Daily Practice · Higher Plus
December 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 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.
- 2nd December 2025The probability of winning a game is 1/2. A player expects 36 wins. How many games did they play?
- 3rd December 2025A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 4th December 2025Simplify sqrt(80) + sqrt(180), giving your answer in the form a sqrt(b).
- 5th December 2025f(x) = 5x + 2 and g(x) = 6x - 8. Work out fg(-3).
- 6th December 2025y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 7th December 2025In a vector proof you find that vector PQ = 3a - 5b and vector RS = 9a - 15b. What does this show about PQ and RS?
- 8th December 2025A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 9th December 2025On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th December 2025A rectangle is 5 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th December 2025The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 12th December 2025y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 13th December 2025A cuboid measures 5 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th December 2025A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th December 2025A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 16th December 2025Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 17th December 2025A quadratic sequence starts 8, 21, 44, 77. Work out the second difference, and the coefficient of n^2.
- 18th December 2025y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 9.
- 19th December 2025A cuboid measures 14 cm by 6 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th December 2025A bag holds 4 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st December 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?
- 22nd December 2025A block has mass 410 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd December 2025Solve x^2 + 6x - 7 < 0.
- 24th December 2025A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 25th December 2025The 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.
- 26th December 2025A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 27th December 2025A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 28th December 2025x = 77 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th December 2025Write x^2 - 12x - 13 in the form (x + a)^2 + b.
- 30th December 2025y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 31st December 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.