Daily Practice · Higher Plus
November 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2025 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2025In 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.
- 2nd November 2025The probability of winning a game is 1/4. A player expects 15 wins. How many games did they play?
- 3rd November 2025On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th November 2025Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 5th November 2025Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
- 6th November 2025A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 7th November 2025In a vector proof you find that vector PQ = 4a - b and vector RS = 12a - 3b. What does this show about PQ and RS?
- 8th November 2025A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 9th November 2025A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 10th November 2025A block has mass 660 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th November 2025Use the iteration x(n+1) = cube root of (12x(n) + 1) with x(0) = 4. Work out x(1) to 3 decimal places.
- 12th November 2025y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 13th November 2025A cuboid measures 10 cm by 7 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th November 2025A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th November 2025On 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?
- 16th November 2025x = 71 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th November 2025Work out the nth term of the quadratic sequence 7, 15, 31, 55, ...
- 18th November 2025y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 19th November 2025A cuboid measures 6 cm by 8 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th November 2025A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st November 2025A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 22nd November 2025A car covers 870 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd November 2025The point (5, 3) lies on y = f(x). Write down its image on y = -f(x).
- 24th November 2025y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 25.
- 25th November 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.
- 26th November 2025A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 27th November 2025On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th November 2025Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 29th November 2025Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 30th November 2025A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.