Daily Practice · Higher
October 2024 - Higher 5-a-day
Every Higher sheet published in October 2024, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' October 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2024A right-angled triangle has a hypotenuse of 15 cm and one shorter side of 9 cm. Work out the other shorter side.
- 2nd October 20247 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd October 2024A histogram class is 20 units wide and contains 10 values. Work out the frequency density.
- 4th October 2024A bill is £120 including VAT at 20%. Work out the amount before VAT.
- 5th October 2024A line has equation y = 2x + 8. Work out the gradient of any line perpendicular to it.
- 6th October 2024y is inversely proportional to x. When x = 7, y = 2. Work out y when x = 2.
- 7th October 2024ABCD is a cyclic quadrilateral. Angle ABC is 52°. Work out angle ADC.
- 8th October 202428 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th October 2024Four classes in order have frequencies 8, 5, 5, 7. Write down the cumulative frequency at the end of the third class.
- 10th October 2024A code is 3 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 11th October 2024For the curve y = 20/x, work out y when x = -2, and write down the equation of its vertical asymptote.
- 12th October 2024y is directly proportional to x^2. When x = 6, y = 144. Work out y when x = 5.
- 13th October 2024A, B and C are points on a circle with centre O. Angle AOC is 98°. Work out angle ABC, where B is on the major arc.
- 14th October 20244 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th October 202450 beetles are marked and released. Later 44 are caught, of which 4 are marked. Estimate the population.
- 16th October 2024Work out (10 x 10^11) / (2 x 10^3). Give your answer in standard form.
- 17th October 2024Expand and simplify (x - 4)(x + 4)(x + 5).
- 18th October 2024y is directly proportional to x. When x = 9, y = 45. Work out y when x = 3.
- 19th October 2024A cone has base radius 5 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 20th October 202419 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st October 2024A cumulative frequency graph is drawn for 144 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 22nd October 2024Write the recurring decimal 0.777... as a fraction in its simplest form.
- 23rd October 2024Make x the subject of y = 3x^2 - 4.
- 24th October 2024A town's population is 34500 and grows by 5% each year. Work out the population after 6 years, to the nearest whole number.
- 25th October 2024In triangle ABC, angle A is 79°, angle B is 64° and side a is 18 cm. Use the sine rule to work out side b, to 1 decimal place.
- 26th October 20245 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th October 2024A box plot has a minimum of 5 and a maximum of 50. Work out the range.
- 28th October 2024Work out 81^(3/2).
- 29th October 2024Factorise x^2 - 4.
- 30th October 2024A block has volume 175 cm^3 and density 11 g/cm^3. Work out its mass.
- 31st October 2024A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Work out the angle opposite the 6 cm side, to 1 decimal place.