MASH Bath: Question Bank

Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $a$ the subject.

Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $u$ the subject.

Rearraning the constant acceleration equation $s=ut+\frac{1}{2}at^2$ to make $a$ the subject.

Rearraning the constant acceleration equation $s=ut+\frac{1}{2}at^2$ to make $u$ the subject.

Rearraning the constant acceleration equation $v=u+at$ to make $t$ the subject.

Rearraning the constant acceleration equation $v=u+at$ to make $a$ the subject.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

Given the vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, calculate $(\mathbf a \times \mathbf b) \times \mathbf c$ and $\mathbf a \times (\mathbf b \times \mathbf c)$.

Find a perpendicular vector to a pair of vectors.

Calculate the vector product between two vectors.

Given three 3-dimensional vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, calculate the scalar product between $\mathbf a$ and $\mathbf b$, the angle between $\mathbf a$ and $\mathbf b$, and $\mathbf a (\mathbf b \cdot \mathbf c)$,

Given three 2-dimensional vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, calculate the scalar product between $\mathbf a$ and $\mathbf b$, the angle between $\mathbf a$ and $\mathbf b$, and $\mathbf a (\mathbf b \cdot \mathbf c)$,

Finding a vector when given the magnitude of the vector and a parallel vector.

Given the coordinates of three 2-dimensional points $A$, $B$ and $C$, find the vectors $\vec{AB}$, $\vec{AC}$ and $\vec{CB}$.

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.

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 $af(x)$.