Daily Practice · Higher Plus
March 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2013Work out the coordinates of the turning point of y = x^2 - 6x + 1.
- 2nd March 2013A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd March 2013The 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.
- 4th March 2013A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
- 5th March 2013A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 6th March 2013A rectangle is 17 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th March 2013Simplify (x^2 + 10x + 24)/(x + 4).
- 8th March 2013y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 9th March 2013In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 10th March 2013The probability of winning a game is 5/8. A player expects 75 wins. How many games did they play?
- 11th March 2013On 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?
- 12th March 2013Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 13th March 2013In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 14th March 2013y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 15th March 2013In a vector proof you find that vector PQ = 2a - 6b and vector RS = 10a - 30b. What does this show about PQ and RS?
- 16th March 2013A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 17th March 2013A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 18th March 2013A block has mass 570 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th March 2013Make x the subject of 6x + 7 = y(x + 7).
- 20th March 2013y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 9.
- 21st March 2013A cuboid measures 11 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd March 2013A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd March 2013On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th March 2013x = 60 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th March 2013Write 7/(x + 3) + 4/(x + 2) as a single fraction.
- 26th March 2013A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 27th March 2013A cuboid measures 12 cm by 10 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th March 2013A bag holds 6 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th March 2013A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 30th March 2013A car covers 880 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st March 2013Solve 8x^2 - 6x + 1 = 0.