Daily Practice · Higher
December 2017 - Higher 5-a-day
Every Higher sheet published in December 2017, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2017 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2017A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 12 cm. Work out the other shorter side.
- 2nd December 20172 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd December 2017A box plot has a minimum of 3 and a maximum of 16. Work out the range.
- 4th December 2017Work out (49 x 10^11) / (7 x 10^4). Give your answer in standard form.
- 5th December 2017A line has equation y = -5x + 3. Work out the gradient of any line perpendicular to it.
- 6th December 2017A block has volume 15 cm^3 and density 8 g/cm^3. Work out its mass.
- 7th December 2017ABCD is a cyclic quadrilateral. Angle ABC is 120°. Work out angle ADC.
- 8th December 201715 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th December 2017A box plot has minimum 8, lower quartile 16, median 23, upper quartile 25 and maximum 33. Work out the interquartile range.
- 10th December 2017Write the recurring decimal 0.111... as a fraction in its simplest form.
- 11th December 2017For the curve y = -10/x, work out y when x = 10, and write down the equation of its vertical asymptote.
- 12th December 2017x : y = 4 : 7. Write y in terms of x.
- 13th December 2017A, B and C are points on a circle with centre O. Angle AOC is 72°. Work out angle ABC, where B is on the major arc.
- 14th December 20171 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th December 2017A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 16th December 2017Work out 125^(2/3).
- 17th December 2017Expand and simplify (x - 5)(x - 3)(x - 5).
- 18th December 2017A price rises by 15% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 19th December 2017A cone has base radius 7 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
- 20th December 201721 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st December 2017A histogram class is 20 units wide and contains 40 values. Work out the frequency density.
- 22nd December 2017Write sqrt(12) in the form a sqrt(b), where b is as small as possible.
- 23rd December 2017Make x the subject of y = 7x^2 - 10.
- 24th December 2017y is inversely proportional to x. When x = 4, y = 36. Work out y when x = 12.
- 25th December 2017In triangle ABC, angle A is 38°, angle B is 69° and side a is 14 cm. Use the sine rule to work out side b, to 1 decimal place.
- 26th December 20176 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th December 2017Four classes in order have frequencies 5, 7, 4, 9. Write down the cumulative frequency at the end of the third class.
- 28th December 2017A meal deal has 9 mains, 6 sides and 2 drinks. How many different meals are possible?
- 29th December 2017Factorise x^2 - 16.
- 30th December 2017y is directly proportional to x^2. When x = 6, y = 252. Work out y when x = 2.
- 31st December 2017A right-angled triangle has sides 20 cm, 21 cm and 29 cm. Work out the angle opposite the 20 cm side, to 1 decimal place.