**High School**

** Math Curriculum **

**ALGEBRA**

*1) Expressions and Equations*

__A. Variables and expressions;__

I. Writing verbal expression for algebraic expression

II. Writing algebraic expression for verbal expression,

__B. Order of operation;__

__C. Distributive property;__

__D. Equation;__

I. Solving the equation with two variables given a domain.

*2) Linear equation*:

__A. Translate sentence into equation;__

__B. Solving one-step equation by using mathematical operations;__

__C. Solving multi - step equation by using mathematical operations;__

__D. Solving equations with the variables on each side; involving grouping __

__symbols;__

__E. Evaluate absolute value expression;__

__F. Solving absolute value equations.__

*3) Representing linear equation*

__A. Graphing linear equation;__

__B. Solving linear equation by graphing;__

__C. Slope of line;__

__D. Writing and graph linear equation in slope - intercept form;__

__E. Model real world data with equations in slope-intercept form;__

__F. Creating equations of lines in standard form; point-slope form and __

__different forms;__

__G. Parallel and perpendicular lines.__

*4) Linear inequalities*

__A. Solving linear inequalities by using different mathematical operation;__

__B. Solving compound inequalities;__

__C. Solving and graph absolute value inequalities;__

__D. Inequalities in two variables.__

*5) Systems of linear equations and inequalities*

__A. Solving systems of linear equation by graphing, substitution and __

__elimination;__

__B. Applying systems of equation to solve real life problems;__

__C. Matrix equations - Gaussian elimination.__

*6) Polynomials*

__A. Multiplying and dividing polynomials;__

__B. Mathematical operation on polynomials.__

*7) Factoring and quadratic equation*

__A. Factoring monomials - the Greatest Common Factor;__

__B. Solving the quadratic equation using the zero product property;__

__C. Factoring quadratic equation;__

__D. Solving the quadratic equation using the square root property and __

__graph;__

__E. Solving the quadratic equation using the Quadratic Formula.__

*8) Rational expression*

__A. Simplifying rational expression using common factor to reduce;__

__B. Mathematical operation on rational expression;__

__C. Determined the Least Common Denominator.__

*9) Applying fractions*

__A. Ratios and proportions;__

__B. Percent - solving real-world problems;__

__C. Solving equation with fractions;__

__D. Negative exponents - simplifying the expression and using scientific __

__notation.__

*10) Radical function*

__A. Identifying properties of rational number;__

__B. Rational and irrational square roots;__

__C. Mathematical operation on square roots;__

__D. Using the Power Property of Equality to solve the radical equation.__

*11) Pythagoreanâ€™s theorem*

__A. Solving real life problems involving right triangle. __

*12) Relation and function*

__A. Determined the domain and range of function;__

__B. Function one-to-one and onto;__

__C. Graph absolute value and quadratic function;__

__D. Identifying the roots and sketch higher degree polynomial function;__

__E. Perform operation with functions;__

__F. Evaluate the composition of function;__

__G. Find and graph the inverse of function;__

__H. The equation of circle.__

*13) Quadratic function*

__A. Roots of quadratic equations;__

__B. Operation with complex numbers;__

__C. Sum and product of the roots of quadratic equations - Vieta's formulas;__

__D. Graph system of equations involving quadratic equations, line, circles__

__and inequalities.__

*14) Exponential function*

__A. Evaluate expression with exponents;__

__B. Graph exponential function;__

__C. Solve equation with exponents;__

__D. Solve exponential equation and inequalities.__

*15) Logarithmic functions*

__A. Find the inverse of an exponential function;__

__B. Apply logarithmic relationship;__

__C. Solve common logarithmic problems;__

__D. Solve exponential equations requiring logarithms.__

**GEOMETRY**

*1) Fundamental concepts and pattern*

__A. Using inductive and deductive reasoning to explore and recognize __

__geometric pattern;__

__B. Distinguish between inductive and deductive reasoning;__

__C. Identify and apply basic definitions and postulates of geometry;__

__D. Statement in if-then form and their converses;__

__E. Segment construction congruent to a given segment;__

__F. Use the number line to calculate distance;__

__G. Midpoint of given statement;__

__H. Graph point and lines in the coordinate plane.__

*2) Angles, parallel and perpendicular lines*

__A. Parts of an angle;__

__B. Angles classification by their measure;__

__C. Angle relationship - complementary, vertical, congruent - identifying __

__and applying;__

__D. Define and apply perpendicular lines;__

__E. Construct the bisector of a given angle and an angle congruent to a __

__given angle;__

__F. Construct a perpendicular line;__

I. To a line at a given point,

II. From a given point to a line.

__G. Construct the perpendicular bisector of given segment;__

__H. Parallel line and plans - difference;__

I. Definition of slope and finding slope of parallel and perpendicular

line to given.

