Daily Practice · Higher
December 2006 - Higher 5-a-day
Every Higher sheet published in December 2006, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' December 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2006A capture-recapture estimate is made of the snail population of a hedgerow. State one assumption the method relies on.
- 2nd December 2006Write the recurring decimal 0.444... as a fraction in its simplest form.
- 3rd December 2006Expand and simplify (x + 1)(x - 2)(x + 5).
- 4th December 2006A price rises by 15% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 5th December 2006A cone has base radius 6 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
- 6th December 200616 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 7th December 2006A histogram class is 10 units wide and contains 20 values. Work out the frequency density.
- 8th December 2006Work out 100^(3/2).
- 9th December 2006Make x the subject of y = 8x^2 - 9.
- 10th December 2006y is inversely proportional to x. When x = 8, y = 8. Work out y when x = 2.
- 11th December 2006In triangle ABC, angle A is 51°, angle B is 63° and side a is 6 cm. Use the sine rule to work out side b, to 1 decimal place.
- 12th December 20067 of 10 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 13th December 2006Four classes in order have frequencies 5, 11, 3, 7. Write down the cumulative frequency at the end of the third class.
- 14th December 2006Write sqrt(18) in the form a sqrt(b), where b is as small as possible.
- 15th December 2006Factorise x^2 - 4.
- 16th December 2006y is directly proportional to x^2. When x = 4, y = 128. Work out y when x = 5.
- 17th December 2006A right-angled triangle has sides 7 cm, 24 cm and 25 cm. Work out the angle opposite the 7 cm side, to 1 decimal place.
- 18th December 200621 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 19th December 200620 voles are marked and released. Later 77 are caught, of which 7 are marked. Estimate the population.
- 20th December 2006A meal deal has 9 mains, 9 sides and 5 drinks. How many different meals are possible?
- 21st December 2006A region is defined by y < -5x - 4. Should the boundary line be solid or dashed, and why?
- 22nd December 2006y is directly proportional to x. When x = 6, y = 66. Work out y when x = 4.
- 23rd December 2006The point (-5, 6) is enlarged by scale factor -3 about the centre (4, -4). Write down the coordinates of the image.
- 24th December 20062 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 25th December 2006A cumulative frequency graph is drawn for 176 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 26th December 2006A mass is 14.5 kg, correct to 1 decimal place. Write down the lower bound.
- 27th December 2006Factorise x^2 - 2x - 15.
- 28th December 2006A town's population is 31000 and grows by 8% each year. Work out the population after 2 years, to the nearest whole number.
- 29th December 2006Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 32 cm^3. Work out the volume of the smaller.
- 30th December 200620 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 31st December 2006A box plot has a minimum of 3 and a maximum of 50. Work out the range.