Daily Practice · Higher Plus
May 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2019The 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.
- 2nd May 2019A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 3rd May 2019On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th May 2019A car covers 680 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.
- 5th May 2019In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 6th May 2019A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 7th May 2019In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 8th May 2019The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 9th May 2019A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 10th May 2019Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 11th May 2019Make x the subject of 6x + 2 = y(x + 2).
- 12th May 2019y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 13th May 2019In a vector proof you find that vector PQ = 4a + b and vector RS = 12a + 3b. What does this show about PQ and RS?
- 14th May 2019A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 15th May 2019On 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?
- 16th May 2019Simplify sqrt(20) + sqrt(125), giving your answer in the form a sqrt(b).
- 17th May 2019Write 5/(x + 6) + 7/(x - 5) as a single fraction.
- 18th May 2019y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 19th May 2019A cuboid measures 8 cm by 5 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th May 2019A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st May 2019A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 22nd May 2019A rectangle is 8 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd May 2019Solve 8x^2 + 10x + 3 = 0.
- 24th May 2019y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 16.
- 25th May 2019A cuboid measures 9 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th May 2019A bag holds 4 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th May 2019On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th May 2019Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 29th May 2019f(x) = 8x + 4. Work out the inverse function f^-1(x).
- 30th May 2019A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 31st May 2019The 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.