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Course Overview

• Subject: Mathematics A
• Semester: 01

Major Tests

Test 01

• Content: Algebra (Section 1), Functions (Section 2)

Test 02

• Content:
  • Circle geometry and radian measure (Section 3)
  • Trigonometry (Section 4)
  • Complex numbers (Section 5)
  • Volumes and surface area (Section 6)

Important Notes

• Use the course guide alongside the prescribed textbook.
• Effective note-taking and listening skills are essential.

Section One: Algebra Review

Key Concepts

• Significant Figures: Use for accuracy in non-exact numbers.
• Remainder and Factor Theorems: Essential for polynomial manipulation.
• Long Division of Polynomials: Division algorithm used to resolve polynomials.
• Completing the Square: Technique for expressing quadratics.
• Logarithms: Definitions and properties.
• Exponents and Indices: Rules governing the use of powers.
• Application of Theorems: Solving cubic equations and sketching quadratic functions.

Logarithms and Exponents

• Logarithm Definition: If $p^r = q$, then $r = log_p{q}$.
• Properties of Logarithms:
  • Product: $log<em>a{(pq)} = log</em>a{p} + log_a{q}$
  • Quotient: $log<em>a{(p/q)} = log</em>a{p} - log_a{q}$
  • Power: $log<em>a{(p^n)} = n \cdot log</em>a{p}$

Methods of Polynomial Division

• Remainder Theorem: $R = f(k)$ when $f(x)$ is divided by $x - k$.
• Factor Theorem: If $f(k) = 0$, then $x - k$ is a factor.

Completing the Square

• Transforming quadratic forms to facilitate graphical analysis and integration techniques.

Binomial Expansion

Formula

• The expansion for $(a + b)^n$ involves coefficients based on Pascal's Triangle.

Binomial Series

• Essential for functions of the form $f(x) = (1+x)^n$ and applicable in calculus for approximations.