Daily Practice · Higher
January 2006 - Higher 5-a-day
Every Higher sheet published in January 2006, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2006Expand and simplify (x + 3)(x - 2)(x + 2).
- 2nd January 2006A price rises by 15% and then falls by 20%. Work out the overall percentage change, to 2 decimal places.
- 3rd January 2006A cone has base radius 2 cm and vertical height 9 cm. Work out its volume, leaving your answer in terms of pi.
- 4th January 200620 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 5th January 2006A histogram class is 10 units wide and contains 40 values. Work out the frequency density.
- 6th January 2006Write the recurring decimal 0.222... as a fraction in its simplest form.
- 7th January 2006Make x the subject of y = 4x^2 - 2.
- 8th January 2006y is inversely proportional to x. When x = 8, y = 24. Work out y when x = 4.
- 9th January 2006In triangle ABC, angle A is 57°, angle B is 76° and side a is 14 cm. Use the sine rule to work out side b, to 1 decimal place.
- 10th January 20065 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 11th January 2006Four classes in order have frequencies 7, 12, 6, 10. Write down the cumulative frequency at the end of the third class.
- 12th January 2006Work out 25^(3/2).
- 13th January 2006Factorise x^2 - 100.
- 14th January 2006y is directly proportional to x^2. When x = 4, y = 32. Work out y when x = 8.
- 15th January 2006A right-angled triangle has sides 9 cm, 12 cm and 15 cm. Work out the angle opposite the 9 cm side, to 1 decimal place.
- 16th January 200629 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 January 200620 fish are marked and released. Later 48 are caught, of which 6 are marked. Estimate the population.
- 18th January 2006Write sqrt(32) in the form a sqrt(b), where b is as small as possible.
- 19th January 2006A region is defined by y < -2x - 4. Should the boundary line be solid or dashed, and why?
- 20th January 2006y is directly proportional to x. When x = 9, y = 108. Work out y when x = 8.
- 21st January 2006The point (2, -3) is enlarged by scale factor -3 about the centre (0, -4). Write down the coordinates of the image.
- 22nd January 20063 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 23rd January 2006A cumulative frequency graph is drawn for 52 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 24th January 2006A meal deal has 5 mains, 7 sides and 5 drinks. How many different meals are possible?
- 25th January 2006Factorise x^2 + x - 30.
- 26th January 2006A town's population is 17000 and grows by 4% each year. Work out the population after 5 years, to the nearest whole number.
- 27th January 2006Two similar solids have lengths in the ratio 1 : 4. The larger has a volume of 384 cm^3. Work out the volume of the smaller.
- 28th January 200612 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 29th January 2006A box plot has a minimum of 15 and a maximum of 56. Work out the range.
- 30th January 2006A mass is 120 kg, correct to the nearest 10. Write down the lower bound.
- 31st January 2006Work out the equation of the line parallel to y = x - 8 that passes through (1, -6).