Daily Practice · Higher
December 1961 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1961Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 135 cm^3. Work out the volume of the smaller.
- 2nd December 196118 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 3rd December 1961A box plot has a minimum of 18 and a maximum of 68. Work out the range.
- 4th December 1961Write the recurring decimal 0.888... as a fraction in its simplest form.
- 5th December 1961Work out the equation of the line parallel to y = -3x - 1 that passes through (2, -16).
- 6th December 1961A block has volume 20 cm^3 and density 3 g/cm^3. Work out its mass.
- 7th December 1961A right-angled triangle has a hypotenuse of 25 cm and one shorter side of 24 cm. Work out the other shorter side.
- 8th December 19611 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 9th December 1961A box plot has minimum 14, lower quartile 23, median 31, upper quartile 36 and maximum 43. Work out the interquartile range.
- 10th December 1961Work out 8^(2/3).
- 11th December 1961A line has equation y = 2x + 2. Work out the gradient of any line perpendicular to it.
- 12th December 1961x : y = 3 : 5. Write y in terms of x.
- 13th December 1961ABCD is a cyclic quadrilateral. Angle ABC is 92°. Work out angle ADC.
- 14th December 196120 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 15th December 1961A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 16th December 1961Write sqrt(12) in the form a sqrt(b), where b is as small as possible.
- 17th December 1961For the curve y = 18/x, work out y when x = 2, and write down the equation of its vertical asymptote.
- 18th December 1961A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 19th December 1961A, B and C are points on a circle with centre O. Angle AOC is 58°. Work out angle ABC, where B is on the major arc.
- 20th December 19611 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 21st December 1961A histogram class is 4 units wide and contains 2 values. Work out the frequency density.
- 22nd December 1961A meal deal has 7 mains, 6 sides and 6 drinks. How many different meals are possible?
- 23rd December 1961Expand and simplify (x + 1)(x + 5)(x - 4).
- 24th December 1961y is inversely proportional to x. When x = 6, y = 10. Work out y when x = 5.
- 25th December 1961A cone has base radius 2 cm and vertical height 9 cm. Work out its volume, leaving your answer in terms of pi.
- 26th December 196118 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 27th December 1961Four classes in order have frequencies 9, 4, 4, 7. Write down the cumulative frequency at the end of the third class.
- 28th December 1961A mass is 230 kg, correct to the nearest 10. Write down the lower bound.
- 29th December 1961Make x the subject of y = 7x^2 - 3.
- 30th December 1961y is directly proportional to x^2. When x = 4, y = 32. Work out y when x = 9.
- 31st December 1961In triangle ABC, angle A is 77°, angle B is 56° and side a is 5 cm. Use the sine rule to work out side b, to 1 decimal place.