Daily Practice · Higher
August 1977 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1977A line has equation y = -3x + 2. Work out the gradient of any line perpendicular to it.
- 2nd August 1977x : y = 3 : 5. Write y in terms of x.
- 3rd August 1977ABCD is a cyclic quadrilateral. Angle ABC is 110°. Work out angle ADC.
- 4th August 197726 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th August 1977A capture-recapture estimate is made of the beetle population of a woodland. State one assumption the method relies on.
- 6th August 1977A bill is £576 including VAT at 20%. Work out the amount before VAT.
- 7th August 1977For the curve y = 7/x, work out y when x = -1, and write down the equation of its vertical asymptote.
- 8th August 1977A price rises by 20% and then falls by 15%. Work out the overall percentage change, to 2 decimal places.
- 9th August 1977A, 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.
- 10th August 19776 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th August 1977A histogram class is 20 units wide and contains 30 values. Work out the frequency density.
- 12th August 1977A code is 2 letters (A to Z) followed by 2 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 13th August 1977Expand and simplify (x - 3)(x + 2)(x - 1).
- 14th August 1977y is inversely proportional to x. When x = 7, y = 15. Work out y when x = 5.
- 15th August 1977A cone has base radius 2 cm and vertical height 18 cm. Work out its volume, leaving your answer in terms of pi.
- 16th August 197728 students study Spanish and 9 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 17th August 1977Four classes in order have frequencies 3, 3, 7, 7. Write down the cumulative frequency at the end of the third class.
- 18th August 1977Work out (12 x 10^6) / (4 x 10^2). Give your answer in standard form.
- 19th August 1977Make x the subject of y = 2x^2 - 10.
- 20th August 1977y is directly proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 21st August 1977In triangle ABC, angle A is 43°, angle B is 58° and side a is 17 cm. Use the sine rule to work out side b, to 1 decimal place.
- 22nd August 19771 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd August 197735 voles are marked and released. Later 48 are caught, of which 8 are marked. Estimate the population.
- 24th August 1977Write the recurring decimal 0.444... as a fraction in its simplest form.
- 25th August 1977Factorise x^2 - 16.
- 26th August 1977y is directly proportional to x. When x = 2, y = 8. Work out y when x = 8.
- 27th August 1977A right-angled triangle has sides 9 cm, 40 cm and 41 cm. Work out the angle opposite the 9 cm side, to 1 decimal place.
- 28th August 197722 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th August 1977A cumulative frequency graph is drawn for 44 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 30th August 1977Work out 216^(2/3).
- 31st August 1977A region is defined by y <= 3x - 1. Should the boundary line be solid or dashed, and why?