Daily Practice · Higher Plus
March 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2021Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 2nd March 2021y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 81.
- 3rd March 2021In a vector proof you find that vector PQ = 3a + 3b and vector RS = 9a + 9b. What does this show about PQ and RS?
- 4th March 2021A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 5th March 2021On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th March 2021A car covers 820 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th March 2021f(x) = 6x - 6 and g(x) = 6x + 3. Work out fg(1).
- 8th March 2021A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 9th March 2021A cuboid measures 6 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th March 2021A 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?
- 11th March 2021A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 12th March 2021Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 13th March 2021The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 14th March 2021y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 15th March 2021A cuboid measures 4 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th March 2021A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th March 2021On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th March 2021Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 19th March 2021A quadratic sequence starts 12, 21, 36, 57. Work out the second difference, and the coefficient of n^2.
- 20th March 2021y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 21st March 2021The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 22nd March 2021A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 23rd March 2021A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 24th March 2021A rectangle is 9 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th March 2021Solve x^2 + 7x + 6 > 0.
- 26th March 2021y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 25.
- 27th March 2021In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 28th March 2021The probability of winning a game is 1/4. A player expects 15 wins. How many games did they play?
- 29th March 2021On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th March 2021Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 31st March 2021Write x^2 + 14x - 9 in the form (x + a)^2 + b.