Daily Practice · Higher Plus
October 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2011A car covers 100 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd October 2011Write x^2 - 6x - 12 in the form (x + a)^2 + b.
- 3rd October 2011y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 4th October 2011A cuboid measures 6 cm by 5 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th October 2011A bag holds 5 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th October 2011A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 7th October 2011Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 8th October 2011Work out the coordinates of the turning point of y = x^2 + 14x - 2.
- 9th October 2011y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 64.
- 10th October 2011The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 11th October 2011A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
- 12th October 2011On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th October 2011Simplify sqrt(50) + sqrt(50), giving your answer in the form a sqrt(b).
- 14th October 2011Simplify (x^2 + 4x - 32)/(x + 8).
- 15th October 2011A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
- 16th October 2011In 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.
- 17th October 2011The probability of winning a game is 2/5. A player expects 14 wins. How many games did they play?
- 18th October 2011A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 19th October 2011A rectangle is 29 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th October 2011In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 21st October 2011y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 22nd October 2011In a vector proof you find that vector PQ = a + 2b and vector RS = 2a + 4b. What does this show about PQ and RS?
- 23rd October 2011A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 24th October 2011On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th October 2011Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 26th October 2011Make x the subject of 4x + 3 = y(x + 3).
- 27th October 2011y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 28th October 2011A cuboid measures 10 cm by 8 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th October 2011A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th October 2011A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 31st October 2011A block has mass 560 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.