Daily Practice · Higher Plus
October 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2025y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 2nd October 2025In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 3rd October 2025The probability of winning a game is 9/10. A player expects 18 wins. How many games did they play?
- 4th October 2025A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 5th October 2025x = 102 and y = 66, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th October 2025In an algebraic proof, how would you write a multiple of 3 in terms of an integer n?
- 7th October 2025y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 4.
- 8th October 2025In a vector proof you find that vector PQ = 3a + 2b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 9th October 2025A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 10th October 2025On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 11th October 2025A car covers 610 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th October 2025Make x the subject of 3x + 5 = y(x + 5).
- 13th October 2025A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 14th October 2025A cuboid measures 10 cm by 5 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th October 2025A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th October 2025A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 17th October 2025Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 18th October 2025Write 6/(x - 2) + 3/(x + 5) as a single fraction.
- 19th October 2025y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 20th October 2025A cuboid measures 14 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st October 2025A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd October 2025On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd October 2025Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
- 24th October 2025Solve 6x^2 + 13x + 5 = 0.
- 25th October 2025y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 26th October 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 October 2025A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 28th October 2025A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 29th October 2025A rectangle is 24 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th October 2025f(x) = 3x - 9. Work out the inverse function f^-1(x).
- 31st October 2025y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 36.