Our Curriculum - Kumar Academy

Our Curriculum

Structured programs designed to build mastery, confidence, and independent thinking. Each curriculum is personalized to meet your student exactly where they are.

SAT Math Curriculum

Test Prep • 12-16 Sessions

Who It's For

Students preparing for the SAT or PSAT who want to maximize their math scores and build confidence in their problem-solving abilities.

What We Cover

  • Heart of Algebra (linear equations, systems, inequalities)
  • Problem Solving & Data Analysis (ratios, percentages, statistics)
  • Passport to Advanced Math (quadratics, exponentials, functions)
  • Additional Topics (geometry, trigonometry, complex numbers)
  • Calculator and non-calculator strategies
  • Time management and test-taking techniques
  • Common traps and how to avoid them

Our Structure

We start with a diagnostic assessment to identify strengths and weaknesses, then create a personalized learning plan. Each session focuses on targeted skill building, practice problem analysis, and strategy development. Regular practice tests track progress and build test-day confidence.

Typical Outcomes: Students typically see 50-100+ point improvements in their math section score, along with increased confidence and faster problem-solving abilities.

Algebra 1 Curriculum

High School Math • 13 Units

Who It's For

Students currently taking Algebra 1 who need help understanding concepts, improving grades, or building a strong foundation for future math courses.

Our Complete 13-Unit Curriculum

Unit 1: Foundations & Number Sense
Goal: Build algebra readiness and eliminate gaps

Order of operations, integers, absolute value, fractions, decimals, percents, prime/composite numbers, GCF/LCM, properties of real numbers, estimation

Unit 2: Variables & Algebraic Expressions
Goal: Introduce algebraic language

Variables, constants, algebraic expressions, writing expressions from words, evaluating expressions, combining like terms, coefficients, simplifying, substitution

Unit 3: Linear Equations
Goal: Solve equations confidently

One-step, two-step, and multi-step equations, variables on both sides, distribution, equations with fractions, checking solutions, special cases, absolute value equations

Unit 4: Linear Inequalities
Goal: Understand and graph solution sets

Inequality symbols, one-step and multi-step inequalities, compound inequalities (AND/OR), graphing on number lines, interval notation, absolute value inequalities, word problems

Unit 5: Graphing Linear Equations
Goal: Connect equations to graphs

Coordinate plane, ordered pairs, plotting points, intercepts, slope (rise over run, types), slope-intercept form, graphing methods, writing equations, parallel and perpendicular lines, scatter plots, line of best fit

Unit 6: Systems of Linear Equations
Goal: Solve real-world problems with multiple variables

Solving by graphing, substitution, and elimination; special cases; word problems; interpreting solutions

Unit 6b: Direct & Inverse Variation
Goal: Understand proportional and inversely proportional relationships

Direct variation (y = kx), inverse variation (y = k/x), constant of variation, graphing, distinguishing from tables and graphs, real-world applications

Unit 7: Exponents & Powers
Goal: Build exponent fluency

Exponent notation, laws of exponents (product, quotient, power rules), zero and negative exponents, scientific notation, operations, real-world applications

Unit 8: Polynomials
Goal: Understand polynomial structure

Monomials, binomials, trinomials, degree and classification, adding/subtracting polynomials, multiplying (distributive, FOIL), simplifying

Unit 9: Factoring
Goal: Break expressions apart

Factoring out GCF, factoring trinomials (a = 1 and a ≠ 1), difference of squares, perfect square trinomials, factoring by grouping

Unit 10: Quadratic Equations
Goal: Solve second-degree equations

Standard form, solving by factoring, square roots, completing the square, quadratic formula, discriminant, real vs imaginary solutions, word problems

Unit 11: Functions & Relations
Goal: Prepare for Algebra 2

Definition of function, input-output, function notation, evaluating functions, domain and range, vertical line test, real-world examples

Unit 11b: Exponential Functions
Goal: Introduce exponential growth and decay

Exponential function form (y = ab^x), distinguishing from linear functions, graphing, growth vs decay, population growth, compound interest (intro), geometric sequences as exponential functions

Unit 12: Statistics & Data
Goal: Apply algebra to real situations and interpret data

Word problems, linear modeling, scatter plots, line of best fit, linear regression, measures of center, measures of spread, normal distribution (intro), z-scores (intro), box-and-whisker plots and histograms

Our Structure

We align our tutoring with your student's current coursework and teacher's curriculum. Sessions focus on understanding concepts deeply, not just memorizing procedures. We work ahead when possible and provide targeted support for tests and challenging units.

