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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January 2025

31 sheets · 155 questions · Grades 6-7

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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.

  1. 1st January 2025Four classes in order have frequencies 9, 8, 6, 11. Write down the cumulative frequency at the end of the third class.
  2. 2nd January 2025Work out 216^(2/3).
  3. 3rd January 2025Work out the equation of the line parallel to y = -2x + 9 that passes through (5, -15).
  4. 4th January 2025y is directly proportional to x^2. When x = 3, y = 36. Work out y when x = 4.
  5. 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.
  6. 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.
  7. 7th January 202550 beetles are marked and released. Later 12 are caught, of which 4 are marked. Estimate the population.
  8. 8th January 2025Write sqrt(48) in the form a sqrt(b), where b is as small as possible.
  9. 9th January 2025A line has equation y = 5x + 5. Work out the gradient of any line perpendicular to it.
  10. 10th January 2025y is directly proportional to x. When x = 5, y = 10. Work out y when x = 15.
  11. 11th January 2025ABCD is a cyclic quadrilateral. Angle ABC is 57°. Work out angle ADC.
  12. 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.
  13. 13th January 2025A cumulative frequency graph is drawn for 184 values. What cumulative frequency do you read across from to estimate the lower quartile?
  14. 14th January 2025A meal deal has 6 mains, 7 sides and 4 drinks. How many different meals are possible?
  15. 15th January 2025For the curve y = 30/x, work out y when x = 10, and write down the equation of its vertical asymptote.
  16. 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.
  17. 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.
  18. 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.
  19. 19th January 2025A box plot has a minimum of 15 and a maximum of 67. Work out the range.
  20. 20th January 2025A mass is 350 kg, correct to the nearest 10. Write down the lower bound.
  21. 21st January 2025Expand and simplify (x + 5)(x - 4)(x + 1).
  22. 22nd January 2025A block has volume 185 cm^3 and density 7.5 g/cm^3. Work out its mass.
  23. 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.
  24. 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.
  25. 25th January 2025A box plot has minimum 5, lower quartile 13, median 23, upper quartile 29 and maximum 38. Work out the interquartile range.
  26. 26th January 2025Write 5^-2 as a fraction.
  27. 27th January 2025Make x the subject of y = 3x^2 - 12.
  28. 28th January 2025x : y = 5 : 6. Write y in terms of x.
  29. 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.
  30. 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.
  31. 31st January 2025A capture-recapture estimate is made of the ladybird population of a garden. State one assumption the method relies on.

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