Daily Practice · Higher Plus
May 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2024A rectangle is 23 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd May 2024Work out the coordinates of the turning point of y = x^2 + 16x - 15.
- 3rd May 2024A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
- 4th May 2024The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 5th May 2024A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 6th May 2024A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 7th May 2024Expand and simplify (8 + sqrt(2))(8 - sqrt(2)).
- 8th May 2024Simplify (x^2 - 2x - 15)/(x - 5).
- 9th May 2024y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 10th May 2024In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 11th May 2024The probability of winning a game is 4/5. A player expects 64 wins. How many games did they play?
- 12th May 2024On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th May 2024A block has mass 300 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th May 2024In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 15th May 2024y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 16th May 2024In a vector proof you find that vector PQ = 5a - b and vector RS = 25a - 5b. What does this show about PQ and RS?
- 17th May 2024A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 18th May 2024A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 19th May 2024x = 148 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th May 2024Make x the subject of 6x + 7 = y(x + 7).
- 21st May 2024y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 9.
- 22nd May 2024A cuboid measures 7 cm by 11 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd May 2024A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th May 2024On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th May 2024A car covers 130 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th May 2024Write 2/(x + 6) + 7/(x - 4) as a single fraction.
- 27th May 2024A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 28th May 2024A cuboid measures 9 cm by 13 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th May 2024A bag holds 4 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th May 2024A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 31st May 2024Rationalise the denominator of 45/sqrt(5), giving your answer in its simplest form.