Daily Practice · Higher Plus
June 2026 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2026, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2026 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2026
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2026A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 2nd June 2026Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 3rd June 2026Use the iteration x(n+1) = cube root of (9x(n) + 3) with x(0) = 2. Work out x(1) to 3 decimal places.
- 4th June 2026y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 36.
- 5th June 2026In a vector proof you find that vector PQ = 6a - 3b and vector RS = 30a - 15b. What does this show about PQ and RS?
- 6th June 2026A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 7th June 2026On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th June 2026A block has mass 640 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th June 2026Work out the nth term of the quadratic sequence -2, 2, 10, 22, ...
- 10th June 2026A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 11th June 2026A cuboid measures 11 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th June 2026A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th June 2026A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 14th June 2026x = 168 and y = 76, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th June 2026The point (6, -2) lies on y = f(x). Write down its image on y = -f(x).
- 16th June 2026y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 17th June 2026A cuboid measures 10 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th June 2026A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th June 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?
- 20th June 2026A car covers 540 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st June 2026Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 22nd June 2026y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 23rd June 2026The 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.
- 24th June 2026A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 25th June 2026A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 26th June 2026Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 27th June 2026f(x) = 4x + 6 and g(x) = 5x - 2. Work out fg(-3).
- 28th June 2026y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 16.
- 29th June 2026In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 30th June 2026The probability of winning a game is 1/10. A player expects 10 wins. How many games did they play?