Daily Practice · Higher Plus
July 2026 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2026, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2026 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2026
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2026On 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?
- 2nd July 2026Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 3rd July 2026The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 4th July 2026A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 5th July 2026In a vector proof you find that vector PQ = a + 4b and vector RS = 2a + 8b. What does this show about PQ and RS?
- 6th July 2026A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 7th July 2026A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 8th July 2026A rectangle is 16 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th July 2026A quadratic sequence starts 5, 10, 19, 32. Work out the second difference, and the coefficient of n^2.
- 10th July 2026y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 11th July 2026A cuboid measures 10 cm by 6 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th July 2026A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th July 2026On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 14th July 2026Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 15th July 2026Solve x^2 + 13x + 42 > 0.
- 16th July 2026y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 17th July 2026A cuboid measures 10 cm by 11 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th July 2026A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th July 2026A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 20th July 2026A block has mass 860 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st July 2026Write x^2 + 16x - 6 in the form (x + a)^2 + b.
- 22nd July 2026y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 64.
- 23rd July 2026The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 24th July 2026A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 25th July 2026On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th July 2026x = 178 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th July 2026Work out the coordinates of the turning point of y = x^2 + 10x - 1.
- 28th July 2026A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 29th July 2026In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 30th July 2026The probability of winning a game is 3/4. A player expects 18 wins. How many games did they play?
- 31st July 2026A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?