Daily Practice · Higher Plus
September 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2015 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2015In a vector proof you find that vector PQ = 3a - 2b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 2nd September 2015A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 3rd September 2015A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 4th September 2015Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 5th September 2015Work out the coordinates of the turning point of y = x^2 + 16x + 1.
- 6th September 2015y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 7th September 2015A cuboid measures 10 cm by 13 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th September 2015A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th September 2015On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th September 2015Simplify sqrt(75) + sqrt(108), giving your answer in the form a sqrt(b).
- 11th September 2015Simplify (x^2 + x - 56)/(x + 8).
- 12th September 2015y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 13th September 2015A cuboid measures 13 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th September 2015A bag holds 5 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th September 2015A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 16th September 2015A rectangle is 21 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th September 2015In an algebraic proof, how would you write a multiple of 3 in terms of an integer n?
- 18th September 2015y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 36.
- 19th September 2015The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 20th September 2015A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 21st September 2015On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd September 2015Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 23rd September 2015Make x the subject of 5x + 3 = y(x + 3).
- 24th September 2015A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.
- 25th September 2015In 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.
- 26th September 2015The probability of winning a game is 1/4. A player expects 2 wins. How many games did they play?
- 27th September 2015A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 28th September 2015A block has mass 690 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th September 2015Write 4/(x - 6) + 3/(x + 6) as a single fraction.
- 30th September 2015y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.