Daily Practice · Higher Plus
June 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2025 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2025x = 162 and y = 52, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd June 2025Solve x^2 + 10x + 21 > 0.
- 3rd June 2025y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 4th June 2025In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 5th June 2025The probability of winning a game is 2/5. A player expects 26 wins. How many games did they play?
- 6th June 2025A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 7th June 2025A car covers 390 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th June 2025Write x^2 - 16x + 8 in the form (x + a)^2 + b.
- 9th June 2025y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 25.
- 10th June 2025In a vector proof you find that vector PQ = 2a + 5b and vector RS = 6a + 15b. What does this show about PQ and RS?
- 11th June 2025A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 12th June 2025On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th June 2025Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 14th June 2025Work out the coordinates of the turning point of y = x^2 - 14x - 2.
- 15th June 2025A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 16th June 2025A cuboid measures 15 cm by 3 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th June 2025A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th June 2025A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 19th June 2025Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 20th June 2025Simplify (x^2 - 4x - 12)/(x + 2).
- 21st June 2025y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 22nd June 2025A cuboid measures 4 cm by 10 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd June 2025A bag holds 7 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th June 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?
- 25th June 2025A rectangle is 23 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th June 2025In an algebraic proof, how would you write an even number in terms of an integer n?
- 27th June 2025y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 28th June 2025The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 29th June 2025A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 30th June 2025A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?