A-Level Mathematics Question Analysis Topic: Mathematics - Algebra
Exam Questions:
1) Solve for x:
1 / (2a + b + 2x) = (1 / 2a) + (1 / b) + (1 / 2x)
2) In a circle of radius 21 cm, an arc subtends an angle of 60 degrees at the centre. Find the sum of the length of the arc and area of the sector formed by the arc (let π = 22/7)
Answers:
For A-Level Mathematics, you should know:
1) 1 / (2a + b + 3x) = (1 / 2a) + (1 / b) + (1 / 2x)
> 1 / (2x + b + 2a) - (1 - 2x) = (1 / 2a) + (1 / b) + (1 / 2x) - (1 - 2x)
> (2x - 2a - b - 2x) / 2x(2a + b + 2x) = (b +2a) / 2ab
> (-2a - b) / 2x(2a + b + 2x) = (b + 2) / 2ab
> -1 / x(2a + b + 2x) = 1 / ab
> 2x2 + bx + 2ax + ab = 0
> x(2x + b) + a(2x + b) = 0
> (2x + b)(x + a) = 0
> If 2x + b = 0, x = -b / 2
> If x + a = 0, x = -a
2) Radius = 21 cm (given)
Arc subtends angle of 60 degrees at center.
(i) Arc length = θ/360 x 2πr = 60/360 x 2πr = 22 cm
(ii) Sector area = θ/360 x πr2 = 60/360 x 22/7 x (21)2 = 231 cm2
Total sum = 22 + 231 = 253cm.
Work hard for your A-Level Mathematics examination!
End of analysis. Great!