Solve a pair of linear equations by writing an equivalent matrix equation.

These practice questions cover:

• resolving axial forces in a truss structure
• stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
• use of Mohr's circle for determining principal stresses for a 2D plane stress case
• calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses

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Resolving forces in a simple truss, and 2D stresses in a uniaxially loaded bar.

Solving quadratic equations using a formula

Solving quadratic equations using a formula,

Solving quadratic equations using a formula,

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Selection of Quadratic Equations to Solve

Several quadratics are given and students are asked to complete the square.

Several quadratics are given and students are asked to complete the square.

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

Several quadratics are given and students are asked to complete the square.

Solving quadratic equations using a formula,

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Two questions on solving systems of simultaneous equations.

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Several quadratics are given and students are asked to complete the square.

Finding values which satisfy an inequality.

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Solving quadratic equations using a formula,

Solving for a geometric series

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Solving inequalities that involve a quadratic and where the right-hand side is 0.

Solving inequalities that involve a quadratic and where the right-hand side is not 0. 

Solving linear equations to find the value of x.

Given a graph of some function $f(x)$ (a cubic), the student is asked to write the coordinates of the maximum and minimum points. The student then finds the maximum and minimum points of a second cubic function without using a graph, by finding the derivative, solving the quadratic equation that results from setting the derivative equal to zero, and finally testing the value of the second derivative.

Basic solving of linear equations.

Solving quadratic equations using a formula,