Typical Outcomes: Students develop strong algebraic thinking skills, improved problem-solving confidence, and typically see grade improvements of 1-2 letter grades.

Geometry Curriculum

High School Math • 14 Units

Who It's For

Students currently taking Geometry who want to build mastery in proofs, spatial reasoning, and measurement - or who need help connecting geometric concepts to algebra.

Our Complete 14-Unit Curriculum

Unit 1: Foundations of Geometry
Goal: Establish the vocabulary, notation, and tools every later unit builds on

Points, lines, planes, segments, rays, angles, angle pair relationships, segment and angle bisectors, midpoint and distance formulas, basic constructions

Unit 2: Parallel & Perpendicular Lines
Goal: Identify angle relationships formed by parallel lines

Parallel lines and transversals, corresponding/alternate interior/alternate exterior/co-interior angles, proving lines parallel, slopes of parallel and perpendicular lines

Unit 3: Logic and Proof
Goal: Develop reasoning skills for formal geometric proofs

Inductive and deductive reasoning, conditional statements, biconditional statements, Laws of Detachment and Syllogism, two-column proofs, paragraph proofs

Unit 4: Transformations
Goal: Understand rigid motions and dilations

Translations, reflections, rotations, dilations, rigid motions and preserved properties, compositions of transformations, line and rotational symmetry

Unit 5: Triangle Congruence
Goal: Prove triangles congruent and apply congruence

Triangle angle sum and exterior angle theorems, congruence criteria (SSS, SAS, ASA, AAS, HL), congruence proofs, CPCTC, isosceles and equilateral triangle theorems

Unit 6: Triangle Relationships
Goal: Explore special segments, points, and inequalities within triangles

Midsegment theorem, perpendicular bisectors, angle bisectors, medians, altitudes, points of concurrency, triangle inequality theorem

Unit 7: Quadrilaterals & Polygons
Goal: Classify and apply properties of quadrilaterals

Interior and exterior angle sums, properties of parallelograms, special parallelograms (rectangles, rhombuses, squares), trapezoids, kites

Unit 8: Area and Perimeter
Goal: Calculate area and perimeter of 2D figures

Perimeter of polygons, area formulas, composite figures, area on the coordinate plane, geometric probability

Unit 9: Similarity
Goal: Define and apply similarity transformations

Ratios and proportions, similar figures and scale factors, triangle similarity criteria (AA, SSS, SAS), Triangle Proportionality Theorem, indirect measurement

Unit 10: Right Triangles & Trigonometry
Goal: Solve right triangles using trig ratios

Pythagorean Theorem, special right triangles (45-45-90, 30-60-90), sine/cosine/tangent (SOH-CAH-TOA), angles of elevation and depression

Unit 11: Circles
Goal: Apply theorems about circles, arcs, and angles

Parts of a circle, central and inscribed angles, chord/secant/tangent relationships, arc length, sector area, equation of a circle

Unit 12: Coordinate Geometry
Goal: Use algebraic methods to prove geometric theorems

Slope, distance, and midpoint as proof tools, proving properties of triangles and quadrilaterals on a coordinate plane

Unit 13: Surface Area & Volume
Goal: Calculate surface area and volume of 3D figures

Prisms, cylinders, pyramids, cones, spheres, lateral vs total surface area, volume formulas, similar solids

Unit 14: Probability
Goal: Apply probability concepts to real-world problems

Theoretical and experimental probability, geometric probability, compound probability, conditional probability, permutations and combinations

Our Structure

Our Geometry curriculum is aligned with the Common Core State Standards. We emphasize both conceptual understanding and proof-writing skills, helping students develop the logical reasoning that carries through every future math course.

