Daily Practice · Higher Plus
October 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2023A cuboid measures 14 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd October 2023A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd October 2023A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 4th October 2023A rectangle is 25 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th October 2023Write x^2 - 10x - 8 in the form (x + a)^2 + b.
- 6th October 2023y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 7th October 2023The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 8th October 2023A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 9th October 2023On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th October 2023Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 11th October 2023Work out the coordinates of the turning point of y = x^2 - 4x + 2.
- 12th October 2023y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 13th October 2023In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 14th October 2023The probability of winning a game is 3/8. A player expects 42 wins. How many games did they play?
- 15th October 2023A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 16th October 2023A block has mass 210 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th October 2023Simplify (x^2 + 6x + 8)/(x + 2).
- 18th October 2023y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 81.
- 19th October 2023In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 20th October 2023A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 21st October 2023On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 22nd October 2023x = 108 and y = 52, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd October 2023In an algebraic proof, how would you write an odd number in terms of an integer n?
- 24th October 2023A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 25th October 2023A cuboid measures 12 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th October 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?
- 27th October 2023A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 28th October 2023A car covers 340 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th October 2023Make x the subject of 7x + 3 = y(x + 3).
- 30th October 2023y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 31st October 2023A cuboid measures 11 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.