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.
Printing for a group?
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.
- 1st January 2021y is directly proportional to x. When x = 6, y = 42. Work out y when x = 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.
- 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.
- 4th January 2021A cumulative frequency graph is drawn for 152 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 5th January 2021Write the recurring decimal 0.666... as a fraction in its simplest form.
- 6th January 2021Factorise x^2 - 9.
- 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.
- 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.
- 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.
- 10th January 2021A box plot has a minimum of 16 and a maximum of 26. Work out the range.
- 11th January 2021Work out 8^(2/3).
- 12th January 2021A region is defined by y <= -2x + 2. Should the boundary line be solid or dashed, and why?
- 13th January 2021A block has volume 110 cm^3 and density 4 g/cm^3. Work out its mass.
- 14th January 2021The point (3, 2) is enlarged by scale factor -2 about the centre (3, -2). Write down the coordinates of the image.
- 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.
- 16th January 2021A box plot has minimum 6, lower quartile 16, median 19, upper quartile 28 and maximum 31. Work out the interquartile range.
- 17th January 2021Write sqrt(20) in the form a sqrt(b), where b is as small as possible.
- 18th January 2021Factorise x^2 - x - 72.
- 19th January 2021x : y = 5 : 6. Write y in terms of x.
- 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.
- 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.
- 22nd January 2021A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 23rd January 2021A meal deal has 8 mains, 6 sides and 2 drinks. How many different meals are possible?
- 24th January 2021Work out the equation of the line parallel to y = -x - 7 that passes through (6, -2).
- 25th January 2021A price rises by 20% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 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.
- 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.
- 28th January 2021A histogram class is 2 units wide and contains 1 values. Work out the frequency density.
- 29th January 2021A mass is 430 kg, correct to the nearest 10. Write down the lower bound.
- 30th January 2021A line has equation y = 5x + 6. Work out the gradient of any line perpendicular to it.
- 31st January 2021y is inversely proportional to x. When x = 8, y = 12. Work out y when x = 2.