MASH Bath: Question Bank

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS applied to integers.

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

Solving a quadratic equation of the form $ax^2+bx+c=0$.

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

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.

Find the unit vectors in the direction of four 3-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

Find the unit vectors in the direction of four 2-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other 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.

Calculate the magnitude of a 2-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j$.

Calculate the magnitude of a 2-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v1\\v2}$.

Given 3 vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, find the constants $p$, $q$ and $k$ such that $ p\mathbf a + q \mathbf b = \mathbf c$, where $k$ is an unknown component of $\mathbf c$ .

Given 3 vectors $\mathbf v$, $\mathbf a$ and $\mathbf b$, find the constants $c_1$ and $c_2$ such that $\mathbf v = c_1 \mathbf a + c_2 \mathbf b$ .

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