Daily Practice · Higher Plus
September 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2022 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2022A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd September 2022A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 3rd September 2022A car covers 630 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.
- 4th September 2022Simplify (x^2 - 6x - 16)/(x - 8).
- 5th September 2022y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 36.
- 6th September 2022A cuboid measures 8 cm by 7 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th September 2022A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th September 2022On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th September 2022Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 10th September 2022In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 11th September 2022A train slows steadily from 25 m/s to rest in 4 seconds. Work out its deceleration.
- 12th September 2022The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 13th September 2022A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 14th September 2022A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 15th September 2022Simplify sqrt(27) + sqrt(48), giving your answer in the form a sqrt(b).
- 16th September 2022Make x the subject of 8x + 8 = y(x + 8).
- 17th September 2022y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 18th September 2022In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 19th September 2022The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 20th September 2022On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st September 2022A rectangle is 7 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd September 2022Write 4/(x - 3) + 6/(x + 4) as a single fraction.
- 23rd September 2022y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 24th September 2022In a vector proof you find that vector PQ = 4a + 2b and vector RS = 16a + 8b. What does this show about PQ and RS?
- 25th September 2022A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 26th September 2022A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 27th September 2022Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
- 28th September 2022Solve 9x^2 + 18x + 8 = 0.
- 29th September 2022y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
- 30th September 2022A cuboid measures 15 cm by 8 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.