Daily Practice · Higher Plus
August 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2009Make x the subject of 7x + 3 = y(x + 3).
- 2nd August 2009y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 3rd August 2009In a vector proof you find that vector PQ = 3a + 2b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 4th August 2009A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 5th August 2009A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 6th August 2009Simplify sqrt(32) + sqrt(32), giving your answer in the form a sqrt(b).
- 7th August 2009Write 6/(x + 6) + 6/(x + 4) as a single fraction.
- 8th August 2009y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 49.
- 9th August 2009A cuboid measures 5 cm by 9 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th August 2009A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th August 2009On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th August 2009A rectangle is 6 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th August 2009Solve 12x^2 - 11x + 2 = 0.
- 14th August 2009A train slows steadily from 24 m/s to rest in 8 seconds. Work out its deceleration.
- 15th August 2009A cuboid measures 8 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th August 2009A bag holds 3 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th August 2009A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 18th August 2009Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).
- 19th August 2009f(x) = 8x + 8. Work out the inverse function f^-1(x).
- 20th August 2009y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 21st August 2009The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 22nd August 2009A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 23rd August 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?
- 24th August 2009A block has mass 610 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th August 2009Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.
- 26th August 2009y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 27th August 2009In 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.
- 28th August 2009The probability of winning a game is 1/4. A player expects 2 wins. How many games did they play?
- 29th August 2009A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 30th August 2009x = 150 and y = 67, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st August 2009Use the iteration x(n+1) = cube root of (11x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.