Daily Practice · Higher Plus
September 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2024 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2024The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 2nd September 2024A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 3rd September 2024A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 4th September 2024A rectangle is 6 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th September 2024Write 5/(x - 4) + 2/(x + 6) as a single fraction.
- 6th September 2024y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 7th September 2024In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 8th September 2024The probability of winning a game is 3/5. A player expects 45 wins. How many games did they play?
- 9th September 2024On 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?
- 10th September 2024Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 11th September 2024Solve 8x^2 + 6x - 9 = 0.
- 12th September 2024y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 13th September 2024In a vector proof you find that vector PQ = 6a + 2b and vector RS = 12a + 4b. What does this show about PQ and RS?
- 14th September 2024A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 15th September 2024A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 16th September 2024A block has mass 330 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th September 2024f(x) = 5x - 9. Work out the inverse function f^-1(x).
- 18th September 2024y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 25.
- 19th September 2024A cuboid measures 7 cm by 13 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th September 2024A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st September 2024On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd September 2024x = 192 and y = 121, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd September 2024Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 24th September 2024A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
- 25th September 2024A cuboid measures 7 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th September 2024A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th September 2024A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 28th September 2024A car covers 500 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th September 2024Use the iteration x(n+1) = cube root of (7x(n) + 9) with x(0) = 2. Work out x(1) to 3 decimal places.
- 30th September 2024y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.