Typical Outcomes: Students build strong spatial reasoning, master geometric proof-writing, and develop the logical thinking skills needed for Algebra 2, Pre-Calculus, and standardized tests.

Algebra 2 Curriculum

High School Math • 10 Units

Who It's For

Students taking Algebra 2 who want to master advanced algebraic concepts, prepare for Pre-Calculus, or strengthen their mathematical foundation for college.

Our Complete 10-Unit Curriculum

Unit 13: Advanced Linear Equations & Inequalities
Goal: Extend linear reasoning

Absolute value equations and inequalities, piecewise functions, systems of inequalities, linear programming

Unit 14: Advanced Functions
Goal: Deepen function understanding

Advanced function notation, domain and range, transformations, parent functions, inverse functions, composition of functions

Unit 15: Quadratic Functions & Complex Solutions
Goal: Analyze parabolas and solve quadratics including complex solutions

Vertex, standard, and factored forms, completing the square, complex numbers, complex solutions, quadratic regression

Unit 16: Polynomial Functions
Goal: Generalize polynomial behavior

Higher-degree polynomials, end behavior, zeros and multiplicity, synthetic division, remainder and factor theorems

Unit 17: Rational Expressions & Functions
Goal: Handle fractions with variables

Simplifying, multiplying, dividing, adding/subtracting rational expressions, rational equations, graphing rational functions, asymptotes

Unit 18: Radical Expressions, Equations & Functions
Goal: Work with roots and graph radical functions

nth roots, simplifying radicals, rational exponents, radical equations and extraneous solutions, graphing radical functions

Unit 19: Exponential & Logarithmic Functions
Goal: Model growth and decay

Graphing exponential functions, properties of logarithms, natural log and base e, solving exponential and logarithmic equations, compound interest, half-life

Unit 20: Sequences & Series
Goal: Identify numerical patterns

Arithmetic and geometric sequences, explicit and recursive formulas, arithmetic and geometric series, summation notation, binomial theorem

Unit 21: Probability & Statistics
Goal: Interpret data mathematically

Normal distribution, z-scores, conditional probability, permutations, combinations, binomial probability, two-way tables

Unit 22: Comprehensive Review & Applications
Goal: Synthesize all algebra concepts

Mixed problem solving, multi-topic word problems, function modeling, exam-style questions, Algebra 1 + Algebra 2 integration

Our Structure

We provide comprehensive support aligned with your student's class, focusing on the "why" behind the math. Our tutors help students see connections between concepts and develop the analytical thinking needed for higher-level math courses.

Typical Outcomes: Students build confidence in complex problem-solving, develop strong preparation for Pre-Calculus and AP math courses, and typically improve grades significantly.

Pre-Calculus Curriculum

High School Math • 11 Units

Who It's For

Students currently taking Pre-Calculus who want to build mastery in advanced functions, trigonometry, and mathematical reasoning in preparation for Calculus and college-level STEM courses.

Our Complete 11-Unit Curriculum

Unit 0: Fundamental Skills Review
Goal: Ensure algebraic fluency before entering function-heavy content

Laws of exponents, polynomial operations, factoring, rational expressions, radicals and rational exponents, complex numbers review, solving equations and inequalities

Unit 1: Functions and Their Graphs
Goal: Build the function foundation every later unit depends on

Domain and range, function notation, piecewise functions, transformations, even and odd functions, composition, inverse functions, continuity, end behavior

Unit 2: Polynomial and Rational Functions
Goal: Analyze and graph polynomial and rational functions

Polynomial graphs and end behavior, zeros and multiplicity, synthetic division, Fundamental Theorem of Algebra, rational functions, asymptotes, holes

