Daily Practice · Higher Plus
May 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2025 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2025A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 2nd May 2025Rationalise the denominator of 21/sqrt(3), giving your answer in its simplest form.
- 3rd May 2025The point (-5, 6) lies on y = f(x). Write down its image on y = f(x) - 3.
- 4th May 2025y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 5th May 2025In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 6th May 2025The probability of winning a game is 3/4. A player expects 30 wins. How many games did they play?
- 7th May 2025On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th May 2025Simplify sqrt(80) + sqrt(45), giving your answer in the form a sqrt(b).
- 9th May 2025Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 10th May 2025y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 11th May 2025In a vector proof you find that vector PQ = 2a - 6b and vector RS = 4a - 12b. What does this show about PQ and RS?
- 12th May 2025A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 13th May 2025A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 14th May 2025A rectangle is 12 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th May 2025f(x) = 5x - 9 and g(x) = 3x + 7. Work out fg(0).
- 16th May 2025y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 81.
- 17th May 2025A cuboid measures 12 cm by 14 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th May 2025A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th May 2025On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th May 2025Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 21st May 2025The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 22nd May 2025A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd May 2025A cuboid measures 9 cm by 14 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th May 2025A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th May 2025A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 26th May 2025A block has mass 640 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th May 2025A quadratic sequence starts 6, 11, 18, 27. Work out the second difference, and the coefficient of n^2.
- 28th May 2025y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 29th May 2025The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 30th May 2025A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 31st May 2025On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?