Daily Practice · Higher Plus
May 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2017 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2017On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd May 2017Expand and simplify (8 + sqrt(2))(8 - sqrt(2)).
- 3rd May 2017Write x^2 - 4x + 14 in the form (x + a)^2 + b.
- 4th May 2017y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 5th May 2017A cuboid measures 11 cm by 9 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th May 2017A bag holds 4 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th May 2017A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 8th May 2017A block has mass 480 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th May 2017Work out the coordinates of the turning point of y = x^2 - 4x - 1.
- 10th May 2017y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 36.
- 11th May 2017The 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.
- 12th May 2017A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 13th May 2017On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th May 2017x = 73 and y = 41, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th May 2017Simplify (x^2 + 6x + 5)/(x + 5).
- 16th May 2017A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 17th May 2017In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 18th May 2017The probability of winning a game is 3/5. A player expects 72 wins. How many games did they play?
- 19th May 2017A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 20th May 2017A 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.
- 21st May 2017In an algebraic proof, how would you write an odd number in terms of an integer n?
- 22nd May 2017y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 23rd May 2017In a vector proof you find that vector PQ = 3a + 2b and vector RS = 9a + 6b. What does this show about PQ and RS?
- 24th May 2017A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 25th May 2017On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th May 2017Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
- 27th May 2017Make x the subject of 7x + 4 = y(x + 4).
- 28th May 2017y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 29th May 2017A cuboid measures 9 cm by 14 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th May 2017A bag holds 11 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st May 2017A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?