Daily Practice · Higher Plus
May 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2023A block has mass 780 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd May 2023Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 3rd May 2023y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 81.
- 4th May 2023A cuboid measures 11 cm by 7 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th May 2023A bag holds 5 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th May 2023On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th May 2023x = 53 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th May 2023Use the iteration x(n+1) = cube root of (3x(n) + 7) with x(0) = 4. Work out x(1) to 3 decimal places.
- 9th May 2023A train slows steadily from 17 m/s to rest in 8 seconds. Work out its deceleration.
- 10th May 2023The 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.
- 11th May 2023A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 12th May 2023A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 13th May 2023A car covers 900 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th May 2023Work out the nth term of the quadratic sequence -4, -1, 4, 11, ...
- 15th May 2023y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 16th May 2023In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 17th May 2023The probability of winning a game is 3/4. A player expects 9 wins. How many games did they play?
- 18th May 2023On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th May 2023Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.
- 20th May 2023The point (0, -1) lies on y = f(x). Write down its image on y = f(x) - 4.
- 21st May 2023y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 22nd May 2023In a vector proof you find that vector PQ = a - 6b and vector RS = 2a - 12b. What does this show about PQ and RS?
- 23rd May 2023A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 24th May 2023A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 25th May 2023Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
- 26th May 2023Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 27th May 2023y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 81.
- 28th May 2023A cuboid measures 9 cm by 3 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th May 2023A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th May 2023On 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?
- 31st May 2023A rectangle is 5 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.