Daily Practice · Higher Plus
May 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2022A quadratic sequence starts 6, 16, 34, 60. Work out the second difference, and the coefficient of n^2.
- 2nd May 2022y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 3rd May 2022A cuboid measures 6 cm by 5 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th May 2022A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th May 2022A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 6th May 2022Rationalise the denominator of 30/sqrt(3), giving your answer in its simplest form.
- 7th May 2022Solve x^2 + x < 0.
- 8th May 2022y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 9.
- 9th May 2022A cuboid measures 5 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th May 2022A bag holds 6 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th May 2022On 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?
- 12th May 2022Simplify sqrt(80) + sqrt(5), giving your answer in the form a sqrt(b).
- 13th May 2022Write x^2 + 2x - 4 in the form (x + a)^2 + b.
- 14th May 2022A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 15th May 2022The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 16th May 2022A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 17th May 2022A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 18th May 2022A rectangle is 27 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th May 2022Work out the coordinates of the turning point of y = x^2 - 2x - 4.
- 20th May 2022y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 21st May 2022In 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.
- 22nd May 2022The probability of winning a game is 1/2. A player expects 36 wins. How many games did they play?
- 23rd May 2022On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th May 2022Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 25th May 2022Simplify (x^2 - 5x + 6)/(x - 2).
- 26th May 2022y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 27th May 2022In a vector proof you find that vector PQ = 2a + 5b and vector RS = 10a + 25b. What does this show about PQ and RS?
- 28th May 2022A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 29th May 2022A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 30th May 2022A block has mass 660 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st May 2022In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?