Daily Practice · Higher Plus
May 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2011A cuboid measures 9 cm by 10 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd May 2011A bag holds 5 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd May 2011A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 4th May 2011A rectangle is 15 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th May 2011Use the iteration x(n+1) = cube root of (8x(n) + 9) with x(0) = 1. Work out x(1) to 3 decimal places.
- 6th May 2011y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 7th May 2011A cuboid measures 13 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th May 2011A bag holds 6 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th May 2011On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th May 2011Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 11th May 2011Work out the nth term of the quadratic sequence 0, 11, 30, 57, ...
- 12th May 2011y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 13th May 2011The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 14th May 2011A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 15th May 2011A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 16th May 2011A block has mass 500 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th May 2011The point (-3, -4) lies on y = f(x). Write down its image on y = f(x) - 4.
- 18th May 2011y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 64.
- 19th May 2011In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 20th May 2011The probability of winning a game is 1/2. A player expects 14 wins. How many games did they play?
- 21st May 2011On 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?
- 22nd May 2011x = 130 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd May 2011Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 24th May 2011A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 25th May 2011In a vector proof you find that vector PQ = 2a - 6b and vector RS = 8a - 24b. What does this show about PQ and RS?
- 26th May 2011A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th May 2011A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 28th May 2011A car covers 750 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th May 2011f(x) = 6x + 3 and g(x) = 3x + 3. Work out fg(2).
- 30th May 2011y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 31st May 2011A cuboid measures 7 cm by 9 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.