Daily Practice · Higher
January 2023 - Higher 5-a-day
Every Higher sheet published in January 2023, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2023Write the recurring decimal 0.444... as a fraction in its simplest form.
- 2nd January 2023A region is defined by y < 5x - 3. Should the boundary line be solid or dashed, and why?
- 3rd January 2023x : y = 5 : 7. Write y in terms of x.
- 4th January 2023The point (4, 2) is enlarged by scale factor -3 about the centre (-3, -4). Write down the coordinates of the image.
- 5th January 20238 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 6th January 2023A capture-recapture estimate is made of the newt population of a stream. State one assumption the method relies on.
- 7th January 2023Work out 36^(3/2).
- 8th January 2023Factorise x^2 - 3x - 28.
- 9th January 2023A price rises by 10% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 10th January 2023Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 513 cm^3. Work out the volume of the smaller.
- 11th January 202325 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 12th January 2023A histogram class is 10 units wide and contains 5 values. Work out the frequency density.
- 13th January 2023Write sqrt(98) in the form a sqrt(b), where b is as small as possible.
- 14th January 2023Work out the equation of the line parallel to y = 4x + 3 that passes through (6, 14).
- 15th January 2023y is inversely proportional to x. When x = 7, y = 30. Work out y when x = 6.
- 16th January 2023A right-angled triangle has a hypotenuse of 20 cm and one shorter side of 16 cm. Work out the other shorter side.
- 17th January 20234 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 18th January 2023Four classes in order have frequencies 9, 11, 6, 4. Write down the cumulative frequency at the end of the third class.
- 19th January 2023A meal deal has 3 mains, 9 sides and 3 drinks. How many different meals are possible?
- 20th January 2023A line has equation y = 5x + 6. Work out the gradient of any line perpendicular to it.
- 21st January 2023y is directly proportional to x^2. When x = 5, y = 75. Work out y when x = 2.
- 22nd January 2023ABCD is a cyclic quadrilateral. Angle ABC is 63°. Work out angle ADC.
- 23rd January 202315 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 24th January 202350 voles are marked and released. Later 30 are caught, of which 6 are marked. Estimate the population.
- 25th January 2023A mass is 28 kg, correct to the nearest whole number. Write down the lower bound.
- 26th January 2023For the curve y = 10/x, work out y when x = -5, and write down the equation of its vertical asymptote.
- 27th January 2023y is directly proportional to x. When x = 5, y = 55. Work out y when x = 6.
- 28th January 2023A, B and C are points on a circle with centre O. Angle AOC is 114°. Work out angle ABC, where B is on the major arc.
- 29th January 20235 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 30th January 2023A cumulative frequency graph is drawn for 140 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 31st January 2023Write 8^-2 as a fraction.