Algebra I, Algebra II, and Geometry

Algebra 1 – Scheme of Work

Level: Grade 8 or 9 (Algebra 1)
Duration: Full Academic Year (3 Terms / 40 Weeks)
Prerequisites: Pre-Algebra / Middle School Math

🔹 Term 1: Foundations of Algebra (Weeks 1–13)

Weeks 1–2: Algebraic Thinking & Expressions

• Variables, constants, coefficients

• Algebraic expressions: identifying and simplifying

• Order of operations (PEMDAS)

• Substitution and evaluation
  
  

Weeks 3–5: Linear Equations in One Variable

• Solving one-step, two-step, and multi-step equations

• Equations with variables on both sides

• Word problems involving linear equations
  
  

Weeks 6–8: Inequalities

• Solving and graphing inequalities on a number line

• Compound inequalities (AND/OR)

• Word problems with inequalities
  
  

Weeks 9–11: Functions & Relations

• Definition of a function

• Function notation

• Domain and range

• Representations: table, graph, equation, mapping diagram
  
  

Weeks 12–13: Review & Assessment

• Cumulative review of key concepts

• First term test / projects
  
  

🔹 Term 2: Linear & Nonlinear Relationships (Weeks 14–26)

Weeks 14–16: Graphing Linear Equations

• The coordinate plane

• Graphing from a table

• Slope as rate of change

• Slope-intercept form (y = mx + b)
  
  

Weeks 17–19: Writing Linear Equations

• Finding slope from two points

• Point-slope form

• Converting between forms

• Writing equations from real-world data
  
  

Weeks 20–22: Systems of Linear Equations

• Solving systems by graphing

• Solving by substitution

• Solving by elimination

• Application problems
  
  

Weeks 23–24: Exponents & Exponential Functions

• Laws of exponents (product, quotient, power rules)

• Negative and zero exponents

• Scientific notation

• Intro to exponential growth and decay
  
  

Weeks 25–26: Review & Mid-Year Assessment

• Concept maps and cumulative reviews

• Mid-year exams and performance tasks
  
  

🔹 Term 3: Polynomials, Factoring & Quadratics (Weeks 27–40)

Weeks 27–29: Polynomials

• Adding, subtracting, and multiplying polynomials

• Identifying degree and leading coefficient

• Special products (squares and differences of squares)
  
  

Weeks 30–32: Factoring

• Factoring common factors

• Factoring trinomials (x² + bx + c)

• Factoring by grouping

• Solving equations by factoring
  
  

Weeks 33–35: Quadratic Equations & Functions

• Graphing y = ax² + bx + c

• Vertex, axis of symmetry, direction of opening

• Solving quadratics by factoring and square roots

• Application of quadratic models
  
  

Weeks 36–37: Radicals & Irrational Numbers

• Simplifying square roots

• Operations with radicals

• Rational vs irrational numbers
  
  

Weeks 38–40: End-of-Year Review & Exams

• Final exam prep: algebra boot camp

• Practice with integrated problems

• Final exam / project-based assessment
  
  

🧮 Suggested Projects & Activities

• Algebra scavenger hunt (real-life equations)

• “Design a City” using coordinate graphing

• Linear modeling with real-world data (e.g., phone plan costs)

• Algebra board game creation

• Factoring puzzle challenges
  
  

📗 Algebra 2 – Scheme of Work

Level: Grade 10 or 11
Duration: Full Academic Year (3 Terms / 40 Weeks)
Prerequisites: Algebra 1

🔹 Term 1: Advanced Functions & Equations (Weeks 1–13)

Weeks 1–2: Review of Algebra 1 Essentials

• Linear equations and inequalities

• Systems of equations

• Function notation and evaluation

• Domain and range
  
  

Weeks 3–5: Quadratic Functions & Equations

• Graphing parabolas: vertex, axis of symmetry

• Solving quadratics by factoring, completing the square, and using the quadratic formula

• Discriminant and nature of roots

• Applications in real-world problems
  
  

Weeks 6–7: Polynomial Functions

• Polynomial terminology and degrees

• End behavior, turning points

• Long and synthetic division

• The Remainder and Factor Theorems
  
  

Weeks 8–9: Factoring & Solving Higher-Degree Equations

• Factoring sum/difference of cubes

• Solving polynomial equations

• Graphing polynomial functions

• Finding real and complex zeros
  
  

Weeks 10–11: Complex Numbers

• Imaginary unit i

• Operations with complex numbers

• Solving equations with complex solutions

• Complex plane
  
  

Weeks 12–13: Rational Expressions & Equations

• Simplifying rational expressions

• Multiplying and dividing rational expressions

• Solving rational equations

• Applications involving rational models
  
  

🔹 Term 2: Exponentials, Logarithms & Sequences (Weeks 14–26)

Weeks 14–15: Radical Functions & Rational Exponents

• Laws of exponents with rational indices

• Simplifying radicals

• Operations with radical expressions

• Solving radical equations
  
  

Weeks 16–18: Exponential Functions

• Properties of exponential growth and decay

• Exponential equations

• Real-life applications (e.g. compound interest, population growth)
  
  

Weeks 19–21: Logarithmic Functions

• Definition of logarithms and their properties

• Converting between exponential and logarithmic forms

• Laws of logarithms

• Solving logarithmic equations
  
  