Unit 3: Exponential and Logarithmic Functions
Goal: Model growth and decay

Exponential growth and decay, the number e, properties of logarithms, solving exponential and logarithmic equations, compound interest, logistic growth

Unit 4: Trigonometry - The Unit Circle
Goal: Define and evaluate all six trig functions

Radians and degrees, the unit circle, all six trig functions, reference angles, inverse trig functions, right triangle trig, angles of elevation and depression

Unit 5: Trigonometric Graphs and Identities
Goal: Graph trig functions, prove identities, solve trig equations

Graphing sine, cosine, tangent, Pythagorean/reciprocal/quotient identities, sum/difference and double-angle formulas, proving identities, Law of Sines, Law of Cosines

Unit 6: Polar and Parametric Functions
Goal: Represent curves using polar and parametric forms

Polar coordinate system, converting between polar and rectangular coordinates, graphing polar curves, parametric equations

Unit 7: Conic Sections
Goal: Identify, graph, and write equations for all four conic sections

Circles, parabolas, ellipses, hyperbolas, completing the square to identify conics, graphing translated conics

Unit 8: Sequences and Series
Goal: Evaluate and sum arithmetic and geometric sequences

Arithmetic and geometric sequences, summation notation, series, infinite geometric series and convergence, binomial theorem

Unit 9: Limits - Bridge to Calculus
Goal: Develop intuitive and algebraic understanding of limits

Informal definition of a limit, estimating from graphs and tables, one-sided limits, continuity, algebraic techniques, tangent lines, intro to derivatives

Unit 10: Vectors (Optional)
Goal: Represent and operate with vectors

Component form, magnitude and direction, vector operations, dot products, orthogonal vectors, force and work applications

Unit 11: Systems of Equations & Matrices (Optional)
Goal: Solve multi-variable systems and perform matrix operations

Three-variable systems, matrix operations, determinants, inverse matrices, Gaussian elimination, Cramer's Rule

Our Structure

Our Pre-Calculus curriculum is aligned with College Board AP Precalculus, Khan Academy, and standard U.S. scope and sequence. We focus on building deep understanding of functions so students walk into Calculus fully prepared and confident.

Typical Outcomes: Students develop strong conceptual understanding of advanced functions and trigonometry, master the algebraic fluency required for Calculus, and build the analytical thinking skills needed for AP and college-level STEM coursework.

SAT English/Reading Curriculum

Test Prep • 12-16 Sessions

Who It's For

Students preparing for the SAT or PSAT who want to improve their Reading and Writing scores through strategic practice and skill development.

What We Cover

  • Reading comprehension strategies for all passage types
  • Evidence-based reading and analysis
  • Grammar and usage rules (most commonly tested)
  • Sentence structure and punctuation
  • Vocabulary in context
  • Command of evidence questions
  • Author's craft and rhetorical analysis
  • Time management and pacing strategies

Our Structure

Beginning with a diagnostic assessment, we identify specific weaknesses and create a targeted improvement plan. Sessions combine strategy instruction with focused practice, emphasizing pattern recognition and systematic approaches to different question types.

Typical Outcomes: Students typically see 40-80+ point improvements in their Evidence-Based Reading and Writing score, with increased reading speed and accuracy.

English & Writing Support

Academic Support • Customized

Who It's For

Students needing help with school English assignments, essay writing, reading comprehension, literary analysis, or general writing skills improvement.

What We Cover

  • Essay planning and structure
  • Thesis development and argumentation
  • Literary analysis and close reading
  • Grammar, style, and mechanics
  • Research skills and citation
  • Revision and editing strategies
  • Creative writing techniques
  • Reading comprehension for complex texts

Our Structure

This is our most flexible program, customized entirely to your student's current coursework and needs. We provide assignment support, essay feedback, test preparation, and skill-building based on what will help your student most.

Typical Outcomes: Students develop stronger writing voices, improved analytical reading skills, better grades on essays and assignments, and increased confidence in English class.

