Daily Practice · Higher
June 1997 - Higher 5-a-day
Every Higher sheet published in June 1997, with answers. Grades 6-7 - Higher-tier method and manipulation.
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The batch download puts all 5 tiers' June 1997 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1997A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the other shorter side.
- 2nd June 19977 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd June 199755 beetles are marked and released. Later 54 are caught, of which 6 are marked. Estimate the population.
- 4th June 1997Write 5^-2 as a fraction.
- 5th June 1997A line has equation y = 4x + 7. Work out the gradient of any line perpendicular to it.
- 6th June 1997y is directly proportional to x. When x = 3, y = 12. Work out y when x = 4.
- 7th June 1997ABCD is a cyclic quadrilateral. Angle ABC is 71°. Work out angle ADC.
- 8th June 199715 students study Spanish and 5 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th June 1997A cumulative frequency graph is drawn for 232 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 10th June 1997Work out (3 x 10^5) x (3 x 10^-6). Give your answer in standard form.
- 11th June 1997For the curve y = -28/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 12th June 1997A town's population is 20000 and grows by 6% each year. Work out the population after 4 years, to the nearest whole number.
- 13th June 1997A, B and C are points on a circle with centre O. Angle AOC is 160°. Work out angle ABC, where B is on the major arc.
- 14th June 19971 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th June 1997A box plot has a minimum of 18 and a maximum of 56. Work out the range.
- 16th June 1997Write the recurring decimal 0.9696... as a fraction in its simplest form.
- 17th June 1997Expand and simplify (x + 2)(x - 5)(x - 1).
- 18th June 1997A block has volume 160 cm^3 and density 3 g/cm^3. Work out its mass.
- 19th June 1997A cone has base radius 5 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 20th June 199716 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st June 1997A box plot has minimum 8, lower quartile 16, median 18, upper quartile 27 and maximum 36. Work out the interquartile range.
- 22nd June 1997A bill is £744 including VAT at 20%. Work out the amount before VAT.
- 23rd June 1997Make x the subject of y = 6x^2 - 2.
- 24th June 1997x : y = 3 : 8. Write y in terms of x.
- 25th June 1997In triangle ABC, angle A is 41°, angle B is 47° and side a is 16 cm. Use the sine rule to work out side b, to 1 decimal place.
- 26th June 19972 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th June 1997A capture-recapture estimate is made of the fish population of a pond. State one assumption the method relies on.
- 28th June 1997A code is 2 letters (A to Z) followed by 4 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 29th June 1997Factorise x^2 - 25.
- 30th June 1997A price rises by 10% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.