Daily Practice · Higher Plus
December 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2022On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd December 2022Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 3rd December 2022Write x^2 - 12x + 7 in the form (x + a)^2 + b.
- 4th December 2022y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 5th December 2022A cuboid measures 11 cm by 7 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th December 2022A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th December 2022A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 8th December 2022Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 9th December 2022Work out the coordinates of the turning point of y = x^2 - 12x + 8.
- 10th December 2022y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 36.
- 11th December 2022The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 12th December 2022A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 13th December 2022On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th December 2022A rectangle is 11 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th December 2022Simplify (x^2 + 6x + 8)/(x + 4).
- 16th December 2022A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 17th December 2022In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 18th December 2022The probability of winning a game is 1/5. A player expects 15 wins. How many games did they play?
- 19th December 2022A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 20th December 2022Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 21st December 2022In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 22nd December 2022y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 23rd December 2022In a vector proof you find that vector PQ = 4a + 5b and vector RS = 16a + 20b. What does this show about PQ and RS?
- 24th December 2022A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 25th December 2022On 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?
- 26th December 2022A block has mass 710 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th December 2022Make x the subject of 4x + 3 = y(x + 3).
- 28th December 2022y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 29th December 2022A cuboid measures 7 cm by 9 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th December 2022A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st December 2022A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?