Daily Practice · Higher Plus
March 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2010 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2010In a vector proof you find that vector PQ = 2a + 3b and vector RS = 10a + 15b. What does this show about PQ and RS?
- 2nd March 2010A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 3rd March 2010On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4th March 2010Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 5th March 2010Solve 10x^2 - 3x - 4 = 0.
- 6th March 2010y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 7th March 2010A cuboid measures 6 cm by 9 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th March 2010A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th March 2010A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 10th March 2010A rectangle is 25 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th March 2010f(x) = 2x + 2. Work out the inverse function f^-1(x).
- 12th March 2010y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 16.
- 13th March 2010A cuboid measures 4 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th March 2010A bag holds 5 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th March 2010On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th March 2010Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 17th March 2010Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 18th March 2010A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 19th March 2010The 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.
- 20th March 2010A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 21st March 2010A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 22nd March 2010A block has mass 670 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd March 2010Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.
- 24th March 2010y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 25th March 2010In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 26th March 2010The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 27th March 2010On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th March 2010x = 161 and y = 81, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th March 2010Work out the nth term of the quadratic sequence 3, 5, 11, 21, ...
- 30th March 2010y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 31st March 2010In a vector proof you find that vector PQ = 6a + 3b and vector RS = 18a + 9b. What does this show about PQ and RS?