Daily Practice · Higher Plus
September 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2019 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2019x = 165 and y = 125, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd September 2019Solve 5x^2 + 6x + 1 = 0.
- 3rd September 2019A train slows steadily from 29 m/s to rest in 4 seconds. Work out its deceleration.
- 4th September 2019In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 5th September 2019The probability of winning a game is 1/5. A player expects 6 wins. How many games did they play?
- 6th September 2019A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 7th September 2019A car covers 530 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th September 2019f(x) = 4x - 4. Work out the inverse function f^-1(x).
- 9th September 2019y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 10th September 2019In a vector proof you find that vector PQ = 3a - 5b and vector RS = 15a - 25b. What does this show about PQ and RS?
- 11th September 2019A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 12th September 2019On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th September 2019Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 14th September 2019Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 15th September 2019y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 16th September 2019A cuboid measures 5 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th September 2019A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th September 2019A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 19th September 2019Simplify sqrt(75) + sqrt(3), giving your answer in the form a sqrt(b).
- 20th September 2019Use the iteration x(n+1) = cube root of (9x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
- 21st September 2019y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 36.
- 22nd September 2019A cuboid measures 6 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd September 2019A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th September 2019On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th September 2019A rectangle is 14 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th September 2019Work out the nth term of the quadratic sequence -1, 3, 9, 17, ...
- 27th September 2019A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 28th September 2019The 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.
- 29th September 2019A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 30th September 2019A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?