Daily Practice · Higher Plus
March 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2006A rectangle is 24 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd March 2006Write x^2 + 2x - 5 in the form (x + a)^2 + b.
- 3rd March 2006y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 4th March 2006A cuboid measures 9 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th March 2006A bag holds 7 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th March 2006A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 7th March 2006Expand and simplify (8 + sqrt(6))(8 - sqrt(6)).
- 8th March 2006Work out the coordinates of the turning point of y = x^2 + 14x - 10.
- 9th March 2006y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 16.
- 10th March 2006The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 11th March 2006A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 12th March 2006On 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?
- 13th March 2006A block has mass 320 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th March 2006Simplify (x^2 - 2x - 24)/(x + 4).
- 15th March 2006A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 16th March 2006In 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.
- 17th March 2006The probability of winning a game is 1/4. A player expects 12 wins. How many games did they play?
- 18th March 2006A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 19th March 2006x = 95 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th March 2006In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 21st March 2006y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 22nd March 2006In a vector proof you find that vector PQ = 4a - 2b and vector RS = 16a - 8b. What does this show about PQ and RS?
- 23rd March 2006A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 24th March 2006On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th March 2006A car covers 610 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.
- 26th March 2006Make x the subject of 7x + 4 = y(x + 4).
- 27th March 2006y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 28th March 2006A cuboid measures 9 cm by 11 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th March 2006A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th March 2006A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 31st March 2006Rationalise the denominator of 33/sqrt(3), giving your answer in its simplest form.