Daily Practice · Higher Plus
August 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2025Use the iteration x(n+1) = cube root of (9x(n) + 2) with x(0) = 2. Work out x(1) to 3 decimal places.
- 2nd August 2025A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd August 2025In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 4th August 2025The probability of winning a game is 1/8. A player expects 3 wins. How many games did they play?
- 5th August 2025A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 6th August 2025A rectangle is 9 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th August 2025Work out the nth term of the quadratic sequence 2, 11, 28, 53, ...
- 8th August 2025y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 9th August 2025In a vector proof you find that vector PQ = 2a - 4b and vector RS = 6a - 12b. What does this show about PQ and RS?
- 10th August 2025A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 11th August 2025On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th August 2025Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 13th August 2025The point (-4, 0) lies on y = f(x). Write down its image on y = f(-x).
- 14th August 2025y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 15th August 2025A cuboid measures 7 cm by 13 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th August 2025A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th August 2025A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 18th August 2025A block has mass 500 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.
- 19th August 2025Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 20th August 2025y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 9.
- 21st August 2025A cuboid measures 10 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd August 2025A bag holds 5 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd August 2025On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th August 2025x = 93 and y = 81, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th August 2025f(x) = 2x - 6 and g(x) = 5x + 3. Work out fg(0).
- 26th August 2025A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 27th August 2025The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 28th August 2025A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 29th August 2025A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 30th August 2025A car covers 340 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.
- 31st August 2025The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.