Daily Practice · Higher Plus
August 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2005A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd August 2005A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 3rd August 2005A rectangle is 19 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th August 2005Solve x^2 + 4x - 5 < 0.
- 5th August 2005y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 64.
- 6th August 2005A cuboid measures 14 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th August 2005A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th August 2005On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th August 2005Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 10th August 2005Write x^2 + 6x - 11 in the form (x + a)^2 + b.
- 11th August 2005A train slows steadily from 28 m/s to rest in 5 seconds. Work out its deceleration.
- 12th August 2005The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 13th August 2005A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 14th August 2005A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 15th August 2005A block has mass 400 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th August 2005Work out the coordinates of the turning point of y = x^2 - 2x + 6.
- 17th August 2005y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 18th August 2005In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 19th August 2005The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
- 20th August 2005On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st August 2005x = 90 and y = 71, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd August 2005Simplify (x^2 - 3x + 2)/(x - 2).
- 23rd August 2005y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 24th August 2005In a vector proof you find that vector PQ = 4a - 5b and vector RS = 20a - 25b. What does this show about PQ and RS?
- 25th August 2005A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 26th August 2005A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 27th August 2005A car covers 200 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th August 2005In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 29th August 2005y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 16.
- 30th August 2005A cuboid measures 14 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st August 2005A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?