Daily Practice · Higher

August 2022 - Higher 5-a-day

Every Higher sheet published in August 2022, with answers. Grades 6-7 - Higher-tier method and manipulation.

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August 2022

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' August 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in August 2022

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st August 2022In triangle ABC, angle A is 74°, angle B is 60° and side a is 9 cm. Use the sine rule to work out side b, to 1 decimal place.
  2. 2nd August 20221 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  3. 3rd August 2022Four classes in order have frequencies 5, 4, 12, 11. Write down the cumulative frequency at the end of the third class.
  4. 4th August 2022A bill is £600 including VAT at 20%. Work out the amount before VAT.
  5. 5th August 2022Factorise x^2 - 9.
  6. 6th August 2022y is directly proportional to x^2. When x = 5, y = 50. Work out y when x = 6.
  7. 7th August 2022A 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.
  8. 8th August 202229 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  9. 9th August 202215 newts are marked and released. Later 18 are caught, of which 6 are marked. Estimate the population.
  10. 10th August 2022A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
  11. 11th August 2022A region is defined by y <= x + 3. Should the boundary line be solid or dashed, and why?
  12. 12th August 2022y is directly proportional to x. When x = 2, y = 14. Work out y when x = 13.
  13. 13th August 2022The point (2, 3) is enlarged by scale factor -3 about the centre (-3, -4). Write down the coordinates of the image.
  14. 14th August 20222 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  15. 15th August 2022A cumulative frequency graph is drawn for 72 values. What cumulative frequency do you read across from to estimate the lower quartile?
  16. 16th August 2022Work out (54 x 10^10) / (6 x 10^2). Give your answer in standard form.
  17. 17th August 2022Factorise x^2 - x - 56.
  18. 18th August 2022A town's population is 29000 and grows by 3% each year. Work out the population after 4 years, to the nearest whole number.
  19. 19th August 2022Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 72 cm^3. Work out the volume of the smaller.
  20. 20th August 202213 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  21. 21st August 2022A box plot has a minimum of 20 and a maximum of 58. Work out the range.
  22. 22nd August 2022Write the recurring decimal 0.444... as a fraction in its simplest form.
  23. 23rd August 2022Work out the equation of the line parallel to y = -x + 4 that passes through (4, -12).
  24. 24th August 2022A block has volume 85 cm^3 and density 2.5 g/cm^3. Work out its mass.
  25. 25th August 2022A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 24 cm. Work out the other shorter side.
  26. 26th August 20221 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  27. 27th August 2022A box plot has minimum 11, lower quartile 15, median 21, upper quartile 27 and maximum 32. Work out the interquartile range.
  28. 28th August 2022Work out 36^(3/2).
  29. 29th August 2022A line has equation y = -2x + 5. Work out the gradient of any line perpendicular to it.
  30. 30th August 2022x : y = 4 : 9. Write y in terms of x.
  31. 31st August 2022ABCD is a cyclic quadrilateral. Angle ABC is 123°. Work out angle ADC.

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