Daily Practice · Higher Plus
November 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2020 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2020Use the iteration x(n+1) = cube root of (2x(n) + 5) with x(0) = 4. Work out x(1) to 3 decimal places.
- 2nd November 2020y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 64.
- 3rd November 2020In a vector proof you find that vector PQ = 6a - 6b and vector RS = 24a - 24b. What does this show about PQ and RS?
- 4th November 2020A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 5th November 2020On 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?
- 6th November 2020Rationalise the denominator of 6/sqrt(2), giving your answer in its simplest form.
- 7th November 2020Work out the nth term of the quadratic sequence 10, 21, 36, 55, ...
- 8th November 2020A train slows steadily from 17 m/s to rest in 4 seconds. Work out its deceleration.
- 9th November 2020A cuboid measures 15 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th November 2020A 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?
- 11th November 2020A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 12th November 2020Simplify sqrt(50) + sqrt(50), giving your answer in the form a sqrt(b).
- 13th November 2020The point (-2, -6) lies on y = f(x). Write down its image on y = f(-x).
- 14th November 2020y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 15th November 2020A cuboid measures 7 cm by 4 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th November 2020A bag holds 3 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th November 2020On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th November 2020A rectangle is 7 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th November 2020Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 20th November 2020y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 21st November 2020The 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.
- 22nd November 2020A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 23rd November 2020A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 24th November 2020Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 25th November 2020f(x) = 5x + 8 and g(x) = 5x + 5. Work out fg(6).
- 26th November 2020y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 16.
- 27th November 2020In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 28th November 2020The probability of winning a game is 4/5. A player expects 16 wins. How many games did they play?
- 29th November 2020On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th November 2020A block has mass 550 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.