*3) Triangle*

__A. Triangle classification by sides and angles;__

__B. Applying the Triangle angle sum theorem; __

__C. Applying the Isosceles triangle theorem and Exterior angle theorem;__

__D. Identifying and named corresponding part of congruent polygons;__

__E. Prove triangle congruence by AAS, SAS, ASA, SSS theorems;__

__F. Median and altitude of triangle;__

__G. Pythagorean Theorem - applying and its conversions,__

__H. Distance between two points - distance formula.__

*4) Polygons*

__A. Characteristics of quadrilaterals - parallelogram, rectangles, rhombi, __

__trapezoid;__

__B. Regular and non-regular polygons;__

__C. Determined the area and perimeter of quadrilaterals using appropriate __

__theorems and formula;__

__D. Measure of interior and exterior angles of regular and non-regular __

__polygons.__

*5) Ratios, proportion and similarity*

__A. Identification of similar polygons and corresponding parts of similar __

__polygons;__

__B. Applying proportions to problems using similar figures;__

__C. Prove triangles similar using AA, SAS, SSS similarity theorems;__

__D. Relationship between parallel lines and proportional segments in __

__triangles;__

__E. Line and rotation symmetry;__

__F. Determined and construct geometric transformation including __

__reflection, __

__rotation, translation and dilatation;__

__G. Construct transformation of figure on coordinate plane.__

*6) Circles and inscribed polygons*

__A. Area and circumference of circle;__

__B. Applying relationship among inscribed and central angles and arcs of __

__circles;__

__C. Calculate arc length and area of sector;__

__D. Problems with inscribed and circumscribed polygons;__

__E. Identify and apply properties of tangents and secants to circles.__

*7) Surface area and Volume*

__A. Identify and classify solid figure;__

__B. Volume and surface area of solid figure;__

__C. Comparison of linear dimensions, perimeter, surface area, and volume __

__of similar figures;__

__D. Explore net of 3 dimensional figures.__

*8) Right triangle and trigonometry*

__A. Solve problems involving right triangle and special right triangle __

__(45-45-90; 30-60-90);__

__B. Finding the missing part of triangle (angle, side) by using __

__trigonometric functions.__

__TRIGONOMETRY__

*1) Trigonometric functions*

__A. Right angle trigonometry;__

__B. Relationship between trigonometric ratios in the unit circle;__

__C. Reciprocal trigonometric function;__

__D. Exact value chart;__

__E. Reference angles.__

*2) More trigonometric functions*

__A. Conversion between degree and radians;__

__B. Radian measure to find value of trigonometric functions;__

__C. Pythagorean identities;__

__D. Domain and range of trigonometric functions;__

__E. Inverse trigonometric functions;__

__F. Cofunctions identity.__

*3) Graphs of trigonometric functions*

__A. Graph sine and cosine on the coordinate plane;__

__B. Amplitude, frequency, period and phrase shift;__

__C. Graph tangent function;__

__D. Graph reciprocal trigonometric functions;__

__E. Graph inverse trigonometric functions.__

*4) Trigonometric identity*

__A. Prove trigonometric identity;__

__B. Sum and difference formula for sine, cosine and tangent;__

__C. Double angle formulas for sine, cosine and tangent;__

__D. Half angle formulas for sine, cosine and tangent.__

*5) Trigonometric equation*

__A. Solve first degree trigonometric equation;__

__B. Solve second degree trigonometric equations using factoring and the __

__quadratic equation; __

__C. Solve trigonometric equation using substitution.__

*6) Trigonometric application*

__A. Use law of cosines;__

__B. Use law of sines;__

__C. Find the area of triangle.__

*7) Sequence and Series*

__A. Determined the difference between an arithmetic and geometric __

__sequences;__

__B. Determined the difference between an arithmetic, geometric, and __

__infinite series;__

__C. Use sigma notation.__

*8) Statistics*

__A. Gather and organize data;__

__B. Find measures of central tendency;__

__C. Find standard deviation and variance;__

__D. Recognize and use the normal distribution;__

__E. Bivariate statistics and the correlation coefficient;__

__F. Distinguish between exponential, logarithmic, power, quadratic, cubic, __

__and linear regression.__

*9) Probability and binomial theorem*

__A. Counting principles, combination and permutation;__

__B. Calculate probability using at least and at most;__

__C. The normal approximation to the binomial distribution; __

__D. Apply the binomial theorem.__