Daily Practice · Higher Plus
March 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2011y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 2nd March 2011A cuboid measures 9 cm by 10 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd March 2011A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th March 2011A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 5th March 2011A car covers 440 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.
- 6th March 2011Solve x^2 - 7x + 6 < 0.
- 7th March 2011y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 9.
- 8th March 2011A cuboid measures 9 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th March 2011A bag holds 5 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th March 2011On 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?
- 11th March 2011Rationalise the denominator of 21/sqrt(3), giving your answer in its simplest form.
- 12th March 2011Write x^2 - 8x + 3 in the form (x + a)^2 + b.
- 13th March 2011A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
- 14th March 2011The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 15th March 2011A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 16th March 2011A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 17th March 2011Simplify sqrt(8) + sqrt(18), giving your answer in the form a sqrt(b).
- 18th March 2011Work out the coordinates of the turning point of y = x^2 - 2x - 3.
- 19th March 2011y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 20th March 2011In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 21st March 2011The probability of winning a game is 3/4. A player expects 21 wins. How many games did they play?
- 22nd March 2011On 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?
- 23rd March 2011A rectangle is 10 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th March 2011Simplify (x^2 - 5x - 6)/(x + 1).
- 25th March 2011y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 26th March 2011In a vector proof you find that vector PQ = 3a - 3b and vector RS = 9a - 9b. What does this show about PQ and RS?
- 27th March 2011A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 28th March 2011A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 29th March 2011Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 30th March 2011In an algebraic proof, how would you write an even number in terms of an integer n?
- 31st March 2011y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 64.