Daily Practice · Higher Plus
January 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2025A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 2nd January 2025Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).
- 3rd January 2025Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 4th January 2025y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 5th January 2025In 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.
- 6th January 2025The probability of winning a game is 3/5. A player expects 84 wins. How many games did they play?
- 7th January 2025On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th January 2025A rectangle is 29 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th January 2025Use the iteration x(n+1) = cube root of (12x(n) + 1) with x(0) = 3. Work out x(1) to 3 decimal places.
- 10th January 2025y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 11th January 2025In a vector proof you find that vector PQ = 3a + b and vector RS = 15a + 5b. What does this show about PQ and RS?
- 12th January 2025A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 13th January 2025A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 14th January 2025Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 15th January 2025Work out the nth term of the quadratic sequence 8, 16, 26, 38, ...
- 16th January 2025y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 9.
- 17th January 2025A cuboid measures 8 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th January 2025A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th January 2025On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th January 2025A block has mass 210 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st January 2025The point (0, -2) lies on y = f(x). Write down its image on y = f(x - 6).
- 22nd January 2025A train slows steadily from 17 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd January 2025A cuboid measures 12 cm by 11 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th January 2025A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th January 2025A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 26th January 2025x = 64 and y = 21, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th January 2025Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 28th January 2025y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 29th January 2025The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 30th January 2025A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 31st January 2025On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?