Daily Practice · Higher Plus
March 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2023A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 2nd March 2023Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 3rd March 2023A quadratic sequence starts 3, 12, 29, 54. Work out the second difference, and the coefficient of n^2.
- 4th March 2023y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 5th March 2023A cuboid measures 13 cm by 5 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th March 2023A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th March 2023On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 8th March 2023A rectangle is 28 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th March 2023Solve x^2 + x - 2 > 0.
- 10th March 2023y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 11th March 2023The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 12th March 2023A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 13th March 2023A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 14th March 2023Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 15th March 2023Write x^2 + 6x + 2 in the form (x + a)^2 + b.
- 16th March 2023y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 81.
- 17th March 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.
- 18th March 2023The probability of winning a game is 3/5. A player expects 78 wins. How many games did they play?
- 19th March 2023On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th March 2023A block has mass 410 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st March 2023Work out the coordinates of the turning point of y = x^2 + 12x + 2.
- 22nd March 2023A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 23rd March 2023In a vector proof you find that vector PQ = 3a + 3b and vector RS = 6a + 6b. What does this show about PQ and RS?
- 24th March 2023A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 25th March 2023A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 26th March 2023x = 176 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th March 2023Simplify (x^2 + 4x - 5)/(x - 1).
- 28th March 2023y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 29th March 2023A cuboid measures 6 cm by 10 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th March 2023A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st March 2023On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?