The main objective of Algebra-1 is to provide the students with a strong background for all mathematical courses ahead. The basics of algebraic problem-solving are systematically taught. The students will gain a good grasp of the following topics: Basics of Algebra, equations, inequalities, functions at introductory level, linear functions, quadratic functions, equation and inequality systems, exponential functions, polynomials with factoring, radical expressions and equations, and data analysis and probability. Common Core State Standards will be taught and reinforced as the students learn how to practice these concepts in real-life situations. This course prepares students to take Honors Algebra-1, 2 and other upper level related courses.

# Course Catalog

Pre-Algebra or 8th Grade Math, or placement test.

NRN.1, NRN.2, NRN.3, NQ.1, NQ.2, NQ.3, NCN.1, NCN.2, NCN.3, NCN.4, NCN.5, NCN.6, NCN.7, NCN.8, NCN.9, ASSE.1, ASSE.1a, ASSE.1b, ASSE.2, ASSE.3, ASSE.3a, ASSE.3b, ASSE.3c, ASSE.4, AAPR.1, AAPR.2, AAPR.3, AAPR.4, AAPR.5, AAPR.6, AAPR.7, ACED.1, ACED.2, ACED.3, ACED.4, AREI.1, AREI.2, AREI.3, AREI.4, AREI.4a, AREI.4b, AREI.5, AREI.6, AREI.7, AREI.8, AREI.9, AREI.10, AREI.11, AREI.12, F.IF.1, F.IF.2, F.IF.3, F.IF.4, F.IF.5, F.IF.6, F.IF.7, F.IF.7a, F.IF.7b, F.IF.7c, F.IF.7d, F.IF.7e, F.IF.8, F.IF.8a, F.IF.8b, F.IF.9, F.BF.1, F.BF.1a, F.BF.1b, F.BF.1c, F.BF.2, F.BF.3, F.BF.4, F.BF.4a, F.BF.4b, F.BF.4c, F.BF.4d, F.BF.5, F.LE.1, F.LE.1a, F.LE.1b, F.LE.1c, F.LE.2, F.LE.3, F.LE.4, F.LE.5, S.ID.1, S.ID.2, S.ID.3, S.ID.4, S.ID.5, S.ID.6, S.ID.6a, S.ID.6b, S.ID.6c, S.ID.7, S.ID.8, S.ID.9

Mathematics Enhancement Programme

Additional Problem Sets by Problem-Attic

After completing, students will be able to:

- Write expressions and evaluate them with unknown values
- Use properties to simplify expressions
- Identify and differentiate the types of relationships that can be represented by proportions
- Use inverse operations to simplify and find equivalent equations
- Solve equations using mathematical operations and equality properties
- Write and plot inequalities
- Model real-world situations using functions
- Model and analyze real-world situations using a system of equations or inequalities
- Simplify expressions by applying properties of exponents
- Explore the characteristics of exponential functions
- Explore polynomials through adding, subtracting, multiplying and factoring, and apply real number properties to manipulate polynomial expressions
- Plot and identify characteristics of quadratic functions
- Plot and simplify rational expressions
- Figure out different strategies to find solutions for quadratic equations
- Add, subtract, multiply and divide using radicals and learn how to rationalize the denominator of a radical expression
- Multiply and divide rational expressions and divide polynomials
- Interpret data in real-world terms
- Analyze data with multiple approaches

- Review of Pre-Algebra
- Solving Equations
- Solving Inequalities
- Introduction to Functions
- Linear Functions
- Systems of Equations and Inequalities
- Polynomial and Factoring
- Quadratic Functions and Equations
- Radical Expressions and Equations
- Rational Expressions and Functions
- Data Analysis and Probability

This course covers the required concepts of Euclidean geometry including definitions, postulates, and theorems. Throughout the course, Common Core standards are taught and reinforced as the student learns how to apply the concepts in real life situations. Areas of study include tools and language of geometry, reasoning and proof, parallel and perpendicular lines, congruent triangles, relationships within triangles, polygons and quadrilaterals, similarity, right triangles and trigonometry, transformations, area, surface area and volume, circles, and probability. This course prepares students to take Honors Geometry and other upper level related courses.

Algebra I or placement test.

