Daily Practice · Higher
July 2005 - Higher 5-a-day
Every Higher sheet published in July 2005, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' July 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2005In triangle ABC, angle A is 42°, angle B is 92° and side a is 13 cm. Use the sine rule to work out side b, to 1 decimal place.
- 2nd July 20054 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd July 2005A box plot has a minimum of 16 and a maximum of 41. Work out the range.
- 4th July 2005Write sqrt(50) in the form a sqrt(b), where b is as small as possible.
- 5th July 2005Factorise x^2 - 121.
- 6th July 2005A block has volume 180 cm^3 and density 11 g/cm^3. Work out its mass.
- 7th July 2005A right-angled triangle has sides 10 cm, 24 cm and 26 cm. Work out the angle opposite the 10 cm side, to 1 decimal place.
- 8th July 200524 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th July 2005A box plot has minimum 2, lower quartile 7, median 9, upper quartile 17 and maximum 21. Work out the interquartile range.
- 10th July 2005A meal deal has 9 mains, 7 sides and 2 drinks. How many different meals are possible?
- 11th July 2005A region is defined by y <= 4x - 6. Should the boundary line be solid or dashed, and why?
- 12th July 2005x : y = 3 : 5. Write y in terms of x.
- 13th July 2005The point (-3, -5) is enlarged by scale factor -2 about the centre (0, -1). Write down the coordinates of the image.
- 14th July 20053 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th July 2005A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 16th July 2005A mass is 48 kg, correct to the nearest whole number. Write down the upper bound.
- 17th July 2005Factorise x^2 - 5x - 14.
- 18th July 2005A price rises by 10% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 19th July 2005Two similar solids have lengths in the ratio 1 : 2. The larger has a volume of 64 cm^3. Work out the volume of the smaller.
- 20th July 200516 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st July 2005A histogram class is 20 units wide and contains 40 values. Work out the frequency density.
- 22nd July 2005Write 8^-2 as a fraction.
- 23rd July 2005Work out the equation of the line parallel to y = -x + 1 that passes through (3, 5).
- 24th July 2005y is inversely proportional to x. When x = 5, y = 72. Work out y when x = 12.
- 25th July 2005A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 24 cm. Work out the other shorter side.
- 26th July 20053 of 8 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th July 2005Four classes in order have frequencies 10, 4, 6, 6. Write down the cumulative frequency at the end of the third class.
- 28th July 2005Work out (3 x 10^3) x (8 x 10^-4). Give your answer in standard form.
- 29th July 2005A line has equation y = 2x + 3. Work out the gradient of any line perpendicular to it.
- 30th July 2005y is directly proportional to x^2. When x = 6, y = 108. Work out y when x = 3.
- 31st July 2005ABCD is a cyclic quadrilateral. Angle ABC is 115°. Work out angle ADC.