Daily Practice · Higher Plus
August 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2012 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2012A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 2nd August 2012Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
- 3rd August 2012Write x^2 - 6x - 6 in the form (x + a)^2 + b.
- 4th August 2012y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 5th August 2012The 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.
- 6th August 2012A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 7th August 2012On 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?
- 8th August 2012A rectangle is 29 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th August 2012Work out the coordinates of the turning point of y = x^2 - 6x - 14.
- 10th August 2012y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 11th August 2012In 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.
- 12th August 2012The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
- 13th August 2012A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 14th August 2012Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 15th August 2012Simplify (x^2 - 2x - 48)/(x - 8).
- 16th August 2012y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 25.
- 17th August 2012In a vector proof you find that vector PQ = 4a + 5b and vector RS = 16a + 20b. What does this show about PQ and RS?
- 18th August 2012A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 19th August 2012On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th August 2012A block has mass 300 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st August 2012In an algebraic proof, how would you write an even number in terms of an integer n?
- 22nd August 2012A train slows steadily from 16 m/s to rest in 10 seconds. Work out its deceleration.
- 23rd August 2012A cuboid measures 9 cm by 7 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th August 2012A 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?
- 25th August 2012A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 26th August 2012x = 175 and y = 137, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th August 2012Make x the subject of 7x + 7 = y(x + 7).
- 28th August 2012y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 29th August 2012A cuboid measures 9 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th August 2012A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st August 2012On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?