Daily Practice · Higher Plus
September 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2008 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2008In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 2nd September 2008The probability of winning a game is 1/4. A player expects 3 wins. How many games did they play?
- 3rd September 2008A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 4th September 2008Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).
- 5th September 2008Write x^2 + 10x - 10 in the form (x + a)^2 + b.
- 6th September 2008y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 49.
- 7th September 2008In a vector proof you find that vector PQ = 6a - 4b and vector RS = 18a - 12b. What does this show about PQ and RS?
- 8th September 2008A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 9th September 2008On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th September 2008A rectangle is 17 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th September 2008Work out the coordinates of the turning point of y = x^2 + 14x + 7.
- 12th September 2008A train slows steadily from 25 m/s to rest in 4 seconds. Work out its deceleration.
- 13th September 2008A cuboid measures 10 cm by 13 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th September 2008A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th September 2008A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 16th September 2008Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 17th September 2008Simplify (x^2 - 7x - 8)/(x + 1).
- 18th September 2008y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 19th September 2008A cuboid measures 8 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th September 2008A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st September 2008On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd September 2008A block has mass 650 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd September 2008In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 24th September 2008y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 25th September 2008The 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.
- 26th September 2008A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 27th September 2008A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 28th September 2008x = 31 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th September 2008Make x the subject of 3x + 6 = y(x + 6).
- 30th September 2008y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 25.