**Example Problems**

Below, you will find links to questions, organized by subject, that we have been asked by students along with our responses. These are excerpts from our activity on social media channels, primarily YouTube and Yahoo! Answers, as well as our responses to direct questions to us or our blog.

**Pre-Algebra**

- How to convert from square inches to square centimeters, given only the conversion factor for inches to centimeters.
- How to multiply and divide fractions.

**Algebra**

- How to use the order of operations to evaluate an expression.
- How to evaluate an expression in one variable, given the value of the variable.
- How to combine like radicals to simplify radical expressions.
- A talk-through of how to solve multi-step linear equations in one variable.
- Multi-step linear equations in one variable – How to determine when there is no solution.
- How to solve and how to check your work in computationally complex algebra word problems involving fractions.
- How to solve word problems that involve finding consecutive numbers, odd numbers or even numbers.
- How to solve D=RT word problems.
- How to find the equation of the line passing through a point and perpendicular to another line.
- How to find the point on a line closest to a given point that is not on the line.
- How to find the equation of a perpendicular line given the equation of a line.
- How to complete-the-square to simplify expressions.
- How to factor quadratic expressions by splitting the middle term (Example 1).
- How to factor quadratic expressions by splitting the middle term (Example 2: Video walkthrough).
- How to solve quadratic equations, and when and how to use the factoring method.
- When you can use the quadratic equation to solve certain quartic (4th degree polynomial) equations.
- How to find the vertex and axis of symmetry for a parabola whose equation is given in vertex form.
- How to find the vertex and focus of a parabola in the form x = ay².
- How to determine if two functions are inverses.
- Graphing functions – How to determine if you have enough information.

**Geometry**

- How to calculate the area of an equilateral triangle, given its height.
- How to use the areas of two regular polygons to find the ratio of similarity and ratio of perimeters of the polygons.

**Pre-Calculus**

- What the Re(z) and Im(z) notations mean when working with complex numbers.
- Sequences – Constant Sequences. How to prove that a constant sequence is both arithmetic and geometric.
- Proving that two curves in the coordinate plane always intersect.
- How to do a proof by induction and why they work.
- What compound interest is and how to calculate it.

**Calculus**

- How to prove that the limit of a function exists using an Epsilon-Delta proof.
- How to find the equation of the tangent line to a parabola at a given point.
- Calculate definite integrals using u-substitutions and check using online Wolfram integral calculator.
- Calculus 2 Question: How to evaluate an indefinite integral with integrand that involve exponential functions.
- Vector Algebra: How to find the magnitude of a vector expression involving sums and differences.

**Special Topics**