High School (9-12)
High School (9-12)
Algebra Topics
Algebra I Topics
These are the foundations of algebra:
- Variables and expressions: Understanding terms like
3x + 5 - Solving equations: Finding the value of
xin equations like2x + 4 = 10 - Linear equations and graphs: Slope, intercepts, and graphing lines
- Inequalities: Solving and graphing expressions like
x - 3 > 5 - Systems of equations: Solving two equations together
- Exponents and polynomials: Rules for powers and combining like terms
- Factoring: Breaking down expressions like
x² + 5x + 6
📈 Algebra II Topics
These build on Algebra I and introduce more advanced ideas:
- Quadratic equations: Solving
ax² + bx + c = 0by factoring, completing the square, or using the quadratic formula - Functions: Understanding domain, range, and types of functions (linear, quadratic, exponential)
- Complex numbers: Working with
i, wherei² = −1 - Polynomials: Long division, synthetic division, and graphing
- Rational expressions: Simplifying and solving equations with fractions
- Radicals: Simplifying square roots and solving radical equations
- Logarithms and exponentials: Inverse relationships and solving equations like
log(x) = 2
Geometry
High school geometry focuses on reasoning, relationships, and spatial understanding. Key topics include:
- Points, lines, and planes: Understanding basic building blocks of geometry
- Angles: Types (acute, right, obtuse), angle relationships (complementary, supplementary, vertical)
- Triangles: Classification (by sides and angles), triangle congruence (SSS, SAS, ASA, AAS), Pythagorean Theorem
- Quadrilaterals and polygons: Properties of parallelograms, trapezoids, rectangles, rhombuses
- Circles: Radius, diameter, chords, arcs, central and inscribed angles
- Transformations: Translations, rotations, reflections, dilations
- Coordinate geometry: Distance formula, midpoint formula, slope, equations of lines
- Area and perimeter: Calculating for various shapes
- Volume and surface area: Prisms, cylinders, pyramids, cones, spheres
- Proofs and logic: Writing geometric proofs using deductive reasoning
Pre-Calculus Topics
Pre-Calculus bridges Algebra and Calculus. It focuses on functions, advanced algebra, and trigonometry.
Key Concepts Include:
- Functions: Domain, range, transformations, inverses
- Polynomials and rational functions: Factoring, asymptotes, end behavior
- Exponential and logarithmic functions: Properties, solving equations, applications
- Trigonometry: Unit circle, identities, graphs, inverse trig functions
- Sequences and series: Arithmetic and geometric sequences, sigma notation
- Conic sections: Parabolas, ellipses, hyperbolas
- Vectors and parametric equations
📗 Calculus Topics
Calculus explores change and motion using limits, derivatives, and integrals.
Core Ideas Include:
- Limits: Understanding how functions behave near a point
- Derivatives: Rates of change, rules (power, product, quotient, chain), applications (tangent lines, optimization)
- Integrals: Area under curves, antiderivatives, definite and indefinite integrals
- Fundamental Theorem of Calculus: Connecting derivatives and integrals
- Applications: Motion, area, volume, growth/decay models
Step-by-Step Writing Guide
Step 1: Brainstorming
Here’s a question to help you begin:
What’s a moment, challenge, or experience that changed how you see the world—or yourself?
You don’t need a dramatic story. Even small moments (like helping a sibling, failing a test, or switching schools) can be powerful if you reflect on them well.
Take a moment to think. You can jot down a few ideas or tell me one, and I’ll help you shape it into a strong essay.
Ready to brainstorm together at the Doceo Kids Portal platform?
Build Your SAT/ACT Prep Strategy
Let’s build your SAT/ACT prep strategy step by step! Since we’re in Study Mode, I’ll guide you through the key sections, skills, and practice techniques to help you feel confident and ready.
Study Mode Overview
- Step-by-step guidance for effective preparation.
- Targeted skills practice to improve test performance.
- Personalized strategies for reading, writing, and math success.
- Confidence-building techniques for exam day readiness.
What’s on the SAT and ACT?
| Section | SAT | ACT |
|---|---|---|
| Reading | Evidence-based reading | Reading comprehension |
| Writing/English | Grammar, punctuation, style | Grammar, punctuation, style |
| Math | Algebra, geometry, data analysis | Algebra, geometry, trigonometry |
| Science | ❌ No science section | ✅ Science reasoning |
| Essay (optional) | ❌ No longer offered | ✅ Optional writing section |
Study Strategies by Section
Reading
- Practice skimming for main ideas and tone
- Learn to spot inference questions and evidence-based answers
- Time yourself to improve pacing
Writing / English
- Review grammar rules: subject-verb agreement, punctuation, modifiers
- Practice editing sentences for clarity and style
- Learn common question types (e.g., transitions, word choice)
Math
- Master algebra, linear equations, and functions
- Practice geometry and data interpretation
- Use formulas efficiently and avoid calculator overuse
Science (ACT only)
- Focus on interpreting graphs, experiments, and scientific reasoning
- Practice reading quickly and identifying trends
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