Daily Practice · Higher Plus
June 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2024 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2024Solve 9x^2 - 12x + 4 = 0.
- 2nd June 2024y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 3rd June 2024The 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.
- 4th June 2024A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 5th June 2024On 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?
- 6th June 2024Simplify sqrt(45) + sqrt(180), giving your answer in the form a sqrt(b).
- 7th June 2024f(x) = 4x + 12. Work out the inverse function f^-1(x).
- 8th June 2024y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 9th June 2024In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 10th June 2024The probability of winning a game is 1/5. A player expects 11 wins. How many games did they play?
- 11th June 2024A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 12th June 2024A rectangle is 19 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th June 2024Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 14th June 2024y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 49.
- 15th June 2024In a vector proof you find that vector PQ = a + 3b and vector RS = 2a + 6b. What does this show about PQ and RS?
- 16th June 2024A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 17th June 2024On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th June 2024Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 19th June 2024Use the iteration x(n+1) = cube root of (2x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 20th June 2024A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 21st June 2024A cuboid measures 10 cm by 8 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd June 2024A bag holds 11 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd June 2024A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 24th June 2024A block has mass 570 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th June 2024Work out the nth term of the quadratic sequence 10, 17, 26, 37, ...
- 26th June 2024y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 27th June 2024A cuboid measures 9 cm by 12 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th June 2024A bag holds 5 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th June 2024On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th June 2024x = 176 and y = 69, each correct to the nearest whole number. Work out the upper bound of x - y.