Daily Practice · Higher Plus
October 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2009A train slows steadily from 13 m/s to rest in 4 seconds. Work out its deceleration.
- 2nd October 2009In a vector proof you find that vector PQ = 2a - 2b and vector RS = 4a - 4b. What does this show about PQ and RS?
- 3rd October 2009A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 4th October 2009A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 5th October 2009A block has mass 440 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th October 2009A quadratic sequence starts 6, 11, 20, 33. Work out the second difference, and the coefficient of n^2.
- 7th October 2009y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 8th October 2009A cuboid measures 7 cm by 10 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th October 2009A 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?
- 10th October 2009On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th October 2009x = 83 and y = 51, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th October 2009Solve x^2 - 11x + 24 > 0.
- 13th October 2009y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 14th October 2009A cuboid measures 11 cm by 4 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th October 2009A bag holds 4 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th October 2009A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 17th October 2009A car covers 750 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.
- 18th October 2009Write x^2 - 8x - 9 in the form (x + a)^2 + b.
- 19th October 2009y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 64.
- 20th October 2009The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 21st October 2009A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 22nd October 2009On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 23rd October 2009Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 24th October 2009Work out the coordinates of the turning point of y = x^2 - 12x - 3.
- 25th October 2009A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 26th October 2009In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 27th October 2009The probability of winning a game is 3/4. A player expects 18 wins. How many games did they play?
- 28th October 2009A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 29th October 2009Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 30th October 2009Simplify (x^2 + 3x - 18)/(x + 6).
- 31st October 2009y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.