Daily Practice · Higher Plus
March 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2024On 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?
- 2nd March 2024A car covers 790 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.
- 3rd March 2024Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
- 4th March 2024y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 5th March 2024The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 6th March 2024A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 7th March 2024A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 8th March 2024Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 9th March 2024Use the iteration x(n+1) = cube root of (3x(n) + 5) with x(0) = 1. Work out x(1) to 3 decimal places.
- 10th March 2024y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 64.
- 11th March 2024In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 12th March 2024The probability of winning a game is 7/8. A player expects 42 wins. How many games did they play?
- 13th March 2024On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th March 2024Simplify sqrt(45) + sqrt(245), giving your answer in the form a sqrt(b).
- 15th March 2024Work out the nth term of the quadratic sequence 3, 19, 43, 75, ...
- 16th March 2024A train slows steadily from 21 m/s to rest in 4 seconds. Work out its deceleration.
- 17th March 2024In a vector proof you find that vector PQ = 4a + 6b and vector RS = 12a + 18b. What does this show about PQ and RS?
- 18th March 2024A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 19th March 2024A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 20th March 2024A rectangle is 20 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st March 2024The point (1, -5) lies on y = f(x). Write down its image on y = f(x + 4).
- 22nd March 2024y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 23rd March 2024A cuboid measures 9 cm by 4 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th March 2024A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th March 2024On 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?
- 26th March 2024Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 27th March 2024Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 28th March 2024y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 29th March 2024A cuboid measures 7 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th March 2024A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st March 2024A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?