Daily Practice · Higher
December 1953 5-a-day
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The batch download puts all 5 tiers' December 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1953A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 16 cm. Work out the other shorter side.
- 2nd December 19534 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd December 1953A histogram class is 2 units wide and contains 5 values. Work out the frequency density.
- 4th December 1953A bill is £960 including VAT at 20%. Work out the amount before VAT.
- 5th December 1953A line has equation y = 3x + 7. Work out the gradient of any line perpendicular to it.
- 6th December 1953y is inversely proportional to x. When x = 2, y = 48. Work out y when x = 12.
- 7th December 1953ABCD is a cyclic quadrilateral. Angle ABC is 80°. Work out angle ADC.
- 8th December 195314 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th December 1953Four classes in order have frequencies 6, 8, 6, 11. Write down the cumulative frequency at the end of the third class.
- 10th December 1953A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 11th December 1953For the curve y = 4/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 12th December 1953y is directly proportional to x^2. When x = 5, y = 200. Work out y when x = 2.
- 13th December 1953A, B and C are points on a circle with centre O. Angle AOC is 134°. Work out angle ABC, where B is on the major arc.
- 14th December 19536 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th December 195325 newts are marked and released. Later 30 are caught, of which 3 are marked. Estimate the population.
- 16th December 1953Work out (30 x 10^12) / (6 x 10^5). Give your answer in standard form.
- 17th December 1953Expand and simplify (x + 1)(x + 3)(x - 1).
- 18th December 1953y is directly proportional to x. When x = 3, y = 36. Work out y when x = 2.
- 19th December 1953A cone has base radius 8 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 20th December 195311 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st December 1953A cumulative frequency graph is drawn for 104 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 22nd December 1953Write the recurring decimal 0.111... as a fraction in its simplest form.
- 23rd December 1953Make x the subject of y = 2x^2 - 5.
- 24th December 1953A town's population is 14000 and grows by 5% each year. Work out the population after 2 years, to the nearest whole number.
- 25th December 1953In triangle ABC, angle A is 70°, angle B is 59° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
- 26th December 19538 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th December 1953A box plot has a minimum of 5 and a maximum of 58. Work out the range.
- 28th December 1953Work out 16^(3/2).
- 29th December 1953Factorise x^2 - 36.
- 30th December 1953A block has volume 85 cm^3 and density 2.5 g/cm^3. Work out its mass.
- 31st December 1953A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Work out the angle opposite the 6 cm side, to 1 decimal place.