Welcome to Algebra Assessment Training
Course Duration: 35–45 minutes
Algebra is the everyday math of low-voltage work. Solving Ohm's Law for an unknown current, estimating cable footage and cost, sizing a power budget, and reading a voltage-drop chart all rely on the same handful of skills: isolating a variable, evaluating a formula, working with exponents, and reading a straight-line relationship. This course reviews those skills in six short sections, each followed by a knowledge check, and ends with a 10-question final assessment.
What You'll Learn:
- Solve one- and two-step linear equations using inverse operations
- Solve quadratic equations by factoring and by taking square roots
- Use function notation and evaluate a function for a given input
- Apply the product, power, and quotient rules for exponents
- Solve a system of two equations by substitution or elimination
- Identify slope and y-intercept and calculate slope from two points
Course Structure
- Linear Equations
- Quadratic Equations
- Functions
- Exponents and Powers
- Systems of Equations
- Slope-Intercept Form
- Final Assessment — 10 questions, 80% to pass
Each knowledge check gives you two attempts. You will enter your name and email just before you submit the final assessment; your results are then emailed automatically to the training administrator, with a copy to you.
Section 1: Linear Equations
A linear equation is an equation in which the variable appears only to the first power — no x², no √x. Examples are 2x + 5 = 13 and V = I × R when you are solving for one of the letters. Every linear equation in one variable has exactly one solution (unless it simplifies to something always true or never true).
The balance principle
An equation is a balance: whatever you do to one side, you must do to the other. To solve, you undo the operations around the variable using inverse operations, working in the reverse order of operations:
- Simplify each side (distribute, combine like terms).
- Move variable terms to one side and constants to the other by adding or subtracting.
- Divide (or multiply) to leave the variable by itself.
- Check by substituting your answer back into the original equation.
When the variable appears on both sides, collect it on one side first:
Section 2: Quadratic Equations
A quadratic equation has the variable squared as its highest power. Its standard form is ax² + bx + c = 0, where a ≠ 0. Unlike a linear equation, a quadratic can have two solutions, one repeated solution, or no real solution.
Method 1 — Factoring and the zero-product property
If two numbers multiply to zero, at least one of them must be zero. So if you can write the quadratic as a product of two factors, set each factor equal to zero. For x² + bx + c, look for two numbers that multiply to c and add to b.
Method 2 — Taking the square root
When there is no x term, isolate x² and take the square root of both sides. Remember that both a positive and a negative number square to the same value, so the answer carries a ±.
Method 3 — The quadratic formula
Any quadratic can be solved with x = (−b ± √(b² − 4ac)) ÷ 2a. Factoring is faster when it works; the formula always works.
Section 3: Functions
A function is a rule that assigns exactly one output to each input. We write it with function notation: f(x) = 2x + 3 reads "f of x equals two x plus three." The letter in parentheses is the input; f(x) is the output. Note that f(x) does not mean f times x.
Evaluating a function
To evaluate, replace every x in the rule with the input value — in parentheses — and simplify using the order of operations.
Watch the negatives
Always wrap a negative input in parentheses before squaring. (−3)² = 9, but −3² = −9 because the exponent is applied before the negative sign.
Domain and range
The domain is the set of allowed inputs; the range is the set of outputs the function can produce. A function cannot divide by zero, and (with real numbers) cannot take the square root of a negative.
Section 4: Exponents and Powers
An exponent tells you how many times to multiply the base by itself: 2⁴ = 2 × 2 × 2 × 2 = 16. A small set of rules lets you simplify expressions with exponents without multiplying everything out.
| Rule | Pattern | Example |
|---|---|---|
| Product rule | aᵐ × aⁿ = aᵐ⁺ⁿ | 3² × 3⁴ = 3⁶ |
| Quotient rule | aᵐ ÷ aⁿ = aᵐ⁻ⁿ | 7⁵ ÷ 7² = 7³ |
| Power rule | (aᵐ)ⁿ = aᵐˣⁿ | (x²)⁴ = x⁸ |
| Zero exponent | a⁰ = 1 (a ≠ 0) | 9⁰ = 1 |
| Negative exponent | a⁻ⁿ = 1 ÷ aⁿ | 10⁻³ = 0.001 |
The product and quotient rules only apply when the bases are the same. When terms have coefficients, multiply the coefficients and add the exponents of like bases separately:
Section 5: Systems of Equations
A system of equations is two (or more) equations that share the same unknowns. The solution is the pair of values that makes both equations true at the same time — graphically, the point where the two lines cross.
Method 1 — Substitution
Solve one equation for a variable, then substitute that expression into the other equation. This works best when one variable is already alone or has a coefficient of 1.
Method 2 — Elimination
Add or subtract the equations so that one variable cancels. If no variable cancels directly, multiply one equation by a constant first.
Always check the pair in both original equations.
Section 6: Slope-Intercept Form
Every non-vertical straight line can be written in slope-intercept form: y = mx + b. The two numbers tell you everything about the line:
- m — the slope: how much y changes for each 1-unit increase in x ("rise over run"). Positive slopes rise left to right; negative slopes fall.
- b — the y-intercept: the value of y where the line crosses the y-axis, i.e. the value of y when x = 0.
Slope from two points
Given points (x₁, y₁) and (x₂, y₂), the slope is the change in y divided by the change in x: m = (y₂ − y₁) ÷ (x₂ − x₁). Subtract in the same order top and bottom.
If the equation is not already in y = mx + b form, solve it for y first. For example, 2x + y = 7 becomes y = −2x + 7, so the slope is −2 and the intercept is 7.
Final Assessment
Answer all 10 questions. You need 80% to pass. Enter your name and email below the questions, then submit.
Your Information
When you submit, your results are emailed automatically to the training administrator, and a copy is sent to the email address you enter here.
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