Daily Practice · Higher Plus
December 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2019Make x the subject of 3x + 8 = y(x + 8).
- 2nd December 2019y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 4.
- 3rd December 2019In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 4th December 2019The probability of winning a game is 1/5. A player expects 3 wins. How many games did they play?
- 5th December 2019On 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?
- 6th December 2019Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 7th December 2019Write 7/(x - 2) + 3/(x + 4) as a single fraction.
- 8th December 2019A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 9th December 2019In a vector proof you find that vector PQ = 3a - 4b and vector RS = 9a - 12b. What does this show about PQ and RS?
- 10th December 2019A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 11th December 2019A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 12th December 2019Simplify sqrt(50) + sqrt(98), giving your answer in the form a sqrt(b).
- 13th December 2019Solve 6x^2 - 13x - 5 = 0.
- 14th December 2019y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 15th December 2019A cuboid measures 4 cm by 11 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th December 2019A 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?
- 17th December 2019On 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?
- 18th December 2019A rectangle is 16 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th December 2019f(x) = 4x - 2. Work out the inverse function f^-1(x).
- 20th December 2019y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 21st December 2019A cuboid measures 11 cm by 13 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd December 2019A bag holds 5 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd December 2019A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 24th December 2019Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 25th December 2019Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 26th December 2019y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 64.
- 27th December 2019The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 28th December 2019A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 29th December 2019On 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?
- 30th December 2019A block has mass 380 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st December 2019Use the iteration x(n+1) = cube root of (3x(n) + 4) with x(0) = 3. Work out x(1) to 3 decimal places.