Daily Practice · Higher Plus
December 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2021A rectangle is 27 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd December 2021f(x) = 2x + 3. Work out the inverse function f^-1(x).
- 3rd December 2021y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 4th December 2021A cuboid measures 9 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th December 2021A 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?
- 6th December 2021On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th December 2021Expand and simplify (8 + sqrt(6))(8 - sqrt(6)).
- 8th December 2021Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 9th December 2021y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 10th December 2021A cuboid measures 4 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th December 2021A bag holds 5 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th December 2021A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 13th December 2021A block has mass 470 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th December 2021Use the iteration x(n+1) = cube root of (8x(n) + 2) with x(0) = 5. Work out x(1) to 3 decimal places.
- 15th December 2021y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 49.
- 16th December 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 December 2021A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 18th December 2021On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th December 2021x = 110 and y = 87, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th December 2021Work out the nth term of the quadratic sequence -6, -8, -8, -6, ...
- 21st December 2021A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 22nd December 2021In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 23rd December 2021The probability of winning a game is 1/2. A player expects 52 wins. How many games did they play?
- 24th December 2021A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 25th December 2021A car covers 370 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th December 2021The point (-6, 6) lies on y = f(x). Write down its image on y = f(x - 4).
- 27th December 2021y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 28th December 2021In a vector proof you find that vector PQ = 5a - 5b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 29th December 2021A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 30th December 2021On 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?
- 31st December 2021Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.