Daily Practice · Higher Plus
February 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2021 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2021In a vector proof you find that vector PQ = a + 6b and vector RS = 5a + 30b. What does this show about PQ and RS?
- 2nd February 2021A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 3rd February 2021A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 4th February 2021Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
- 5th February 2021Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 6th February 2021y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 81.
- 7th February 2021A cuboid measures 3 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th February 2021A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th February 2021On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th February 2021A rectangle is 14 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th February 2021Use the iteration x(n+1) = cube root of (9x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 12th February 2021A train slows steadily from 37 m/s to rest in 4 seconds. Work out its deceleration.
- 13th February 2021A cuboid measures 4 cm by 10 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th February 2021A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th February 2021A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 16th February 2021Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 17th February 2021Work out the nth term of the quadratic sequence -1, 9, 25, 47, ...
- 18th February 2021y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 19th February 2021The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 20th February 2021A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 21st February 2021On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd February 2021A block has mass 240 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd February 2021The point (-2, 4) lies on y = f(x). Write down its image on y = f(x + 3).
- 24th February 2021y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 25th February 2021In 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.
- 26th February 2021The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 27th February 2021A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 28th February 2021x = 162 and y = 79, each correct to the nearest whole number. Work out the upper bound of x - y.