Daily Practice · Higher Plus
July 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2025Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 2nd July 2025Make x the subject of 5x + 5 = y(x + 5).
- 3rd July 2025y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 4.
- 4th July 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.
- 5th July 2025The probability of winning a game is 1/2. A player expects 50 wins. How many games did they play?
- 6th July 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?
- 7th July 2025A block has mass 740 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th July 2025Write 6/(x + 3) + 4/(x + 1) as a single fraction.
- 9th July 2025A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 10th July 2025In a vector proof you find that vector PQ = 4a + 3b and vector RS = 8a + 6b. What does this show about PQ and RS?
- 11th July 2025A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 12th July 2025A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 13th July 2025x = 176 and y = 83, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th July 2025Solve 2x^2 + 9x + 9 = 0.
- 15th July 2025y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 16th July 2025A cuboid measures 13 cm by 14 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th July 2025A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th July 2025On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th July 2025A car covers 300 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.
- 20th July 2025f(x) = 3x + 2. Work out the inverse function f^-1(x).
- 21st July 2025y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 22nd July 2025A cuboid measures 13 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd July 2025A bag holds 7 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th July 2025A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 25th July 2025Rationalise the denominator of 33/sqrt(3), giving your answer in its simplest form.
- 26th July 2025Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 27th July 2025y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 64.
- 28th July 2025The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 29th July 2025A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 30th July 2025On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 31st July 2025Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).