Use this as a template to create Shear and Bending Moment diagram problems.   Supports concentrated forces and moments, uniformly distributed loads, and uniformly varying loads.

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

Algebra:  Quadratic Factorisation.

              Coefficient of squared term is 1.

Straight line graph formula

Calculate reactions and shear and bending moment at a point for an overhanging beam with a constant or uniformly varying distributed load.

Shows how to use the lpad function to format a time in HH:MM format so that leading zeros are used for numbers less than 10.

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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.

Recoginising different forms of calculus notation.

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. 

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

The student is shown a circuit diagram with three logic gates. It's always in the form (a OP b) OP (b OP c).

They have to fill in a truth table for the circuit. There is a step which expands the truth table, adding a column for each of the first two gates.

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

Part 1: multiply a 3D vector by an integer scalar
Part 2: perform scalar multiplication and subtraction in one expression with two 3D vectors

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

of a random cubic spline

of a random cubic spline

of a random cubic spline

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

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

Rewrite the expression $\frac{cx+d}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$.