Daily Practice · Higher

August 2023 - Higher 5-a-day

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

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August 2023

31 sheets · 155 questions · Grades 6-7

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

Every sheet in August 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 August 2023x : y = 5 : 8. Write y in terms of x.
  2. 2nd August 2023ABCD is a cyclic quadrilateral. Angle ABC is 124°. Work out angle ADC.
  3. 3rd August 202314 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  4. 4th August 2023A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
  5. 5th August 2023A meal deal has 5 mains, 6 sides and 4 drinks. How many different meals are possible?
  6. 6th August 2023For the curve y = -50/x, work out y when x = -5, and write down the equation of its vertical asymptote.
  7. 7th August 2023A price rises by 25% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
  8. 8th August 2023A, B and C are points on a circle with centre O. Angle AOC is 126°. Work out angle ABC, where B is on the major arc.
  9. 9th August 20231 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  10. 10th August 2023A histogram class is 5 units wide and contains 15 values. Work out the frequency density.
  11. 11th August 2023A mass is 380 kg, correct to the nearest 10. Write down the upper bound.
  12. 12th August 2023Expand and simplify (x - 5)(x + 5)(x + 5).
  13. 13th August 2023y is inversely proportional to x. When x = 2, y = 10. Work out y when x = 10.
  14. 14th August 2023A cone has base radius 7 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
  15. 15th August 202316 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  16. 16th August 2023Four classes in order have frequencies 8, 6, 4, 10. Write down the cumulative frequency at the end of the third class.
  17. 17th August 2023Write 4^-2 as a fraction.
  18. 18th August 2023Make x the subject of y = 3x^2 - 5.
  19. 19th August 2023y is directly proportional to x^2. When x = 5, y = 125. Work out y when x = 4.
  20. 20th August 2023In triangle ABC, angle A is 44°, angle B is 31° and side a is 6 cm. Use the sine rule to work out side b, to 1 decimal place.
  21. 21st August 20233 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  22. 22nd August 202325 voles are marked and released. Later 16 are caught, of which 4 are marked. Estimate the population.
  23. 23rd August 2023Work out (9 x 10^3) x (6 x 10^-3). Give your answer in standard form.
  24. 24th August 2023Factorise x^2 - 4.
  25. 25th August 2023y is directly proportional to x. When x = 9, y = 108. Work out y when x = 11.
  26. 26th August 2023A right-angled triangle has sides 7 cm, 24 cm and 25 cm. Work out the angle opposite the 7 cm side, to 1 decimal place.
  27. 27th August 202315 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  28. 28th August 2023A cumulative frequency graph is drawn for 140 values. What cumulative frequency do you read across from to estimate the lower quartile?
  29. 29th August 2023Write the recurring decimal 0.4040... as a fraction in its simplest form.
  30. 30th August 2023A region is defined by y <= 2x + 7. Should the boundary line be solid or dashed, and why?
  31. 31st August 2023A town's population is 35000 and grows by 5% each year. Work out the population after 3 years, to the nearest whole number.

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