Daily Practice · Higher
January 2025 - Higher 5-a-day
Every Higher sheet published in January 2025, with answers. Grades 6-7 - Higher-tier method and manipulation.
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The batch download puts all 5 tiers' January 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2025Four classes in order have frequencies 9, 8, 6, 11. Write down the cumulative frequency at the end of the third class.
- 2nd January 2025Work out 216^(2/3).
- 3rd January 2025Work out the equation of the line parallel to y = -2x + 9 that passes through (5, -15).
- 4th January 2025y is directly proportional to x^2. When x = 3, y = 36. Work out y when x = 4.
- 5th January 2025A right-angled triangle has a hypotenuse of 10 cm and one shorter side of 6 cm. Work out the other shorter side.
- 6th January 20251 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 7th January 202550 beetles are marked and released. Later 12 are caught, of which 4 are marked. Estimate the population.
- 8th January 2025Write sqrt(48) in the form a sqrt(b), where b is as small as possible.
- 9th January 2025A line has equation y = 5x + 5. Work out the gradient of any line perpendicular to it.
- 10th January 2025y is directly proportional to x. When x = 5, y = 10. Work out y when x = 15.
- 11th January 2025ABCD is a cyclic quadrilateral. Angle ABC is 57°. Work out angle ADC.
- 12th January 202512 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 13th January 2025A cumulative frequency graph is drawn for 184 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 14th January 2025A meal deal has 6 mains, 7 sides and 4 drinks. How many different meals are possible?
- 15th January 2025For the curve y = 30/x, work out y when x = 10, and write down the equation of its vertical asymptote.
- 16th January 2025A town's population is 30500 and grows by 6% each year. Work out the population after 4 years, to the nearest whole number.
- 17th January 2025A, B and C are points on a circle with centre O. Angle AOC is 88°. Work out angle ABC, where B is on the major arc.
- 18th January 20254 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 19th January 2025A box plot has a minimum of 15 and a maximum of 67. Work out the range.
- 20th January 2025A mass is 350 kg, correct to the nearest 10. Write down the lower bound.
- 21st January 2025Expand and simplify (x + 5)(x - 4)(x + 1).
- 22nd January 2025A block has volume 185 cm^3 and density 7.5 g/cm^3. Work out its mass.
- 23rd January 2025A cone has base radius 7 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
- 24th January 202523 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 25th January 2025A box plot has minimum 5, lower quartile 13, median 23, upper quartile 29 and maximum 38. Work out the interquartile range.
- 26th January 2025Write 5^-2 as a fraction.
- 27th January 2025Make x the subject of y = 3x^2 - 12.
- 28th January 2025x : y = 5 : 6. Write y in terms of x.
- 29th January 2025In triangle ABC, angle A is 31°, angle B is 93° and side a is 17 cm. Use the sine rule to work out side b, to 1 decimal place.
- 30th January 20251 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 31st January 2025A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.