Weeks 22–24: Sequences & Series

• Arithmetic and geometric sequences

• Recursive and explicit formulas

• Summation notation (Σ)

• Infinite geometric series
  
  

Weeks 25–26: Mid-Year Review & Assessment

• Comprehensive review

• Mid-year exams and projects
  
  

🔹 Term 3: Advanced Topics & Applications (Weeks 27–40)

Weeks 27–28: Probability & Combinatorics

• Fundamental counting principle

• Permutations and combinations

• Independent and dependent events

• Binomial theorem (introduction)
  
  

Weeks 29–30: Statistics

• Measures of central tendency (mean, median, mode)

• Standard deviation and variance

• Box plots and histograms

• Normal distribution (introductory)
  
  

Weeks 31–33: Trigonometry Essentials

• Radian and degree measure

• Right triangle trigonometry

• Graphing sine and cosine functions

• Applications in real-world modeling
  
  

Weeks 34–35: Systems of Equations and Inequalities (Advanced)

• Systems with three variables

• Solving nonlinear systems graphically and algebraically

• Inequalities in two variables
  
  

Weeks 36–37: Matrices and Linear Programming

• Matrix operations and applications

• Determinants and inverses

• Solving systems using matrices

• Linear programming (introductory optimization)
  
  

Weeks 38–40: Final Review & Assessment

• Cumulative review

• Final exams and/or major projects

• Student feedback and reflection
  
  

🧮 Suggested Enrichment Projects

• Graphing portfolio (transformation gallery)

• Compound interest calculator (Excel or coding project)

• Real-life data modeling (exponential/logarithmic fit)

• Sequence-based puzzle or game design

• Build-a-Business simulation (using matrices and systems)

📐 Geometry – Scheme of Work

Level: Grade 9 or 10
Duration: Full Academic Year (3 Terms / 40 Weeks)
Prerequisites: Algebra 1

🔹 Term 1: Basics, Proofs & Lines (Weeks 1–13)

Weeks 1–2: Foundations of Geometry

• Points, lines, planes, and space

• Line segments and rays

• Measuring and classifying angles

• Angle pairs (complementary, supplementary, vertical, linear pair)
  
  

Weeks 3–4: Reasoning and Proof

• Inductive vs deductive reasoning

• Conditional statements, converses, contrapositives

• Properties of equality and congruence

• Writing formal geometric proofs
  
  

Weeks 5–7: Parallel and Perpendicular Lines

• Properties of parallel lines cut by a transversal

• Proving lines parallel

• Perpendicular lines and slopes

• Equations of parallel and perpendicular lines
  
  

Weeks 8–10: Triangles and Congruence

• Classifying triangles by sides and angles

• Triangle sum theorem and exterior angle theorem

• Congruence postulates: SSS, SAS, ASA, AAS, HL

• Triangle proofs using congruence
  
  

Weeks 11–13: Special Segments in Triangles

• Medians, altitudes, perpendicular bisectors, angle bisectors

• Centroid, orthocenter, incenter, circumcenter

• Triangle inequality theorem

• Coordinate proofs involving triangles
  
  

🔹 Term 2: Polygons, Quadrilaterals & Similarity (Weeks 14–26)

Weeks 14–15: Polygons and Angles

• Interior and exterior angle sums

• Regular and irregular polygons

• Diagonals and symmetry in polygons
  
  

Weeks 16–18: Quadrilaterals

• Properties of parallelograms

• Rhombus, rectangle, square, trapezoid, kite

• Proving and classifying quadrilaterals

• Midsegment theorem for trapezoids
  
  

Weeks 19–21: Similarity

• Similar polygons and triangles

• AA, SSS, SAS similarity criteria

• Proportions and scale factors

• Indirect measurement and real-life applications
  
  

Weeks 22–24: Right Triangles and Trigonometry

• Pythagorean Theorem and its converse

• Special right triangles (30-60-90 and 45-45-90)

• Trigonometric ratios: sine, cosine, tangent

• Solving right triangles using trigonometry
  
  

Weeks 25–26: Mid-Year Review and Assessment

• Cumulative review

• Mid-year test or performance-based project
  
  

🔹 Term 3: Circles, Area, Surface Area & Volume (Weeks 27–40)

Weeks 27–29: Circles

• Parts of a circle (radius, diameter, chord, arc, sector)

• Central and inscribed angles

• Arc length and sector area

• Circle theorems and proofs
  
  

Weeks 30–32: Transformations

• Translations, rotations, reflections, and dilations

• Congruence and similarity through transformations

• Compositions of transformations

• Symmetry and tessellations
  
  

Weeks 33–35: Area of Plane Figures

• Area of triangles, quadrilaterals, and polygons

• Area of composite figures

• Surface area of prisms, pyramids, cylinders, cones, and spheres
  
  

Weeks 36–38: Volume of Solids

• Volume of prisms and cylinders

• Volume of cones, pyramids, and spheres

• Applications involving density and 3D modeling
  
  

Weeks 39–40: End-of-Year Review and Final Assessment

• Full review of geometry concepts

• Final exam / project presentations

• Student reflections and feedback
  
  

🧮 Enrichment & Project Ideas

• "Design Your Dream Home" using geometric constructions

• Origami or tessellation design project

• Mini-architecture models with surface area & volume calculations

• Create a Geometry Proof Scrapbook

• Trig scavenger hunt (real-world angle measurements)