Daily Practice · Higher Plus
November 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2023 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2023A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd November 2023On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd November 2023Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 4th November 2023Write 6/(x - 6) + 7/(x - 5) as a single fraction.
- 5th November 2023y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 6th November 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.
- 7th November 2023A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 8th November 2023A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 9th November 2023Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 10th November 2023Solve 2x^2 + 11x - 6 = 0.
- 11th November 2023y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 36.
- 12th November 2023In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 13th November 2023The probability of winning a game is 4/5. A player expects 104 wins. How many games did they play?
- 14th November 2023On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th November 2023A rectangle is 14 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th November 2023f(x) = 4x + 11. Work out the inverse function f^-1(x).
- 17th November 2023A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 18th November 2023In a vector proof you find that vector PQ = 2a - 4b and vector RS = 10a - 20b. What does this show about PQ and RS?
- 19th November 2023A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 20th November 2023A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 21st November 2023Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).
- 22nd November 2023Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 23rd November 2023y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 24th November 2023A cuboid measures 14 cm by 11 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th November 2023A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th November 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?
- 27th November 2023A block has mass 820 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.
- 28th November 2023Use the iteration x(n+1) = cube root of (8x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 29th November 2023y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 30th November 2023A cuboid measures 8 cm by 5 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.