Daily Practice · Higher Plus
February 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2023 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2023Work out the nth term of the quadratic sequence -6, -6, -4, 0, ...
- 2nd February 2023A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd February 2023A cuboid measures 13 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th February 2023A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th February 2023A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 6th February 2023A block has mass 450 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th February 2023The point (1, -5) lies on y = f(x). Write down its image on y = f(x) - 6.
- 8th February 2023y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 9th February 2023The 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.
- 10th February 2023A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 11th February 2023On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th February 2023x = 60 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th February 2023Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 14th February 2023y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 15th February 2023In 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.
- 16th February 2023The probability of winning a game is 3/4. A player expects 9 wins. How many games did they play?
- 17th February 2023A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 18th February 2023A car covers 760 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.
- 19th February 2023f(x) = 4x + 2 and g(x) = 6x + 1. Work out fg(4).
- 20th February 2023y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 36.
- 21st February 2023In a vector proof you find that vector PQ = 6a + 2b and vector RS = 24a + 8b. What does this show about PQ and RS?
- 22nd February 2023A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 23rd February 2023On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th February 2023Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 25th February 2023The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 26th February 2023A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 27th February 2023A cuboid measures 4 cm by 3 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th February 2023A 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?