Daily Practice · Higher Plus
September 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2011 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2011Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 2nd September 2011Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 3rd September 2011y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 4th September 2011A cuboid measures 8 cm by 13 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th September 2011A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th September 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?
- 7th September 2011A rectangle is 19 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th September 2011f(x) = 4x - 2 and g(x) = 3x + 4. Work out fg(-3).
- 9th September 2011y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 10th September 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.
- 11th September 2011A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 12th September 2011A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 13th September 2011Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 14th September 2011The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 15th September 2011y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 36.
- 16th September 2011In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 17th September 2011The probability of winning a game is 3/10. A player expects 24 wins. How many games did they play?
- 18th September 2011On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th September 2011A block has mass 350 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th September 2011A quadratic sequence starts 6, 17, 36, 63. Work out the second difference, and the coefficient of n^2.
- 21st September 2011A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd September 2011In a vector proof you find that vector PQ = 2a - 4b and vector RS = 6a - 12b. What does this show about PQ and RS?
- 23rd September 2011A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 24th September 2011A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 25th September 2011x = 138 and y = 93, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th September 2011Solve x^2 + 11x + 28 < 0.
- 27th September 2011y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 28th September 2011A cuboid measures 3 cm by 8 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th September 2011A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th September 2011On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?