College Readiness Program

College Prep • 17-31 Sessions

Who It's For

High school juniors and seniors who want a structured, personalized approach to the college application process - from building a college list to submitting every application with confidence. This program is built for students who need more than a checklist. They need someone guiding them through every decision.

How It Works

The College Readiness Program uses the same session bundles as our tutoring programs. The parent chooses a bundle, and together we allocate sessions across the modules that matter most to your student. Some students move through a module in one session. Others need two or three. You decide what your student needs - we make sure every session counts.

The Program - 12 Modules Across 5 Phases

Phase 1: Foundation
Module 1 - Student Profile & Goal Setting | 1-2 sessions

We review your student's GPA, test scores, course rigor, and extracurriculars. We identify target majors, school types, and what makes your student's story unique. This becomes the foundation for every other decision in the process.

Module 2 - College List Building | 1-3 sessions

We build a balanced list of 10-15 schools across reach, target, and likely tiers - factoring in major, location, campus culture, financial fit, and updated test score requirements for the current cycle.

Module 3 - Test Prep Planning | 1-2 sessions

We assess current scores, set realistic target scores, choose between the SAT and ACT, and build a test schedule that works around application deadlines. Test prep sessions are handled by our SAT tutors within your existing bundle.

Phase 2: Application Strategy
Module 4 - Application Timeline & Deadlines | 1 session

We map every deadline across your student's full school list - Common App, FAFSA, CSS Profile, EA/ED, and scholarship deadlines - and build a week-by-week action calendar from August through January.

Module 5 - Extracurricular Positioning | 1-2 sessions

We help your student present their activities in the strongest possible light, write the Common App activities section, and develop a narrative strategy that reflects who they actually are.

Module 6 - Recommendation Letter Strategy | 1 session

We identify the right recommenders, help your student write a brag sheet to give to teachers, and brief them on what themes to reinforce. Strong letters don't happen by accident.

Phase 3: Essays
Module 7 - Common App Personal Statement | 2-4 sessions

The most important essay in the application. We brainstorm topics, choose the strongest one, and guide your student through drafting and multiple rounds of revision. Essay sessions are led by our English tutors, with strategic oversight from your advisor.

Module 8 - Supplemental Essays | 3-8 sessions

Every school on the list has additional prompts - "Why us?", "Why this major?", short-answer questions. We draft and revise each one, and strategically reuse strong writing across schools wherever possible. Session count depends on school list size.

Phase 4: Financial Aid
Module 9 - Financial Aid & Scholarship Guidance | 1-2 sessions

We walk families through FAFSA and CSS Profile requirements, identify which schools require which forms, surface merit scholarship opportunities at target schools, and build a tracker for external scholarships. Filing early is one of the most impactful things a family can do.

Phase 5: Final Preparation
Module 10 - Interview Prep | 1-2 sessions

We identify which schools offer or require alumni interviews, practice the most common questions, and run a full mock interview with detailed feedback.

Module 11 - Application Review & Submission | 1-2 sessions

Final review of every application before it goes out - essays correctly assigned, materials submitted, test scores sent. Nothing gets missed.

Module 12 - Decision & Next Steps | 1-2 sessions

When decisions arrive, we help your student compare financial aid offers, write waitlist appeal letters if needed, and make a confident final choice.

Who Delivers It

Your student works with a dedicated advisor for strategy and planning sessions, and with our English tutors for all essay drafting and revision. Every session is logged and reported to the parent just like our tutoring sessions - no surprises, full visibility.

Typical Outcomes: Students complete every application organized, on time, and with essays that genuinely sound like them. Parents stay informed at every step without having to chase anyone down.

Personalized to Your Student

While we have structured curricula for each subject, every student's journey is unique. We adapt our approach based on diagnostic assessments, learning style, and individual goals. Some students move faster through certain topics, while others need more time - and that's exactly how it should be. Our tutors meet your student where they are and help them grow at their own pace.

Ready to Get Started?

Schedule a free consultation to discuss your student's needs and find the perfect curriculum match.

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