Algebra 2

What this covers

• Simplifying, multiplying and adding rational expressions, then solving rational equations and checking for excluded values
• Rational exponents and radical equations, including when squaring both sides introduces false solutions
• Exponential and logarithmic functions: converting between forms, log laws, solving 3^x = 40, and compound growth and decay models
• Complex numbers — arithmetic with i, conjugates, and interpreting a negative discriminant
• Function transformations, composition, and finding and verifying inverse functions
• Arithmetic and geometric sequences and series, including explicit versus recursive rules and finite sums

Where learners get stuck

Treating log(a + b) as log a + log b

The product law log(ab) = log a + log b looks close enough that students generalise it to addition inside the argument. The habit is reinforced by distributing over parentheses everywhere else in algebra, where the function notation looks like multiplication.

Cancelling terms rather than factors in rational expressions, e.g. crossing the x out of (x + 3)/x

Earlier work with numeric fractions rewards cancelling matching symbols. Students need to see the expression as a single product of factors before anything can be removed, and that reframing rarely happens automatically.

Solving a radical or rational equation correctly but skipping the check, then reporting an extraneous root

Squaring both sides or multiplying by a denominator is not reversible — it can create solutions the original equation never had. Nothing in the algebra itself signals this, so the check has to be a deliberate final step.

What a session looks like

A typical 25-40 minute session starts with one problem you are stuck on or a diagnostic question on the week's topic. You explain your reasoning out loud; the tutor listens for the specific step that broke — a misapplied log law, a lost domain restriction — and asks targeted questions rather than giving the answer. Work is usually written on your own paper and described aloud, with the tutor pausing for you to compute. Sessions typically close with a restatement of the rule in your own words and one similar problem to try independently.

Helpful to know first

• Confident factoring of quadratics and simple higher-degree expressions
• Solving quadratic equations by factoring, completing the square and the quadratic formula
• Working with exponent rules for integer powers
• Function notation, domain and range, and reading graphs of linear and quadratic functions

Questions

What is the difference between Algebra 1 and Algebra 2?

Algebra 1 establishes linear equations, basic factoring and introductory quadratics. Algebra 2 extends to rational and radical expressions, exponential and logarithmic functions, complex numbers, sequences and series, and general function behaviour such as inverses and transformations. Most Algebra 2 topics assume the Algebra 1 manipulations are already fast.

My child understands the steps but keeps getting wrong answers on tests. What is going on?

In Algebra 2 that pattern is usually domain and verification errors rather than procedural gaps — extraneous roots from radical equations, excluded values in rational equations, or sign slips with i. Sessions target the checking step specifically, since it is the part that gets skipped under time pressure.

Do you cover logarithms from the beginning?

Yes. Logs can be started from the definition as the inverse of exponentiation, with time spent on converting between exponential and log form before touching the log laws or solving equations.

Is Algebra 2 needed for pre-calculus?

Pre-calculus assumes fluency with logarithms, rational functions, complex numbers and function composition, all of which are Algebra 2 content. Weak spots here tend to resurface in trigonometric equations and limits later.