Daily Practice · Higher
December 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1957A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 2nd December 1957Make x the subject of y = 4x^2 - 10.
- 3rd December 1957x : y = 2 : 3. Write y in terms of x.
- 4th December 1957In triangle ABC, angle A is 61°, angle B is 85° and side a is 9 cm. Use the sine rule to work out side b, to 1 decimal place.
- 5th December 19575 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 6th December 1957A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 7th December 1957Work out (54 x 10^7) / (9 x 10^4). Give your answer in standard form.
- 8th December 1957Factorise x^2 - 81.
- 9th December 1957A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 10th December 1957A right-angled triangle has sides 12 cm, 16 cm and 20 cm. Work out the angle opposite the 12 cm side, to 1 decimal place.
- 11th December 195726 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 12th December 1957A histogram class is 4 units wide and contains 16 values. Work out the frequency density.
- 13th December 1957Write the recurring decimal 0.666... as a fraction in its simplest form.
- 14th December 1957A region is defined by y <= x + 3. Should the boundary line be solid or dashed, and why?
- 15th December 1957y is inversely proportional to x. When x = 5, y = 36. Work out y when x = 12.
- 16th December 1957The point (-2, 6) is enlarged by scale factor -1 about the centre (3, 1). Write down the coordinates of the image.
- 17th December 19571 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 18th December 1957Four classes in order have frequencies 3, 10, 7, 4. Write down the cumulative frequency at the end of the third class.
- 19th December 1957Work out 25^(3/2).
- 20th December 1957Factorise x^2 - 8x + 7.
- 21st December 1957y is directly proportional to x^2. When x = 3, y = 54. Work out y when x = 9.
- 22nd December 1957Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 296 cm^3. Work out the volume of the smaller.
- 23rd December 195715 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 24th December 195755 newts are marked and released. Later 50 are caught, of which 5 are marked. Estimate the population.
- 25th December 1957Write sqrt(50) in the form a sqrt(b), where b is as small as possible.
- 26th December 1957Work out the equation of the line parallel to y = -x - 6 that passes through (5, -8).
- 27th December 1957y is directly proportional to x. When x = 8, y = 88. Work out y when x = 3.
- 28th December 1957A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Work out the other shorter side.
- 29th December 19572 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 30th December 1957A cumulative frequency graph is drawn for 156 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 31st December 1957A meal deal has 9 mains, 4 sides and 3 drinks. How many different meals are possible?