Daily Practice · Higher Plus
December 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2023A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd December 2023A 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?
- 3rd December 2023x = 177 and y = 27, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th December 2023Work out the nth term of the quadratic sequence 8, 19, 34, 53, ...
- 5th December 2023y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 36.
- 6th December 2023The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 7th December 2023A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 8th December 2023On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th December 2023A car covers 670 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th December 2023The point (-2, 6) lies on y = f(x). Write down its image on y = f(x) + 4.
- 11th December 2023A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 12th December 2023In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 13th December 2023The probability of winning a game is 3/4. A player expects 33 wins. How many games did they play?
- 14th December 2023A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 15th December 2023Rationalise the denominator of 35/sqrt(5), giving your answer in its simplest form.
- 16th December 2023Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 17th December 2023y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 18th December 2023In a vector proof you find that vector PQ = 3a + b and vector RS = 6a + 2b. What does this show about PQ and RS?
- 19th December 2023A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 20th December 2023On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st December 2023Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 22nd December 2023f(x) = 4x - 1 and g(x) = 4x + 5. Work out fg(-3).
- 23rd December 2023y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 24th December 2023A cuboid measures 12 cm by 5 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th December 2023A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th December 2023A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 27th December 2023A rectangle is 29 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th December 2023The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 29th December 2023y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
- 30th December 2023A cuboid measures 4 cm by 8 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st December 2023A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?