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Simplifying indices.

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This shows how to use variable name annotations inside \simplify to display a 3D vector in terms of the standard unit vectors $\boldsymbol{i}$, $\boldsymbol{j}$, $\boldsymbol{k}$

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Shows how to create a simplified JME subexpression, and substitute it into a string variable.

Two part question:

a) Simplify commutative elements

b) Solve 1-step equation

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

This question was modified from a Newcastle University question. Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students need to work out a ratio and simplify it.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$.

There is a video included explaining the rules of logarithms by going through simplification of logs of numbers rather than algebraic expressions.

Algebraic manipulation/simplification.

Simplify $\displaystyle \frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.

Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$.

Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.

Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.

Express $\displaystyle ax+b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{x + b} +\frac{c}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{x + b} +\frac{cx+d}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Simplifying equations/collecting like terms