Daily Practice · Higher
January 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1957x : y = 5 : 8. Write y in terms of x.
- 2nd January 1957In triangle ABC, angle A is 40°, angle B is 51° and side a is 11 cm. Use the sine rule to work out side b, to 1 decimal place.
- 3rd January 19573 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 4th January 1957A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 5th January 1957A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 6th January 1957Factorise x^2 - 25.
- 7th January 1957A price rises by 15% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 8th January 1957A right-angled triangle has sides 5 cm, 12 cm and 13 cm. Work out the angle opposite the 5 cm side, to 1 decimal place.
- 9th January 195718 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 10th January 1957A histogram class is 4 units wide and contains 10 values. Work out the frequency density.
- 11th January 1957Work out (63 x 10^10) / (9 x 10^3). Give your answer in standard form.
- 12th January 1957A region is defined by y <= -4x + 2. Should the boundary line be solid or dashed, and why?
- 13th January 1957y is inversely proportional to x. When x = 2, y = 20. Work out y when x = 5.
- 14th January 1957The point (3, -4) is enlarged by scale factor -3 about the centre (1, -3). Write down the coordinates of the image.
- 15th January 19573 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 16th January 1957Four classes in order have frequencies 12, 3, 11, 8. Write down the cumulative frequency at the end of the third class.
- 17th January 1957Write the recurring decimal 0.777... as a fraction in its simplest form.
- 18th January 1957Factorise x^2 + 11x + 28.
- 19th January 1957y is directly proportional to x^2. When x = 3, y = 72. Work out y when x = 4.
- 20th January 1957Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 1728 cm^3. Work out the volume of the smaller.
- 21st January 195716 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 22nd January 195720 newts are marked and released. Later 35 are caught, of which 7 are marked. Estimate the population.
- 23rd January 1957Work out 27^(2/3).
- 24th January 1957Work out the equation of the line parallel to y = 5x + 6 that passes through (5, 14).
- 25th January 1957y is directly proportional to x. When x = 8, y = 72. Work out y when x = 2.
- 26th January 1957A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 12 cm. Work out the other shorter side.
- 27th January 19574 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 28th January 1957A cumulative frequency graph is drawn for 68 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 29th January 1957Write sqrt(48) in the form a sqrt(b), where b is as small as possible.
- 30th January 1957A line has equation y = 5x + 3. Work out the gradient of any line perpendicular to it.
- 31st January 1957A town's population is 17000 and grows by 4% each year. Work out the population after 4 years, to the nearest whole number.