Daily Practice · Higher Plus
May 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2021y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 2nd May 2021In a vector proof you find that vector PQ = 4a + 2b and vector RS = 12a + 6b. What does this show about PQ and RS?
- 3rd May 2021A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 4th May 2021On 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?
- 5th May 2021A rectangle is 26 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th May 2021Solve 8x^2 - 10x - 25 = 0.
- 7th May 2021y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 8th May 2021A cuboid measures 5 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th May 2021A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th May 2021A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 11th May 2021Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 12th May 2021f(x) = 7x - 1. Work out the inverse function f^-1(x).
- 13th May 2021y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 25.
- 14th May 2021A cuboid measures 6 cm by 9 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th May 2021A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th May 2021On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th May 2021A block has mass 310 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th May 2021Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 19th May 2021A train slows steadily from 36 m/s to rest in 5 seconds. Work out its deceleration.
- 20th May 2021The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 21st May 2021A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 22nd May 2021A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 23rd May 2021x = 146 and y = 11, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th May 2021Use the iteration x(n+1) = cube root of (6x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 25th May 2021y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 26th May 2021In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 27th May 2021The probability of winning a game is 3/4. A player expects 84 wins. How many games did they play?
- 28th May 2021On 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?
- 29th May 2021A car covers 470 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.
- 30th May 2021Work out the nth term of the quadratic sequence 6, 8, 14, 24, ...
- 31st May 2021y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.