Daily Practice · Higher Plus
September 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2017 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2017y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 2nd September 2017A cuboid measures 6 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd September 2017A bag holds 4 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th September 2017A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 5th September 2017Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 6th September 2017Make x the subject of 2x + 7 = y(x + 7).
- 7th September 2017y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 25.
- 8th September 2017The 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.
- 9th September 2017A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 10th September 2017On 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?
- 11th September 2017A block has mass 220 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th September 2017Write 4/(x - 1) + 5/(x + 1) as a single fraction.
- 13th September 2017A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 14th September 2017In 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.
- 15th September 2017The probability of winning a game is 1/2. A player expects 48 wins. How many games did they play?
- 16th September 2017A 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?
- 17th September 2017x = 178 and y = 36, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th September 2017Solve 12x^2 - x - 1 = 0.
- 19th September 2017y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 20th September 2017In a vector proof you find that vector PQ = 6a - b and vector RS = 18a - 3b. What does this show about PQ and RS?
- 21st September 2017A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 22nd September 2017On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd September 2017A car covers 490 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.
- 24th September 2017f(x) = 5x + 1. Work out the inverse function f^-1(x).
- 25th September 2017y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 26th September 2017A cuboid measures 10 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th September 2017A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th September 2017A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 29th September 2017Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 30th September 2017Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.