Daily Practice · Higher Plus
August 2026 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2026, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2026 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2026
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2026A car covers 750 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd August 2026Simplify (x^2 + 9x + 14)/(x + 2).
- 3rd August 2026y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 4th August 2026In a vector proof you find that vector PQ = 4a + 6b and vector RS = 12a + 18b. What does this show about PQ and RS?
- 5th August 2026A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 6th August 2026On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th August 2026Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 8th August 2026In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 9th August 2026y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 10th August 2026A cuboid measures 12 cm by 14 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th August 2026A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th August 2026A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 13th August 2026Simplify sqrt(27) + sqrt(48), giving your answer in the form a sqrt(b).
- 14th August 2026Make x the subject of 6x + 5 = y(x + 5).
- 15th August 2026y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 25.
- 16th August 2026A cuboid measures 7 cm by 7 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th August 2026A bag holds 7 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th August 2026On 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?
- 19th August 2026A rectangle is 5 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th August 2026Write 2/(x - 1) + 4/(x + 5) as a single fraction.
- 21st August 2026A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 22nd August 2026The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 23rd August 2026A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 24th August 2026A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 25th August 2026Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 26th August 2026Solve 10x^2 - 21x - 10 = 0.
- 27th August 2026y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 28th August 2026In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 29th August 2026The probability of winning a game is 3/10. A player expects 6 wins. How many games did they play?
- 30th August 2026On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st August 2026A block has mass 570 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.