Daily Practice · Higher
June 2005 - Higher 5-a-day
Every Higher sheet published in June 2005, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' June 2005 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2005Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 296 cm^3. Work out the volume of the smaller.
- 2nd June 200511 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 3rd June 2005A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 4th June 2005A bill is £168 including VAT at 20%. Work out the amount before VAT.
- 5th June 2005Work out the equation of the line parallel to y = 4x - 5 that passes through (5, 10).
- 6th June 2005A price rises by 25% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 7th June 2005A right-angled triangle has a hypotenuse of 10 cm and one shorter side of 8 cm. Work out the other shorter side.
- 8th June 20051 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 9th June 2005A histogram class is 5 units wide and contains 20 values. Work out the frequency density.
- 10th June 2005A code is 3 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 11th June 2005A line has equation y = -4x + 3. Work out the gradient of any line perpendicular to it.
- 12th June 2005y is inversely proportional to x. When x = 2, y = 50. Work out y when x = 10.
- 13th June 2005ABCD is a cyclic quadrilateral. Angle ABC is 112°. Work out angle ADC.
- 14th June 200523 students study Spanish and 10 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 15th June 2005Four classes in order have frequencies 3, 3, 7, 12. Write down the cumulative frequency at the end of the third class.
- 16th June 2005Work out (18 x 10^7) / (3 x 10^4). Give your answer in standard form.
- 17th June 2005For the curve y = 4/x, work out y when x = 2, and write down the equation of its vertical asymptote.
- 18th June 2005y is directly proportional to x^2. When x = 6, y = 180. Work out y when x = 3.
- 19th June 2005A, B and C are points on a circle with centre O. Angle AOC is 144°. Work out angle ABC, where B is on the major arc.
- 20th June 20053 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 21st June 200510 beetles are marked and released. Later 80 are caught, of which 8 are marked. Estimate the population.
- 22nd June 2005Write the recurring decimal 0.222... as a fraction in its simplest form.
- 23rd June 2005Expand and simplify (x + 5)(x - 4)(x + 4).
- 24th June 2005y is directly proportional to x. When x = 3, y = 36. Work out y when x = 11.
- 25th June 2005A cone has base radius 4 cm and vertical height 21 cm. Work out its volume, leaving your answer in terms of pi.
- 26th June 200520 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 27th June 2005A cumulative frequency graph is drawn for 76 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 28th June 2005Work out 216^(2/3).
- 29th June 2005Make x the subject of y = 9x^2 - 2.
- 30th June 2005A town's population is 20000 and grows by 6% each year. Work out the population after 3 years, to the nearest whole number.