Daily Practice · Higher Plus
November 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2021 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2021A block has mass 580 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd November 2021Simplify (x^2 - 5x - 14)/(x - 7).
- 3rd November 2021A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 4th November 2021A cuboid measures 4 cm by 10 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th November 2021A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th November 2021A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 7th November 2021x = 69 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th November 2021In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 9th November 2021y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 10th November 2021A cuboid measures 8 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th November 2021A bag holds 3 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th November 2021On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th November 2021A car covers 380 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.
- 14th November 2021Make x the subject of 8x + 6 = y(x + 6).
- 15th November 2021y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 16th November 2021The 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.
- 17th November 2021A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 18th November 2021A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 19th November 2021Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 20th November 2021Write 7/(x - 4) + 4/(x - 1) as a single fraction.
- 21st November 2021y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 16.
- 22nd November 2021In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 23rd November 2021The probability of winning a game is 1/8. A player expects 7 wins. How many games did they play?
- 24th November 2021On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th November 2021Simplify sqrt(45) + sqrt(245), giving your answer in the form a sqrt(b).
- 26th November 2021Solve 6x^2 + 5x - 4 = 0.
- 27th November 2021A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 28th November 2021In a vector proof you find that vector PQ = 4a + 5b and vector RS = 20a + 25b. What does this show about PQ and RS?
- 29th November 2021A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 30th November 2021A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?