Daily Practice · Higher Plus
May 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2018A bag holds 7 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd May 2018A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 3rd May 2018Simplify sqrt(50) + sqrt(8), giving your answer in the form a sqrt(b).
- 4th May 2018Work out the nth term of the quadratic sequence 2, 10, 24, 44, ...
- 5th May 2018y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 81.
- 6th May 2018The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 7th May 2018A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 8th May 2018On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th May 2018A rectangle is 16 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th May 2018The point (1, -1) lies on y = f(x). Write down its image on y = f(x) + 4.
- 11th May 2018A train slows steadily from 12 m/s to rest in 10 seconds. Work out its deceleration.
- 12th May 2018In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 13th May 2018The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 14th May 2018A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 15th May 2018Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 16th May 2018Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 17th May 2018y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 18th May 2018In a vector proof you find that vector PQ = 3a - 6b and vector RS = 6a - 12b. What does this show about PQ and RS?
- 19th May 2018A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 20th May 2018On 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?
- 21st May 2018A block has mass 430 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd May 2018f(x) = 5x + 6 and g(x) = 2x - 2. Work out fg(0).
- 23rd May 2018y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 24th May 2018A cuboid measures 11 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th May 2018A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th May 2018A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 27th May 2018x = 75 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th May 2018The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 29th May 2018y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 9.
- 30th May 2018A cuboid measures 8 cm by 10 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st May 2018A bag holds 4 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?