Daily Practice · Higher Plus
August 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2023y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 2nd August 2023A cuboid measures 9 cm by 6 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd August 2023A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th August 2023A 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?
- 5th August 2023A car covers 280 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th August 2023f(x) = 5x - 10. Work out the inverse function f^-1(x).
- 7th August 2023y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 81.
- 8th August 2023The 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.
- 9th August 2023A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 10th August 2023On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th August 2023Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 12th August 2023Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 13th August 2023A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 14th August 2023In 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.
- 15th August 2023The probability of winning a game is 7/8. A player expects 42 wins. How many games did they play?
- 16th August 2023A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 17th August 2023Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
- 18th August 2023Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 5. Work out x(1) to 3 decimal places.
- 19th August 2023y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 20th August 2023In a vector proof you find that vector PQ = 4a - b and vector RS = 12a - 3b. What does this show about PQ and RS?
- 21st August 2023A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 22nd August 2023On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd August 2023A rectangle is 17 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th August 2023Work out the nth term of the quadratic sequence 8, 19, 34, 53, ...
- 25th August 2023y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 26th August 2023A cuboid measures 8 cm by 11 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th August 2023A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th August 2023A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 29th August 2023Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
- 30th August 2023The point (-4, -1) lies on y = f(x). Write down its image on y = f(x) - 2.
- 31st August 2023y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 49.