The figure includes one triangle and one quadrilateral. Every angle is measured in degrees. In the triangle, the angles are marked $3b + 10$, $a + 2b$ and $2a$. In the quadrilateral, the angles are marked $8a$, $3a + 2b$, $4b - 2a$ and $b + 50$. NOT TO SCALE.
(a(i))[1]
For the triangle, demonstrate that $3a + 5b = 170$.
(a(ii))[1]
For the quadrilateral, demonstrate that $9a + 7b = 310$.
(a(iii))[3]
Solve these simultaneous equations. Show every step of your working.
(a(iv))[1]
Determine the measure of the smallest angle in the triangle.
(b)[2]
Solve $6x - 3 = -12$ for $x$.
(c)[3]
Rearrange $2(4x - y) = 5x - 3$ so that $y$ is the subject.
(d)[2]
Simplify the expression $(27x^9)^{\frac{2}{3}}$.
(e)[3]
Simplify $\frac{x^2 + 5x}{x^2 - 25}$.
Worked solution & mark scheme
This 16-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Hence, $2a+a+2b+3b+10=180 \Rightarrow 3a+5b=170$” …