Daily Practice · Higher

January 2023 - Higher 5-a-day

Every Higher sheet published in January 2023, with answers. Grades 6-7 - Higher-tier method and manipulation.

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January 2023

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' January 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 2023

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 2023Write the recurring decimal 0.444... as a fraction in its simplest form.
  2. 2nd January 2023A region is defined by y < 5x - 3. Should the boundary line be solid or dashed, and why?
  3. 3rd January 2023x : y = 5 : 7. Write y in terms of x.
  4. 4th January 2023The point (4, 2) is enlarged by scale factor -3 about the centre (-3, -4). Write down the coordinates of the image.
  5. 5th January 20238 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  6. 6th January 2023A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
  7. 7th January 2023Work out 36^(3/2).
  8. 8th January 2023Factorise x^2 - 3x - 28.
  9. 9th January 2023A price rises by 10% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
  10. 10th January 2023Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 513 cm^3. Work out the volume of the smaller.
  11. 11th January 202325 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  12. 12th January 2023A histogram class is 10 units wide and contains 5 values. Work out the frequency density.
  13. 13th January 2023Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
  14. 14th January 2023Work out the equation of the line parallel to y = 4x + 3 that passes through (6, 14).
  15. 15th January 2023y is inversely proportional to x. When x = 7, y = 30. Work out y when x = 6.
  16. 16th January 2023A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 16 cm. Work out the other shorter side.
  17. 17th January 20234 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  18. 18th January 2023Four classes in order have frequencies 9, 11, 6, 4. Write down the cumulative frequency at the end of the third class.
  19. 19th January 2023A meal deal has 3 mains, 9 sides and 3 drinks. How many different meals are possible?
  20. 20th January 2023A line has equation y = 5x + 6. Work out the gradient of any line perpendicular to it.
  21. 21st January 2023y is directly proportional to x^2. When x = 5, y = 75. Work out y when x = 2.
  22. 22nd January 2023ABCD is a cyclic quadrilateral. Angle ABC is 63°. Work out angle ADC.
  23. 23rd January 202315 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  24. 24th January 202350 voles are marked and released. Later 30 are caught, of which 6 are marked. Estimate the population.
  25. 25th January 2023A mass is 28 kg, correct to the nearest whole number. Write down the lower bound.
  26. 26th January 2023For the curve y = 10/x, work out y when x = -5, and write down the equation of its vertical asymptote.
  27. 27th January 2023y is directly proportional to x. When x = 5, y = 55. Work out y when x = 6.
  28. 28th January 2023A, B and C are points on a circle with centre O. Angle AOC is 114°. Work out angle ABC, where B is on the major arc.
  29. 29th January 20235 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  30. 30th January 2023A cumulative frequency graph is drawn for 140 values. What cumulative frequency do you read across from to estimate the lower quartile?
  31. 31st January 2023Write 8^-2 as a fraction.

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