Daily Practice · Higher Plus
February 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2020 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2020In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 2nd February 2020The probability of winning a game is 1/2. A player expects 4 wins. How many games did they play?
- 3rd February 2020On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th February 2020Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
- 5th February 2020A quadratic sequence starts 0, 5, 12, 21. Work out the second difference, and the coefficient of n^2.
- 6th February 2020y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 7th February 2020In a vector proof you find that vector PQ = 6a - 5b and vector RS = 30a - 25b. What does this show about PQ and RS?
- 8th February 2020A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 9th February 2020A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 10th February 2020A block has mass 350 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th February 2020Solve x^2 + 4x < 0.
- 12th February 2020y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 4.
- 13th February 2020A cuboid measures 6 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th February 2020A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th February 2020On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th February 2020x = 64 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th February 2020Write x^2 + 6x - 11 in the form (x + a)^2 + b.
- 18th February 2020A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 19th February 2020A cuboid measures 13 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th February 2020A bag holds 3 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st February 2020A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 22nd February 2020A car covers 360 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.
- 23rd February 2020Work out the coordinates of the turning point of y = x^2 + 6x + 13.
- 24th February 2020y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 25th February 2020The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 26th February 2020A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 27th February 2020On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th February 2020Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 29th February 2020Simplify (x^2 - 36)/(x - 6).