Daily Practice · Higher Plus
January 2026 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2026, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2026 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2026
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2026The probability of winning a game is 3/4. A player expects 9 wins. How many games did they play?
- 2nd January 2026On 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?
- 3rd January 2026A car covers 650 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th January 2026Work out the coordinates of the turning point of y = x^2 - 8x + 1.
- 5th January 2026y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 6th January 2026In a vector proof you find that vector PQ = 6a + 5b and vector RS = 18a + 15b. What does this show about PQ and RS?
- 7th January 2026A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 8th January 2026A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 9th January 2026Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 10th January 2026Simplify (x^2 + 7x + 6)/(x + 1).
- 11th January 2026y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 16.
- 12th January 2026A cuboid measures 12 cm by 13 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th January 2026A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th January 2026On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th January 2026Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 16th January 2026In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 17th January 2026A train slows steadily from 21 m/s to rest in 4 seconds. Work out its deceleration.
- 18th January 2026A cuboid measures 6 cm by 8 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th January 2026A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th January 2026A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 21st January 2026A rectangle is 26 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd January 2026Make x the subject of 8x + 4 = y(x + 4).
- 23rd January 2026y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 24th January 2026The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 25th January 2026A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 26th January 2026On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th January 2026Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 28th January 2026Write 6/(x - 3) + 4/(x + 1) as a single fraction.
- 29th January 2026y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 30th January 2026In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 31st January 2026The probability of winning a game is 3/5. A player expects 9 wins. How many games did they play?