Daily Practice · Higher Plus
November 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2016 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2016A 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?
- 2nd November 2016On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd November 2016Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 4th November 2016Make x the subject of 8x + 6 = y(x + 6).
- 5th November 2016A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 6th November 2016A cuboid measures 12 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th November 2016A bag holds 3 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th November 2016A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 9th November 2016A rectangle is 8 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th November 2016Write 2/(x - 3) + 6/(x + 5) as a single fraction.
- 11th November 2016y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 12th November 2016The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 13th November 2016A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 14th November 2016On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th November 2016Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 16th November 2016Solve 2x^2 - 13x + 20 = 0.
- 17th November 2016y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 18th November 2016In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 19th November 2016The probability of winning a game is 3/8. A player expects 27 wins. How many games did they play?
- 20th November 2016A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 21st November 2016A block has mass 880 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd November 2016f(x) = 5x + 8. Work out the inverse function f^-1(x).
- 23rd November 2016y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 64.
- 24th November 2016In a vector proof you find that vector PQ = 5a - 4b and vector RS = 25a - 20b. What does this show about PQ and RS?
- 25th November 2016A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 26th November 2016On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th November 2016x = 121 and y = 107, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th November 2016Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 29th November 2016A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
- 30th November 2016A cuboid measures 10 cm by 5 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.