Daily Practice · Higher
December 1993 - Higher 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1993A cone has base radius 2 cm and vertical height 12 cm. Work out its volume, leaving your answer in terms of pi.
- 2nd December 199317 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 3rd December 1993A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 4th December 1993Work out 25^(3/2).
- 5th December 1993Make x the subject of y = 2x^2 - 2.
- 6th December 1993A price rises by 15% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 7th December 1993In triangle ABC, angle A is 58°, angle B is 38° and side a is 19 cm. Use the sine rule to work out side b, to 1 decimal place.
- 8th December 19934 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 9th December 1993A histogram class is 20 units wide and contains 80 values. Work out the frequency density.
- 10th December 1993Write sqrt(12) in the form a sqrt(b), where b is as small as possible.
- 11th December 1993Factorise x^2 - 144.
- 12th December 1993y is inversely proportional to x. When x = 8, y = 25. Work out y when x = 5.
- 13th December 1993A right-angled triangle has sides 12 cm, 16 cm and 20 cm. Work out the angle opposite the 12 cm side, to 1 decimal place.
- 14th December 199320 students study Spanish and 3 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 15th December 1993Four classes in order have frequencies 10, 3, 10, 11. Write down the cumulative frequency at the end of the third class.
- 16th December 1993A meal deal has 6 mains, 5 sides and 6 drinks. How many different meals are possible?
- 17th December 1993A region is defined by y <= -4x - 5. Should the boundary line be solid or dashed, and why?
- 18th December 1993y is directly proportional to x^2. When x = 6, y = 324. Work out y when x = 4.
- 19th December 1993The point (0, -2) is enlarged by scale factor -2 about the centre (-3, 1). Write down the coordinates of the image.
- 20th December 19933 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 21st December 199335 beetles are marked and released. Later 48 are caught, of which 8 are marked. Estimate the population.
- 22nd December 1993A mass is 67 kg, correct to the nearest whole number. Write down the upper bound.
- 23rd December 1993Factorise x^2 - x - 56.
- 24th December 1993y is directly proportional to x. When x = 9, y = 45. Work out y when x = 6.
- 25th December 1993Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 54 cm^3. Work out the volume of the smaller.
- 26th December 199324 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 27th December 1993A cumulative frequency graph is drawn for 232 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 28th December 1993Write 7^-2 as a fraction.
- 29th December 1993Work out the equation of the line parallel to y = -2x + 5 that passes through (4, 4).
- 30th December 1993A town's population is 28000 and grows by 5% each year. Work out the population after 2 years, to the nearest whole number.
- 31st December 1993A right-angled triangle has a hypotenuse of 25 cm and one shorter side of 24 cm. Work out the other shorter side.