Daily Practice · Higher Plus
April 2025 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2025, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2025 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2025
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2025On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd April 2025A rectangle is 19 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd April 2025Solve 3x^2 - 10x + 8 = 0.
- 4th April 2025A train slows steadily from 28 m/s to rest in 5 seconds. Work out its deceleration.
- 5th April 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.
- 6th April 2025The probability of winning a game is 1/8. A player expects 13 wins. How many games did they play?
- 7th April 2025A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 8th April 2025Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 9th April 2025f(x) = 7x - 10. Work out the inverse function f^-1(x).
- 10th April 2025y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 11th April 2025In a vector proof you find that vector PQ = 5a - 5b and vector RS = 20a - 20b. What does this show about PQ and RS?
- 12th April 2025A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 13th April 2025On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th April 2025A block has mass 410 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th April 2025Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 16th April 2025y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 17th April 2025A cuboid measures 15 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th April 2025A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th April 2025A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 20th April 2025x = 180 and y = 109, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st April 2025Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 22nd April 2025y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 25.
- 23rd April 2025A cuboid measures 5 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th April 2025A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th April 2025On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th April 2025A car covers 680 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th April 2025Work out the nth term of the quadratic sequence 3, 18, 41, 72, ...
- 28th April 2025A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 29th April 2025The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 30th April 2025A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.