Daily Practice · Higher Plus
October 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2008 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2008In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 2nd October 2008The probability of winning a game is 3/5. A player expects 90 wins. How many games did they play?
- 3rd October 2008On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th October 2008A car covers 260 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th October 2008Write 3/(x - 4) + 4/(x + 1) as a single fraction.
- 6th October 2008A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 7th October 2008In a vector proof you find that vector PQ = a + 5b and vector RS = 2a + 10b. What does this show about PQ and RS?
- 8th October 2008A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 9th October 2008A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 10th October 2008Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.
- 11th October 2008Solve 9x^2 - 16 = 0.
- 12th October 2008y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 13th October 2008A cuboid measures 12 cm by 10 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th October 2008A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th October 2008On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th October 2008Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
- 17th October 2008f(x) = 8x + 3. Work out the inverse function f^-1(x).
- 18th October 2008y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 19th October 2008A cuboid measures 10 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th October 2008A bag holds 3 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st October 2008A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 22nd October 2008A rectangle is 9 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd October 2008Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 24th October 2008y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 49.
- 25th October 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 October 2008A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 27th October 2008On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th October 2008Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).
- 29th October 2008Use the iteration x(n+1) = cube root of (4x(n) + 7) with x(0) = 5. Work out x(1) to 3 decimal places.
- 30th October 2008A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 31st October 2008In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.