Daily Practice · Higher Plus
September 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2023 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2023A cuboid measures 11 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd September 2023A bag holds 5 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd September 2023On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th September 2023A block has mass 380 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.
- 5th September 2023Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 6th September 2023A train slows steadily from 28 m/s to rest in 8 seconds. Work out its deceleration.
- 7th September 2023The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 8th September 2023A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 9th September 2023A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 10th September 2023x = 76 and y = 44, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th September 2023f(x) = 6x - 8 and g(x) = 6x - 9. Work out fg(-3).
- 12th September 2023y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 13th September 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.
- 14th September 2023The probability of winning a game is 3/4. A player expects 30 wins. How many games did they play?
- 15th September 2023On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th September 2023A car covers 580 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th September 2023The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 18th September 2023y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 19th September 2023In a vector proof you find that vector PQ = 2a - 2b and vector RS = 8a - 8b. What does this show about PQ and RS?
- 20th September 2023A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 21st September 2023A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 22nd September 2023Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
- 23rd September 2023A quadratic sequence starts 5, 19, 43, 77. Work out the second difference, and the coefficient of n^2.
- 24th September 2023y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 4.
- 25th September 2023A cuboid measures 12 cm by 4 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th September 2023A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th September 2023On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th September 2023Simplify sqrt(80) + sqrt(5), giving your answer in the form a sqrt(b).
- 29th September 2023Solve x^2 - 16 > 0.
- 30th September 2023A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.