G.CO.1, G.CO.2, G.CO.3, G.CO.4, G.CO.5, G.CO.6, G.CO.7, G.CO.8, G.CO.9, G.CO.10, G.CO.11, G.CO.12, G.CO.13, G.SRT.1, G.SRT.1a, G.SRT.1b, G.SRT.2, G.SRT.3, G.SRT.4, G.SRT.5, G.SRT.6, G.SRT.7, G.SRT.8, G.SRT.9, G.SRT.10, G.SRT.11, G.C.1, G.C.2, G.C.3, G.C.4, G.C.5, G.GPE.1, G.GPE.2, G.GPE.3, G.GPE.4, G.GPE.5, G.GPE.6, G.GPE.7, G.GMD.1, G.GMD.2, G.GMD.3, G.GMD.4, G.MG.1, G.MG.2, G.MG.3

Mathematics Enhancement Programme

Additional Problem Sets by Problem-Attic

Upon completion of this course, you should be able to:

- Understand and use the tools and language of Geometry through the exploration of points, lines, planes and angles
- Understand, apply and use logical reasoning
- Understand and apply the properties of parallel and perpendicular lines
- Understand how special lines in triangles relate, and prove that two triangles are congruent
- Understand and apply the properties of different types of polygons
- Prove triangles are similar, and how to use the fact that two triangles are similar to find lengths of sides, and find out how the sides of a right triangle are related
- Perform transformations and apply them to the real world
- Use and apply area formulas, and finding the surface areas and volumes of three-dimensional figures
- Apply theorems you learned in earlier chapters to segments touching circles
- Use conditional probability, rules or probability, to use probability to make decisions

- The Tools and Language of Geometry
- Reasoning and Proof
- Parallel and Perpendicular Lines
- Congruent Triangles
- Relationships within Triangles
- Polygons and Quadrilaterals
- Similarity
- Right Triangles and Trigonometry
- Transformations
- Area
- Surface Area and Volume
- Circles
- Probability

Algebra 2 is designed to build on algebraic and geometric concepts. Throughout the course, Common Core standards are taught and reinforced as the student learns how to apply the concepts in real-life situations. It develops advanced Algebra skills such as Algebra 2 review, function families, quadratic functions and complex numbers, polynomials expressions and equations, exponential and logarithmic functions, rational functions, statistics, periodic functions and trigonometry, and applying trigonometric functions. This course prepares students to take other upper level related courses.

Algebra 1 and Geometry, or placement test.

NRN.1, NRN.2, NQ.2, NCN.1, NCN.2, NCN.7, NCN.8, NCN.9, ASSE.1a, ASSE.2, ASSE.3a, ASSE.4, AAPR.1, AAPR.2, AAPR.3, AAPR.4, AAPR.5, AAPR.6, ACED.1, ACED.2, ACED.3, ACED.4, AREI.1, AREI.2, AREI.4, AREI.4a, AREI.4b, AREI.6, AREI.7, AREI.11, F.TF.1, F.TF.2, F.TF.5, F.TF.8, F.IF.1, F.IF.2, F.IF.3, F.IF.4, F.IF.5, F.IF.6, F.IF.7, F.IF.7b, F.IF.7c, F.IF.7e, F.IF.8, F.IF.9, F.BF.1, F.BF.1b, F.BF.3, F.BF.4, F.BF.4a, F.LE.4, S.ID.4, S.ID.6, S.IC.1, S.IC.2, S.IC.3, S.IC.4, S.IC.5, S.IC.6, S.MD.6, S.MD.7

Mathematics Enhancement Programme

Additional Problem Sets by Problem-Attic

Upon completion of this course, you should be able to:

- Use algebraic expressions to represent patterns
- Solve equations and inequalities
- Solve absolute value equations
- Use functions to model real world situations
- Work with functions
- Analyze transformations and characteristics of function families
- Find the vertex and standard form of a quadratic equation
- Factor quadratic expressions
- Solve quadratic equations
- Gain an understanding of complex numbers
- Classify, graph, and define end behavior of polynomial functions
- Analyze the factored form of the polynomials and write polynomial functions from their zeros
- Solve polynomial functions by graphing and factoring
- Divide polynomials by long division and synthetic division
- Model polynomial functions and identify the effect of transformations of polynomial functions
- Work with radicals as a part of a function, equation, or by themselves
- Add, subtract, multiply and divide functions
- Find the composite of two functions
- Find the inverse of a relation or a function
- Understand the relationship between exponential and logarithmic functions and model exponential and logarithmic functions
- Graph rational functions
- Solve rational equations
- Apply theoretical and experimental probabilities and compare data sets
- Relate geometric measurements to trigonometry, to define radians, how to use radian measures and write and graph functions to describe periodic data
- Verify trigonometric identity
- Solve trigonometric equations and to solve real-world problems involving right triangles by using trigonometric ratios

