Daily Practice · Higher Plus
February 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2024 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2024Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 2nd February 2024In an algebraic proof, how would you write an even number in terms of an integer n?
- 3rd February 2024y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 4th February 2024The 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.
- 5th February 2024A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 6th February 2024On 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?
- 7th February 2024A rectangle is 19 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th February 2024Make x the subject of 7x + 5 = y(x + 5).
- 9th February 2024y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 10th February 2024In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 11th February 2024The probability of winning a game is 4/5. A player expects 104 wins. How many games did they play?
- 12th February 2024A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 13th February 2024Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 14th February 2024Write 3/(x + 3) + 4/(x - 2) as a single fraction.
- 15th February 2024y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 16.
- 16th February 2024In a vector proof you find that vector PQ = 5a - 2b and vector RS = 15a - 6b. What does this show about PQ and RS?
- 17th February 2024A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 18th February 2024On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th February 2024A block has mass 790 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th February 2024Solve 6x^2 + 17x + 5 = 0.
- 21st February 2024A train slows steadily from 18 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd February 2024A cuboid measures 3 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd February 2024A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th February 2024A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 25th February 2024x = 49 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th February 2024f(x) = 6x - 11. Work out the inverse function f^-1(x).
- 27th February 2024y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 28th February 2024A cuboid measures 10 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th February 2024A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?