Daily Practice · Higher Plus
December 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2016A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd December 2016A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 3rd December 2016A car covers 390 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th December 2016Use the iteration x(n+1) = cube root of (10x(n) + 1) with x(0) = 1. Work out x(1) to 3 decimal places.
- 5th December 2016y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 6th December 2016A cuboid measures 10 cm by 7 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th December 2016A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th December 2016On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th December 2016Rationalise the denominator of 110/sqrt(11), giving your answer in its simplest form.
- 10th December 2016Work out the nth term of the quadratic sequence 11, 28, 53, 86, ...
- 11th December 2016y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 12th December 2016The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 13th December 2016A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 14th December 2016A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 15th December 2016Simplify sqrt(50) + sqrt(8), giving your answer in the form a sqrt(b).
- 16th December 2016The point (-1, 2) lies on y = f(x). Write down its image on y = f(x) + 1.
- 17th December 2016y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
- 18th December 2016In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 19th December 2016The probability of winning a game is 3/4. A player expects 15 wins. How many games did they play?
- 20th December 2016On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st December 2016A rectangle is 20 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd December 2016Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 23rd December 2016A train slows steadily from 38 m/s to rest in 8 seconds. Work out its deceleration.
- 24th December 2016In a vector proof you find that vector PQ = 3a - 4b and vector RS = 12a - 16b. What does this show about PQ and RS?
- 25th December 2016A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 26th December 2016A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 27th December 2016Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 28th December 2016f(x) = 6x - 3 and g(x) = 2x + 4. Work out fg(5).
- 29th December 2016y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 30th December 2016A cuboid measures 6 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st December 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?