- Review of Algebra 1 topics
- Quadratic Functions and Complex Numbers
- Polynomial Expressions and Equations
- Radical Functions
- Composite and Inverse Functions
- Exponential and Logarithmic Functions
- Rational Functions
- Statistics
- Periodic Functions and Trigonometry
- Applying Trigonometric Functions

The course is intended for students with a strong background in Trigonometry and Algebra. It prepares students to take AP Calculus AB or a college calculus course. A range of topics including polynomial functions, rational functions, arithmetic and geometric progressions, trigonometric functions and their inverses, trigonometric identities, plots of trigonometric functions, combinations and permutation, theory of equations, polar coordinates, mathematical induction, and parametric equations is covered.

Algebra 1, 2 and Geometry, or better or equivalent by testing.

MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7, MP.8, N-CN.1, N-CN.2, N-CN.3, N-CN.4, N-CN.5, N-CN.6, N-CN.7, N-CN.8, N-CN.9, N-VM.1, N-VM.2, N-VM.3, N-VM.4, N-VM.4a, N-VM.4b, N-VM.4c, N-VM.5, N-VM.5a, N-VM.5b, N-VM.6, N-VM.7, N-VM.8, N-VM.9, N-VM.10, N-VM.11, N-VM.12, A-REI.3, A-REI.4, A-REI.4a, A-REI.4b, A-REI.5, A-REI.6, A-REI.7, A-REI.8, A-REI.9, A-REI.10, A-REI.11, A-REI.12, A-APR.2, A-APR.3, A-APR.4, A-APR.5, A-APR.6, A-APR.7, F-IF.2, F-IF.3, F-IF.4, F-IF.5, F-IF.7, F-IF.7a, F-IF.7b, F-IF.7c, F-IF.7d, F-IF.7e, F-IF.8, F-IF.8a, F-BF.1, F-BF.1a, F-BF.1b, F-BF.1c, F-BF.2, F-BF.3, F-BF.4, F-BF.4a, F-BF.4b, F-BF.4c, F-BF.4d, F-TF.1, F-TF.2, F-TF.3, F-TF.4, F-TF.5, F-TF.6, F-TF.7, F-TF.8, F-TF.9, G-SRT.6, G-SRT.7, G-SRT.8, G-SRT.9, G-SRT.10, G-SRT.11, G-GPE.1, G-GPE.2, G-GPE.3

Mathematics Enhancement Programme

Additional Problem Sets by Problem-Attic

After successful completion of this course, students should be able to:

- Determine derivatives of functions and explain the results with respect to their application
- Calculate marginal cost, marginal revenue and marginal profit using derivatives
- Calculate higher derivatives and interpret the results
- Draw plots of polynomial functions
- Determine domains and limits of rational functions and polynomials
- Determine inflection points, critical points and relative extreme points, and present the results in various settings
- Calculate average and total sales using results obtained through integration via substitution
- Understand and apply the Generalized Power Rule and the Chain Rule
- Conduct optimization of the continuous functions on closed intervals
- Solve problems involving depreciation, interest, demand, revenue, advertising, decay and elasticity of demand using logarithmic and exponential functions
- Integrate definite and indefinite exponential, logarithmic and polynomial functions and express the results in various application formats
- Calculate derivative using implicit differentiation
- Calculate the area between curves and the average value over an interval using integration

- Functions and Graphs: Basic, Composite and Inverse functions and their graphs
- Polynomial and Rational Functions
- Trigonometric Functions
- Analytic Trigonometry
- Additional Topics in Trigonometry: Polar Coordinates, Matrices, Complex Numbers in Polar Form (DeMoivre’s Theorem)
- Conic Sections and Analytic Geometry: The Ellipse, Hyperbola, Parabola, Parametric Equations
- Sequences, Induction, and Probability
- Introduction to Calculus

This course covers the main topics in middle school math. Students will be mastering these topics while solving challenging problems. Students go above and beyond Common Core standards in this brain-stimulating course. Students will also solve mathematical puzzles and cyphers and learn topics that are typically not covered at traditional school settings.

Although this course is typically recommended for students in grades 4th-8th, and anyone in 8th grade or below may enroll, we encourage younger students to participate as well!

