Checklist with steps for: algebra, binomial, coordinate geometry, differentiation, logs, graphs, tri

Algebra

Pre-test: Evaluate simple algebraic expressions and solve for a variable.

Review the properties of exponents and radicals.

Solve linear and quadratic equations, including completing the square.

Work with inequalities and their graphical representations.

Understand and manipulate algebraic fractions and rational expressions.

Explore sequences and series, including arithmetic and geometric sequences.

Test: Solve complex algebraic problems and analyze sequences and series.

Binomial

Pre-test: Expand simple binomial expressions (e.g., (a + b)^n for small n).

Review the Binomial Theorem and its applications.

Calculate specific coefficients in binomial expansions.

Explore binomial probabilities and the concept of combinations.

Investigate the relationship between binomial coefficients and Pascal's Triangle.

Solve problems involving binomial identities and proofs.

Test: Expand and manipulate advanced binomial expressions and solve related problems.

Coordinate Geometry

Pre-test: Plot points and identify coordinates on the Cartesian plane.

Review the equation of a straight line (slope-intercept and point-slope forms).

Calculate distances between two points and find midpoints.

Analyze the equations of circles and their properties in the coordinate plane.

Understand the concept of conic sections and their equations (parabolas, ellipses).

Solve problems involving gradients and perpendicular lines.

Test: Analyze advanced coordinate geometry problems, including conics and transformations.

Differentiation

Pre-test: Identify different types of functions and basic graphical characteristics.

Review the concept of limits and continuity.

Apply differentiation rules (product, quotient, and chain rules) to polynomial functions.

Differentiate trigonometric, exponential, and logarithmic functions.

Investigate implicit differentiation and its applications.

Explore applications of differentiation: maxima, minima, and points of inflection.

Test: Differentiate complex functions and apply derivatives to optimization problems.

Logs

Pre-test: Convert between exponential and logarithmic forms correctly.

Review the laws of logarithms and apply them to simplify expressions.

Solve logarithmic equations and inequalities.

Explore the relationship between logarithmic and exponential functions.

Investigate applications of logarithmic functions in real-world contexts (e.g., pH, sound intensity).

Test: Solve advanced logarithmic problems and demonstrate a thorough understanding of logarithmic properties.

Graphs

Pre-test: Identify and classify basic functions and their graphs (linear, quadratic, etc.).

Review transformations of functions (translations, stretches, reflections).

Analyze key features of graphs, including intercepts, asymptotes, and end behavior.

Sketch and interpret graphs of polynomial and rational functions.

Investigate the concept of inverse functions and their graphical representations.

Test: Solve complex problems related to graphing functions and interpreting graphical data.

Trigonometry

Pre-test: Recall and use fundamental trigonometric ratios for right triangles.

Review the unit circle, including angles in radians and degrees.

Apply the sine, cosine, and tangent functions to solve triangles.

Explore trigonometric identities, including Pythagorean, sum, and difference identities.

Investigate the graphs of trigonometric functions and their transformations.

Apply the laws of sines and cosines to solve non-right triangles and real-world problems.

Test: Solve complex trigonometric equations and apply trigonometric concepts in various contexts.

Feel free to adjust any of the steps to better align with specific curriculum requirements or student needs!