Daily Practice · Higher

January 2021 - Higher 5-a-day

Every Higher sheet published in January 2021, with answers. Grades 6-7 - Higher-tier method and manipulation.

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January 2021

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' January 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 2021

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 2021y is directly proportional to x. When x = 6, y = 42. Work out y when x = 2.
  2. 2nd January 2021In triangle ABC, angle A is 55°, angle B is 48° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
  3. 3rd January 20211 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  4. 4th January 2021A cumulative frequency graph is drawn for 152 values. What cumulative frequency do you read across from to estimate the lower quartile?
  5. 5th January 2021Write the recurring decimal 0.666... as a fraction in its simplest form.
  6. 6th January 2021Factorise x^2 - 9.
  7. 7th January 2021A town's population is 19000 and grows by 3% each year. Work out the population after 2 years, to the nearest whole number.
  8. 8th January 2021A 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.
  9. 9th January 202124 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  10. 10th January 2021A box plot has a minimum of 16 and a maximum of 26. Work out the range.
  11. 11th January 2021Work out 8^(2/3).
  12. 12th January 2021A region is defined by y <= -2x + 2. Should the boundary line be solid or dashed, and why?
  13. 13th January 2021A block has volume 110 cm^3 and density 4 g/cm^3. Work out its mass.
  14. 14th January 2021The point (3, 2) is enlarged by scale factor -2 about the centre (3, -2). Write down the coordinates of the image.
  15. 15th January 20214 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  16. 16th January 2021A box plot has minimum 6, lower quartile 16, median 19, upper quartile 28 and maximum 31. Work out the interquartile range.
  17. 17th January 2021Write sqrt(20) in the form a sqrt(b), where b is as small as possible.
  18. 18th January 2021Factorise x^2 - x - 72.
  19. 19th January 2021x : y = 5 : 6. Write y in terms of x.
  20. 20th January 2021Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 896 cm^3. Work out the volume of the smaller.
  21. 21st January 202112 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  22. 22nd January 2021A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
  23. 23rd January 2021A meal deal has 8 mains, 6 sides and 2 drinks. How many different meals are possible?
  24. 24th January 2021Work out the equation of the line parallel to y = -x - 7 that passes through (6, -2).
  25. 25th January 2021A price rises by 20% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
  26. 26th January 2021A right-angled triangle has a hypotenuse of 41 cm and one shorter side of 40 cm. Work out the other shorter side.
  27. 27th January 20212 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  28. 28th January 2021A histogram class is 2 units wide and contains 1 values. Work out the frequency density.
  29. 29th January 2021A mass is 430 kg, correct to the nearest 10. Write down the lower bound.
  30. 30th January 2021A line has equation y = 5x + 6. Work out the gradient of any line perpendicular to it.
  31. 31st January 2021y is inversely proportional to x. When x = 8, y = 12. Work out y when x = 2.

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