Daily Practice · Higher Plus
December 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2020The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 2nd December 2020A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 3rd December 2020In a vector proof you find that vector PQ = 6a - 2b and vector RS = 18a - 6b. What does this show about PQ and RS?
- 4th December 2020A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 5th December 2020A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 6th December 2020x = 134 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th December 2020A quadratic sequence starts 5, 17, 35, 59. Work out the second difference, and the coefficient of n^2.
- 8th December 2020y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 9th December 2020A cuboid measures 9 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th December 2020A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th December 2020On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th December 2020A car covers 810 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.
- 13th December 2020Solve x^2 - 7x < 0.
- 14th December 2020y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 15th December 2020A cuboid measures 11 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th December 2020A bag holds 3 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th December 2020A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 18th December 2020Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
- 19th December 2020Write x^2 - 14x + 13 in the form (x + a)^2 + b.
- 20th December 2020y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 36.
- 21st December 2020The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 22nd December 2020A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 23rd December 2020On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th December 2020Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 25th December 2020Work out the coordinates of the turning point of y = x^2 - 10x - 10.
- 26th December 2020A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 27th December 2020In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 28th December 2020The probability of winning a game is 1/5. A player expects 2 wins. How many games did they play?
- 29th December 2020A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 30th December 2020A rectangle is 28 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st December 2020Simplify (x^2 - x - 56)/(x - 8).