Daily Practice · Higher Plus
January 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2023x = 79 and y = 67, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd January 2023Write 7/(x - 3) + 7/(x - 6) as a single fraction.
- 3rd January 2023y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 16.
- 4th January 2023A cuboid measures 4 cm by 9 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th January 2023A bag holds 3 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th January 2023On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 7th January 2023A car covers 820 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th January 2023Solve 16x^2 + 32x + 15 = 0.
- 9th January 2023A train slows steadily from 32 m/s to rest in 10 seconds. Work out its deceleration.
- 10th January 2023The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 11th January 2023A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 12th January 2023A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 13th January 2023Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 14th January 2023f(x) = 2x + 10. Work out the inverse function f^-1(x).
- 15th January 2023y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 16th January 2023In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 17th January 2023The probability of winning a game is 3/10. A player expects 39 wins. How many games did they play?
- 18th January 2023On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th January 2023Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
- 20th January 2023Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 21st January 2023y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 22nd January 2023In a vector proof you find that vector PQ = 4a + b and vector RS = 8a + 2b. What does this show about PQ and RS?
- 23rd January 2023A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 24th January 2023A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 25th January 2023A rectangle is 25 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th January 2023Use the iteration x(n+1) = cube root of (2x(n) + 4) with x(0) = 2. Work out x(1) to 3 decimal places.
- 27th January 2023y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 9.
- 28th January 2023A cuboid measures 3 cm by 4 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th January 2023A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th January 2023On 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?
- 31st January 2023Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).