Daily Practice · Higher Plus
August 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2021A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 2nd August 2021A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 3rd August 2021Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 4th August 2021Make x the subject of 3x + 8 = y(x + 8).
- 5th August 2021y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 6th August 2021A cuboid measures 15 cm by 15 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th August 2021A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th August 2021On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th August 2021A block has mass 390 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th August 2021Write 4/(x + 4) + 3/(x + 2) as a single fraction.
- 11th August 2021y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 12th August 2021A cuboid measures 5 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th August 2021A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th August 2021A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 15th August 2021x = 123 and y = 107, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th August 2021Solve 20x^2 + 9x - 18 = 0.
- 17th August 2021y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 81.
- 18th August 2021The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 19th August 2021A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 20th August 2021On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st August 2021A car covers 120 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.
- 22nd August 2021f(x) = 5x + 4. Work out the inverse function f^-1(x).
- 23rd August 2021A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 24th August 2021In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 25th August 2021The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 26th August 2021A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 27th August 2021Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 28th August 2021Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
- 29th August 2021y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 30th August 2021In a vector proof you find that vector PQ = 2a + 5b and vector RS = 8a + 20b. What does this show about PQ and RS?
- 31st August 2021A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.