Foundations of Mathematics and Pre-calculus 10

Unit 1: Algebra & Number

Powers with integral exponents and prime factorization — the number foundations that the rest of the course builds on.

• Powers with positive and negative exponents
• The exponent laws with numerical and variable bases
• Prime factorization, GCF, and LCM

Unit 2: Functions & Linear Relations

The heart of the course: what a function is, how linear functions behave, arithmetic sequences as linear patterns, and solving systems of linear equations.

• Is it a function? Relations and the function idea
• Function notation, domain, and range
• Connecting graphs, data, and situations

• Slope: positive, negative, zero, and undefined
• Equations of lines: slope-intercept, point-slope, and general form
• Parallel, perpendicular, horizontal, and vertical lines

• Common difference and the general term
• Connecting sequences to linear functions

• Solving systems graphically and reading the solution
• Substitution and elimination
• Systems in situational contexts

Unit 3: Polynomials: Multiplying & Factoring

Expanding products of polynomials and reversing the process by factoring — the algebra engine for everything quadratic.

• Multiplying binomials with the area model
• Products with trinomials

• Greatest common factor of a polynomial
• Factoring trinomials and the difference of squares

Unit 4: Trigonometry

The primary trigonometric ratios and their use in right-triangle problems, including indirect measurement.

• Sine, cosine, and tangent in right triangles
• Finding missing sides and angles
• Direct and indirect measurement

Unit 5: Financial Literacy

Gross and net pay: what you earn, what gets deducted, and what actually lands in the account.

• Types of income and calculating gross pay
• Deductions and net pay