Daily Practice · Higher Plus
September 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2021 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2021On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 2nd September 2021Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 3rd September 2021Use the iteration x(n+1) = cube root of (4x(n) + 3) with x(0) = 3. Work out x(1) to 3 decimal places.
- 4th September 2021y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 5th September 2021A cuboid measures 11 cm by 4 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th September 2021A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th September 2021A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 8th September 2021A rectangle is 29 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th September 2021Work out the nth term of the quadratic sequence 10, 20, 34, 52, ...
- 10th September 2021y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 49.
- 11th September 2021A cuboid measures 14 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th September 2021A 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?
- 13th September 2021On 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?
- 14th September 2021Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 15th September 2021The point (-1, 6) lies on y = f(x). Write down its image on y = f(x + 4).
- 16th September 2021A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 17th September 2021The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 18th September 2021A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.
- 19th September 2021A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 20th September 2021A block has mass 440 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st September 2021Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 22nd September 2021y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 23rd September 2021In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 24th September 2021The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
- 25th September 2021On 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?
- 26th September 2021x = 147 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th September 2021f(x) = 4x + 8 and g(x) = 5x - 6. Work out fg(1).
- 28th September 2021y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 29th September 2021In a vector proof you find that vector PQ = 5a + 4b and vector RS = 25a + 20b. What does this show about PQ and RS?
- 30th September 2021A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.