. When x = 3, y = 27. Work out y when x = 7.
- 8th December 2018The point (6, 3) is enlarged by scale factor -1 about the centre (-4, -1). Write down the coordinates of the image.
- 9th December 20183 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 10th December 2018A cumulative frequency graph is drawn for 148 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 11th December 2018Work out (6 x 10^7) x (3 x 10^4). Give your answer in standard form.
- 12th December 2018Factorise x^2 + 18x + 81.
- 13th December 2018A town's population is 3000 and grows by 6% each year. Work out the population after 6 years, to the nearest whole number.
- 14th December 2018Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 513 cm^3. Work out the volume of the smaller.
- 15th December 201816 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 16th December 2018A box plot has a minimum of 3 and a maximum of 57. Work out the range.
- 17th December 2018Write the recurring decimal 0.5454... as a fraction in its simplest form.
- 18th December 2018Work out the equation of the line parallel to y = -2x + 1 that passes through (4, -19).
- 19th December 2018A block has volume 35 cm^3 and density 4 g/cm^3. Work out its mass.
- 20th December 2018A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 12 cm. Work out the other shorter side.
- 21st December 20183 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 22nd December 2018A box plot has minimum 10, lower quartile 14, median 19, upper quartile 21 and maximum 23. Work out the interquartile range.
- 23rd December 2018A bill is £528 including VAT at 20%. Work out the amount before VAT.
- 24th December 2018A line has equation y = 4x + 3. Work out the gradient of any line perpendicular to it.
- 25th December 2018x : y = 2 : 7. Write y in terms of x.
- 26th December 2018ABCD is a cyclic quadrilateral. Angle ABC is 89°. Work out angle ADC.
- 27th December 201820 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 28th December 2018A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 29th December 2018A code is 3 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 30th December 2018For the curve y = -100/x, work out y when x = -10, and write down the equation of its vertical asymptote.
- 31st December 2018A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.