Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

A variety of trigonometric equations which can be solved using inverse operations.

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Homework set.  Identify zero force members and utilize special loading conditions to simplify trusses.

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Algebra:  Quadratic Factorisation.

              Coefficient of squared term is 1.

True/false question type to assess basic knowledge of confidence intervals.

Characterise the cosh function as continuous, many-to-one, even, and find the limit as x approaches 1. Part of HELM book 2.4.3.

Given a linear or a quadratic function and asked whether it is continuous. Part of HELM Book 2.4.

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

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 centroid of a shape made up of a rectangle and two triangles.

Find the centroid of a shape made from a rectangle, triangle, and circle.

HELM Book 1.1.5 exercises

Calculating the derivative of a function of the form $ax^n \ln(bx)$ using the product rule.

Calculating the derivative of a function of the form $\frac{(x-a)^2}{bx}$, finding its stationary points and determining their nature.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Solve equations involving logs and exponential functions, by using inverse operations.

Calculating several linear combinations of three 3-dimensional vectors. 

Calculating several linear combinations of three 2-dimensional vectors. 

Calculate the magnitude of a 3-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j + v_3 \mathbf k$.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

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 the position vectors of three 2-dimensional points $A$, $B$ and $C$, find the coordinates of a fourth point $D$ such that $ABCD$ forms a parallelogram. 

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.

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.

Calculating the derivative of a function of the form $(ax+b)^n$ using the chain rule.

Solve linear equations with unknowns on one. Including brackets and fractions. Solutions may require rounding.

Rewriting $\log_{10}(x)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.