Daily Practice · Higher Plus
May 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2016x = 151 and y = 131, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd May 2016f(x) = 6x + 12. Work out the inverse function f^-1(x).
- 3rd May 2016y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 4th May 2016A cuboid measures 12 cm by 6 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th May 2016A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th May 2016On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th May 2016A car covers 660 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th May 2016Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 9th May 2016y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 10th May 2016A cuboid measures 10 cm by 11 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th May 2016A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th May 2016A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 13th May 2016Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
- 14th May 2016Use the iteration x(n+1) = cube root of (5x(n) + 6) with x(0) = 2. Work out x(1) to 3 decimal places.
- 15th May 2016y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 36.
- 16th May 2016The 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.
- 17th May 2016A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 18th May 2016On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th May 2016Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 20th May 2016Work out the nth term of the quadratic sequence 8, 19, 34, 53, ...
- 21st May 2016A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd May 2016In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 23rd May 2016The probability of winning a game is 2/5. A player expects 18 wins. How many games did they play?
- 24th May 2016A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 25th May 2016A rectangle is 26 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th May 2016The point (-1, -3) lies on y = f(x). Write down its image on y = f(-x).
- 27th May 2016y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 28th May 2016In a vector proof you find that vector PQ = 4a + 4b and vector RS = 16a + 16b. What does this show about PQ and RS?
- 29th May 2016A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 30th May 2016On 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?
- 31st May 2016Expand and simplify (8 + sqrt(6))(8 - sqrt(6)).