Daily Practice · Higher Plus
September 2026 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2026, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2026 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2026
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2026f(x) = 5x - 3. Work out the inverse function f^-1(x).
- 2nd September 2026y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 3rd September 2026In a vector proof you find that vector PQ = 2a + 4b and vector RS = 10a + 20b. What does this show about PQ and RS?
- 4th September 2026A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 5th September 2026A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 6th September 2026x = 158 and y = 85, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th September 2026Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 8th September 2026y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 36.
- 9th September 2026A cuboid measures 10 cm by 8 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th September 2026A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th September 2026On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th September 2026A car covers 670 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th September 2026Use the iteration x(n+1) = cube root of (10x(n) + 6) with x(0) = 5. Work out x(1) to 3 decimal places.
- 14th September 2026A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 15th September 2026A cuboid measures 4 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th September 2026A bag holds 6 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th September 2026A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 18th September 2026Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 19th September 2026Work out the nth term of the quadratic sequence 5, 13, 27, 47, ...
- 20th September 2026y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 21st September 2026The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 22nd September 2026A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 23rd September 2026On 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?
- 24th September 2026Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 25th September 2026The point (-1, -2) lies on y = f(x). Write down its image on y = f(x) + 1.
- 26th September 2026y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 27th September 2026In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 28th September 2026The probability of winning a game is 2/5. A player expects 10 wins. How many games did they play?
- 29th September 2026A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 30th September 2026A rectangle is 16 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.