MASH Bath: Question Bank

Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are applied at different angles.

Given two side-lengths and an angle of a triangle, use the sine rule to calculate an unknown angle.

Calculating a section of a sector of a circle when given the arc length and angle of the sector of the circle. This question requires the use of the formulas to find the area of a sector of a circle and to find the area of a triangle. 

Finding the area of a circle when given the arc length and angle of a sector of the circle.

Finding the radius of a circle when given the arc length and angle of a sector of the circle.

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\cos(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\cos(\theta)-B\sin(\theta)$ to $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\sin(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Solving $\sin(3x)=\sin(x)$ for $x\in \left(0,\frac{\pi}{2}\right)$.

Solving $\sin(2x)-\tan(x)=0$ for $x\in \left(0,\frac{\pi}{2}\right)$.

Solving $\sin(nx)=a$ for $x\in (0,\pi)$, where $n$ is an integer and $a\in(0,1)$.

Simplifying the trigonometric expression $\frac{\sin^2(x)}{1\pm \cos(x)}$ using the trigonometric identity $\sin^2(x)+\cos^2(x)=1$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $af(x)$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $af(x)$.

Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $af(x)$.

Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $nf(x)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $af(x)$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(x)+a$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $f(x)+a$.

Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $f(x)+a$.

Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $f(x)+n$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(x)+a$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(ax)$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $f(ax)$.

Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $f(ax)$.

Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $f(nx)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(ax)$.