This course will familiarize students with the essential concepts and techniques in Pre-Algebra, Algebra I, Geometry, Number Theory and Combinatorics. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.

As of the completion of this course, students will:

- Have complete mastery of concepts covered in standard Pre-Algebra, Algebra I and Geometry courses, as well as topics not covered in traditional school curriculum.
- Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.
- Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.

Students are expected to actively participate in class. We will employ the Socratic method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.

The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand-picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.

Information on Summer Camp Attendance Options (Academic Year Courses cover all topics)

**Full-Day Program:**

Students who would like to master all topics should register for our full-day program.

**Half-Day Program:**

Students who would like to master only Pre-Algebra and Algebra-I topics alongside Number Theory can choose this option. Students can also choose to enroll only in morning classes.

Algebra

- Ratios and Proportions
- Algebraic Expressions
- Linear Equations
- Functions
- Inequalities
- Polynomial Expressions
- Pascal’s Triangle
- Binomial Theorem
- Quadratic Equations

Combinatorics

- Counting
- Statistics
- Probability
- Permutations
- Combinations

Number Theory

- Divisibility
- GCD and LCM
- Prime Factorization
- Radicals and Exponents
- Modular Arithmetic
- Sequences and Series
- Gauss’s Formula

Geometry

- Angles
- Triangles
- Pythagorean Theorem
- Polygons
- Circles
- Perimeter, Area and Volume
- Coordinate Geometry
- 3D Geometry

This course covers the entire high school curriculum including: trigonometry, advanced algebra, precalculus and advanced geometry, but excludes calculus. Our curriculum also includes some additional challenging and brain-stimulating topics outside of the traditional school curriculum.

Although we do not limit students by grade level, this course is typically recommended for advanced 7th and 8th graders and high school students.

This course will familiarize students with the essential concepts and techniques in Algebra II, Precalculusß, Combinatorics, Number Theory, and Geometry. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.

As of the completion of this course, students will:

- Have complete mastery of concepts covered in standard Algebra II and Precalculus courses, as well as more advanced topics (such as Vieta’s formulas, Complex Numbers, and manipulation of Series).
- Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.
- Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.

Students are expected to actively participate in class. We will employ the Socratic method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.

The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand-picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.

Information on Summer Camp Attendance Options (Academic Year Courses cover all topics)

Students who would like to master all topics should register for our full-day program.

Students who would like to master only Algebra II or Pre-Calculus topics alongside Number Theory can choose this option. Students can also choose to enroll only in morning classes.

Algebra

- Quadratics/Discriminants & Conic Sections
- System of Equations
- Polynomial Division
- Rational Root Theorem
- Fundamental Theorem of Algebra
- Vieta’s Formulas
- Sequences and Series
- Induction
- Radicals and Rationalizing Denominators
- Algebraic Factorizations
- Complex Numbers
- Inequalities
- Functions
- Exponents and Logarithms

Combinatorics

- Basic Counting: Constructive and Complimentary
- Sets, Bijections, and Logic
- Principle of Inclusion Exclusion
- Combinations and Permutations
- Pascal’s Triangle
- Binomial Theorem
- Combinatorial Identities
- Pigeonhole Principle
- Expected Value
- Stars & Bars
- Recursion
- Fibonacci Numbers

Number Theory

- Prime Factorization
- Divisibility Rules
- Euclidean Algorithm
- Diophantine Equations
- Bezout’s Identity
- Modular Arithmetic & Exponentiation
- Fermat’s Little Theorem
- Wilson’s Theorem
- Chinese Remainder Theorem
- Multiplicative Functions
- Euler’s Theorem

Geometry

- Congruent & Similar Triangles
- Special Parts of a Triangle
- Triangle Area Formulas
- Quadrilaterals
- Angles in Polygons
- Inscribed Angles in Circles
- Power of a Point
- Three-Dimensional Geometry
- Trigonometry for Right Triangles
- Unit Circle & Radians
- Trigonometric Identities
- Extended Law of Sines & Law of Cosines
- Polar Coordinates & Geometry of Complex Numbers

Click below to see sample lecture notes

AMC-Lecture-Notes-Systems-Of-Equations.pdf

**AUTHORS**

Justin Stevens: Accelerated Math Program Coordinator

University of Alberta

[email protected]

(909) 713-4398

Forest Kobayashi: Curriculum Designer & Harvey Mudd College

Alex Toller: Curriculum Designer