Daily Practice · Higher Plus
August 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2011On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 2nd August 2011Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 3rd August 2011f(x) = 5x - 9. Work out the inverse function f^-1(x).
- 4th August 2011A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 5th August 2011A cuboid measures 12 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th August 2011A bag holds 4 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th August 2011A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 8th August 2011A block has mass 360 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th August 2011Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 10th August 2011y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 11th August 2011The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 12th August 2011A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 13th August 2011On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th August 2011x = 140 and y = 125, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th August 2011Use the iteration x(n+1) = cube root of (9x(n) + 3) with x(0) = 4. Work out x(1) to 3 decimal places.
- 16th August 2011y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 17th August 2011In 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.
- 18th August 2011The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 19th August 2011A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 20th August 2011A car covers 700 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st August 2011Work out the nth term of the quadratic sequence 3, 16, 35, 60, ...
- 22nd August 2011y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 49.
- 23rd August 2011In a vector proof you find that vector PQ = 2a + 2b and vector RS = 4a + 4b. What does this show about PQ and RS?
- 24th August 2011A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 25th August 2011On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th August 2011Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 27th August 2011The point (-2, 4) lies on y = f(x). Write down its image on y = f(-x).
- 28th August 2011A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 29th August 2011A cuboid measures 10 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th August 2011A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st August 2011A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?