Daily Practice · Higher Plus
January 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2021y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 2nd January 2021In a vector proof you find that vector PQ = 2a - 6b and vector RS = 4a - 12b. What does this show about PQ and RS?
- 3rd January 2021A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 4th January 2021On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th January 2021Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 6th January 2021In an algebraic proof, how would you write a multiple of 8 in terms of an integer n?
- 7th January 2021y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 8th January 2021A cuboid measures 11 cm by 11 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th January 2021A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th January 2021A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 11th January 2021A block has mass 610 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th January 2021Make x the subject of 4x + 2 = y(x + 2).
- 13th January 2021y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 25.
- 14th January 2021A cuboid measures 13 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th January 2021A bag holds 6 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th January 2021On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th January 2021x = 49 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th January 2021Write 5/(x - 6) + 3/(x - 1) as a single fraction.
- 19th January 2021A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.
- 20th January 2021The 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.
- 21st January 2021A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 22nd January 2021A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 23rd January 2021A car covers 600 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th January 2021Solve 12x^2 + 35x + 25 = 0.
- 25th January 2021y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 26th January 2021In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 27th January 2021The probability of winning a game is 3/5. A player expects 42 wins. How many games did they play?
- 28th January 2021On 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?
- 29th January 2021Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 30th January 2021f(x) = 8x - 2. Work out the inverse function f^-1(x).
- 31st January 2021y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.