Daily Practice · Higher Plus
December 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2024A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 2nd December 2024On 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?
- 3rd December 2024Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 4th December 2024In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 5th December 2024A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 6th December 2024In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 7th December 2024The probability of winning a game is 1/2. A player expects 56 wins. How many games did they play?
- 8th December 2024A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 9th December 2024A block has mass 480 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.
- 10th December 2024Make x the subject of 7x + 3 = y(x + 3).
- 11th December 2024y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 12th December 2024In a vector proof you find that vector PQ = a + 3b and vector RS = 5a + 15b. What does this show about PQ and RS?
- 13th December 2024A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 14th December 2024On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th December 2024x = 111 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th December 2024Write 6/(x + 3) + 7/(x + 4) as a single fraction.
- 17th December 2024y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 18th December 2024A cuboid measures 6 cm by 12 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th December 2024A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th December 2024A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 21st December 2024A car covers 720 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd December 2024Solve 20x^2 + 3x - 9 = 0.
- 23rd December 2024y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 16.
- 24th December 2024A cuboid measures 14 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th December 2024A bag holds 3 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th December 2024On 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?
- 27th December 2024Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.
- 28th December 2024f(x) = 2x - 1. Work out the inverse function f^-1(x).
- 29th December 2024A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 30th December 2024The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 31st December 2024A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.