Daily Practice · Higher Plus
February 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2022 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2022y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 9.
- 2nd February 2022A cuboid measures 7 cm by 13 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd February 2022A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th February 2022On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th February 2022A car covers 140 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.
- 6th February 2022Work out the coordinates of the turning point of y = x^2 + 6x + 1.
- 7th February 2022A train slows steadily from 37 m/s to rest in 4 seconds. Work out its deceleration.
- 8th February 2022A cuboid measures 8 cm by 8 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th February 2022A bag holds 3 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th February 2022A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 11th February 2022Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 12th February 2022Simplify (x^2 - 3x - 10)/(x - 5).
- 13th February 2022y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 14th February 2022The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 15th February 2022A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 16th February 2022On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th February 2022Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
- 18th February 2022In an algebraic proof, how would you write an odd number in terms of an integer n?
- 19th February 2022y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 20th February 2022In 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.
- 21st February 2022The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 22nd February 2022A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 23rd February 2022A rectangle is 17 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th February 2022Make x the subject of 8x + 4 = y(x + 4).
- 25th February 2022y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 36.
- 26th February 2022In a vector proof you find that vector PQ = 6a - 6b and vector RS = 18a - 18b. What does this show about PQ and RS?
- 27th February 2022A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 28th February 2022On 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?