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8 questions using logarithms. 7 questions use logarithms to solve equations.

A simultaneous equations question with integers only

Simple trig equations with degrees

Simple trig equations with radians

Trigonometric equations with degrees

Trigonometric equations with radians

More difficult trigonometric equations with degrees

More difficult trigonometric equations with radians

Using trig identities to find solutions to equations

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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.

Straightforward solving linear equations question

Straightforward solving linear equations question.

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

A simultaneous equations question with integers only

Shows how to define variables to stop degenerate examples.

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

Find the general solution of $y''+2py'+(p^2-q^2)y=A\sin(fx)$ in the form  $A_1e^{ax}+B_1e^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral. Use initial conditions to find $A_1,B_1$.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Students enter equation and turning point

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.

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