Daily Practice · Higher

January 2020 - Higher 5-a-day

Every Higher sheet published in January 2020, with answers. Grades 6-7 - Higher-tier method and manipulation.

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January 2020

31 sheets · 155 questions · Grades 6-7

Printing for a group?

The batch download puts all 5 tiers' January 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 2020

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 2020A block has volume 55 cm^3 and density 4 g/cm^3. Work out its mass.
  2. 2nd January 2020Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 304 cm^3. Work out the volume of the smaller.
  3. 3rd January 202013 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  4. 4th January 2020A box plot has minimum 12, lower quartile 18, median 21, upper quartile 23 and maximum 30. Work out the interquartile range.
  5. 5th January 2020Write 9^-3 as a fraction.
  6. 6th January 2020Work out the equation of the line parallel to y = 5x + 6 that passes through (2, 11).
  7. 7th January 2020x : y = 5 : 8. Write y in terms of x.
  8. 8th January 2020A right-angled triangle has a hypotenuse of 25 cm and one shorter side of 24 cm. Work out the other shorter side.
  9. 9th January 20203 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  10. 10th January 2020A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
  11. 11th January 2020Work out (9 x 10^3) x (3 x 10^5). Give your answer in standard form.
  12. 12th January 2020A line has equation y = 4x + 8. Work out the gradient of any line perpendicular to it.
  13. 13th January 2020A price rises by 15% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
  14. 14th January 2020ABCD is a cyclic quadrilateral. Angle ABC is 57°. Work out angle ADC.
  15. 15th January 202022 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  16. 16th January 2020A histogram class is 10 units wide and contains 40 values. Work out the frequency density.
  17. 17th January 2020Write the recurring decimal 0.8787... as a fraction in its simplest form.
  18. 18th January 2020For the curve y = -36/x, work out y when x = -4, and write down the equation of its vertical asymptote.
  19. 19th January 2020y is inversely proportional to x. When x = 3, y = 30. Work out y when x = 10.
  20. 20th January 2020A, B and C are points on a circle with centre O. Angle AOC is 80°. Work out angle ABC, where B is on the major arc.
  21. 21st January 20202 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  22. 22nd January 2020Four classes in order have frequencies 11, 4, 8, 6. Write down the cumulative frequency at the end of the third class.
  23. 23rd January 2020A bill is £912 including VAT at 20%. Work out the amount before VAT.
  24. 24th January 2020Expand and simplify (x + 5)(x + 2)(x - 3).
  25. 25th January 2020y is directly proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
  26. 26th January 2020A cone has base radius 3 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
  27. 27th January 202023 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  28. 28th January 202015 beetles are marked and released. Later 96 are caught, of which 8 are marked. Estimate the population.
  29. 29th January 2020A code is 3 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
  30. 30th January 2020Make x the subject of y = 8x^2 - 4.
  31. 31st January 2020y is directly proportional to x. When x = 6, y = 18. Work out y when x = 8.

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