Daily Practice · Higher Plus
February 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2019 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2019A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 2nd February 2019A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 3rd February 2019x = 76 and y = 59, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th February 2019Write 7/(x - 1) + 3/(x + 5) as a single fraction.
- 5th February 2019y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 6th February 2019In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 7th February 2019The probability of winning a game is 2/5. A player expects 8 wins. How many games did they play?
- 8th February 2019On 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?
- 9th February 2019A car covers 830 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th February 2019Solve 9x^2 + 27x + 20 = 0.
- 11th February 2019y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 12th February 2019In a vector proof you find that vector PQ = 5a + 4b and vector RS = 10a + 8b. What does this show about PQ and RS?
- 13th February 2019A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 14th February 2019A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 15th February 2019Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 16th February 2019f(x) = 8x - 2. Work out the inverse function f^-1(x).
- 17th February 2019y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 16.
- 18th February 2019A cuboid measures 7 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th February 2019A 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?
- 20th February 2019On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st February 2019Simplify sqrt(20) + sqrt(45), giving your answer in the form a sqrt(b).
- 22nd February 2019Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 23rd February 2019A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 24th February 2019A cuboid measures 8 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th February 2019A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th February 2019A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 27th February 2019A rectangle is 16 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th February 2019Use the iteration x(n+1) = cube root of (8x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.