Daily Practice · Higher Plus
March 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2003y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 16.
- 2nd March 2003In 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.
- 3rd March 2003The probability of winning a game is 7/10. A player expects 14 wins. How many games did they play?
- 4th March 2003On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th March 2003A rectangle is 7 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th March 2003Write 2/(x - 1) + 7/(x - 2) as a single fraction.
- 7th March 2003A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
- 8th March 2003In a vector proof you find that vector PQ = 2a + 6b and vector RS = 6a + 18b. What does this show about PQ and RS?
- 9th March 2003A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 10th March 2003A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 11th March 2003Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 12th March 2003Solve 6x^2 + x - 1 = 0.
- 13th March 2003y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 14th March 2003A cuboid measures 3 cm by 9 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th March 2003A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th March 2003On 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?
- 17th March 2003A block has mass 880 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th March 2003f(x) = 4x - 10. Work out the inverse function f^-1(x).
- 19th March 2003y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 20th March 2003A cuboid measures 10 cm by 11 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st March 2003A bag holds 3 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd March 2003A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 23rd March 2003x = 195 and y = 179, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th March 2003Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 25th March 2003y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
- 26th March 2003The 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.
- 27th March 2003A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 28th March 2003On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th March 2003A car covers 370 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 30th March 2003Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.
- 31st March 2003A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.