Daily Practice · Higher Plus
September 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2020 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2020Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 2nd September 2020Solve x^2 + 12x + 32 > 0.
- 3rd September 2020y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 4th September 2020In a vector proof you find that vector PQ = 5a - b and vector RS = 25a - 5b. What does this show about PQ and RS?
- 5th September 2020A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 6th September 2020On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th September 2020A block has mass 750 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th September 2020Write x^2 - 12x + 12 in the form (x + a)^2 + b.
- 9th September 2020y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 10th September 2020A cuboid measures 7 cm by 7 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th September 2020A 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?
- 12th September 2020A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 13th September 2020x = 33 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th September 2020Work out the coordinates of the turning point of y = x^2 + 16x + 12.
- 15th September 2020y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 81.
- 16th September 2020A cuboid measures 8 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th September 2020A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th September 2020On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th September 2020A car covers 250 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.
- 20th September 2020Simplify (x^2 + 3x + 2)/(x + 1).
- 21st September 2020A train slows steadily from 36 m/s to rest in 5 seconds. Work out its deceleration.
- 22nd September 2020The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 23rd September 2020A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 24th September 2020A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 25th September 2020Rationalise the denominator of 21/sqrt(3), giving your answer in its simplest form.
- 26th September 2020In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 27th September 2020y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 28th September 2020In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 29th September 2020The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
- 30th September 2020On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?