Daily Practice · Higher
July 1957 5-a-day
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The batch download puts all 5 tiers' July 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1957A, B and C are points on a circle with centre O. Angle AOC is 132°. Work out angle ABC, where B is on the major arc.
- 2nd July 19571 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd July 1957Four classes in order have frequencies 9, 5, 12, 3. Write down the cumulative frequency at the end of the third class.
- 4th July 1957Work out (7 x 10^3) x (8 x 10^-3). Give your answer in standard form.
- 5th July 1957Expand and simplify (x - 3)(x - 1)(x + 2).
- 6th July 1957y is directly proportional to x^2. When x = 6, y = 216. Work out y when x = 3.
- 7th July 1957A cone has base radius 8 cm and vertical height 6 cm. Work out its volume, leaving your answer in terms of pi.
- 8th July 195711 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th July 195745 newts are marked and released. Later 44 are caught, of which 4 are marked. Estimate the population.
- 10th July 1957Write the recurring decimal 0.6969... as a fraction in its simplest form.
- 11th July 1957Make x the subject of y = 3x^2 - 11.
- 12th July 1957y is directly proportional to x. When x = 7, y = 63. Work out y when x = 8.
- 13th July 1957In triangle ABC, angle A is 52°, angle B is 93° and side a is 16 cm. Use the sine rule to work out side b, to 1 decimal place.
- 14th July 19571 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th July 1957A cumulative frequency graph is drawn for 116 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 16th July 1957A bill is £936 including VAT at 20%. Work out the amount before VAT.
- 17th July 1957Factorise x^2 - 64.
- 18th July 1957A town's population is 12500 and grows by 3% each year. Work out the population after 2 years, to the nearest whole number.
- 19th July 1957A right-angled triangle has sides 8 cm, 15 cm and 17 cm. Work out the angle opposite the 8 cm side, to 1 decimal place.
- 20th July 195716 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st July 1957A box plot has a minimum of 13 and a maximum of 53. Work out the range.
- 22nd July 1957A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 23rd July 1957A region is defined by y <= 2x - 6. Should the boundary line be solid or dashed, and why?
- 24th July 1957A block has volume 50 cm^3 and density 8 g/cm^3. Work out its mass.
- 25th July 1957The point (2, 4) is enlarged by scale factor -3 about the centre (0, 4). Write down the coordinates of the image.
- 26th July 19577 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th July 1957A box plot has minimum 8, lower quartile 11, median 20, upper quartile 24 and maximum 34. Work out the interquartile range.
- 28th July 1957Work out (45 x 10^7) / (9 x 10^2). Give your answer in standard form.
- 29th July 1957Factorise x^2 + 11x + 28.
- 30th July 1957x : y = 3 : 7. Write y in terms of x.
- 31st July 1957Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 810 cm^3. Work out the volume of the smaller.