Daily Practice · Higher Plus
September 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2025 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2025y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 2nd September 2025In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 3rd September 2025The probability of winning a game is 3/4. A player expects 45 wins. How many games did they play?
- 4th September 2025On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th September 2025Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 6th September 2025A quadratic sequence starts 6, 15, 26, 39. Work out the second difference, and the coefficient of n^2.
- 7th September 2025y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 8th September 2025In a vector proof you find that vector PQ = 3a + 3b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 9th September 2025A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 10th September 2025A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 11th September 2025Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
- 12th September 2025Solve x^2 + 13x + 42 < 0.
- 13th September 2025y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 81.
- 14th September 2025A cuboid measures 13 cm by 14 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th September 2025A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th September 2025On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th September 2025A rectangle is 15 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th September 2025Write x^2 - 14x + 5 in the form (x + a)^2 + b.
- 19th September 2025A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 20th September 2025A cuboid measures 14 cm by 14 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st September 2025A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd September 2025A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 23rd September 2025Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 24th September 2025Work out the coordinates of the turning point of y = x^2 + 8x + 10.
- 25th September 2025y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 26th September 2025The 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.
- 27th September 2025A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 28th September 2025On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th September 2025A block has mass 270 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th September 2025Simplify (x^2 + 3x - 18)/(x - 3).