Mathematics is not a spectator sport.  It is far beyond mere collection of concepts and skills to be mastered.  Mathematics is learned and appreciated by the learner who engage in doing it.  The study of mathematics includes methods of investigating and reasoning, means of communicating one’s notion of a concept,  making appropriate decisions and finding practical applications of mathematical concepts and skills to real life situations.

FIRST YEAR MATHEMATICS IS ELEMENTARY ALGEBRA.   It reviews basic arithmetical and number theoretical concepts.  The algebra includes the set of real numbers and the properties of its operations, algebraic expressions, first degree equations and inequalities in one variable, linear equations in two variables, special products and factoring.

SECOND YEAR MATHEMATICS IS INTERMEDIATE ALGEBRA.  It deals with systems of linear equations and inequalities, quadratic equations, rational algebraic expressions, and with the search for patterns for sequences and series as applied in real life situations.

THIRD YEAR MATHEMATICS IS BASICALLY GEOMETRY AND AN INTRODUCTION TO TRIGONOMETRY.  The focus is on the logic of geometry, geometric relations,

triangle congruence, perpendicularity, parallelism, properties of quadrilaterals, similarities.  The latter part deals mainly on the trigonometry of the triangle.

FOURTH YEAR MATH IS PRE-CALCULUS AND AN INTRODUCTION TO CALCULUS.  The pre-calculus topics include Advanced Algebra (Inequalities, the functions:  Polynomial, Circular, Exponential, and Logarithmic), Trigonometry (of the right triangle and of the circle), and Combinatorial Mathematics (Counting, Permutation, Combination, and Probability).  Introduction to calculus centers mainly on limits and derivatives.

In all of these courses, the students’ way of thinking is developed, their self-confidence is enhanced, their problem solving skills are polished and their decision-making skills are refined.  Thus, the Ateneo de Naga University High School Mathematics Program does not only prepare the students for more mathematics in college but also for its practical applications in life.

GOALS

At  the end of the students’ four-year course in mathematics, they are expected to:

1.   correlate mathematics concepts with other disciplines and with other fields of broader applications,

2.    develop greater precision in their computational skills,

3.    develop skills to analyze, synthesize, draw logical conclusions and consequently develop logical reasoning,

4.    develop a personal style and approach in solving problems and in facing new situations,

5.    develop a desire to pursue further learning,

6.    recognize their abilities, limitations and potentials,

7.    develop an appreciation for the discipline itself, its application and contribution to the development of the world,

8.    develop their curiosity to explore ideas,

9.    develop an oriented approach to learning varied tasks,

10. take  pride and ownership of their work, and

11. enjoy intellectual and imaginative pursuits.

First Year

MATHEMATICS 1:     ELEMENTARY ALGEBRA

Learning mathematics is sequential.  A student’s success in algebra is greatly dependent on his mastery of arithmetic.  First year math, being the transition from grade school mathematics to high school mathematics is offered as a link between arithmetic and algebra.

First year math is a combination of arithmetic and Elementary Algebra.  It deals with situations and problems involving measurement, real number system, algebraic expressions, first degree equations and inequalities in one variable, linear equations in two variables, special products and factoring.

Course  Objectives:

At the end of the school year, a student is expected to:

1. demonstrate understanding and skills in

a.  operations on decimals, fractions and percent,

          b.  conversion of units,

          c.  operations on polynomials,

          d.  solving equalities and inequalities in one or two variables in one or two variables,

          e.  factoring and finding special products,

          f.  higher order thinking.

     2.  manifest greater precision in computations.

     3.  express an appreciation of the significance of mathematics in his life.

Second Year

MATHEMATICS 2:     INTERMEDIATE ALGEBRA

Algebra, according to the famous mathematician Alfred North Whitehead,  is the intellectual instrument for rendering clear the quantitative aspect of the world.  It is a wonderful tool for problem solving.  Thus, algebra is considered the language of technology.

Mathematics 2 is Intermediate Algebra.  It forms part of the sequential topics of High School Mathematics.  It is a continuation of the first year arithmetic and algebra topics and a preparation for third year math, Geometry.

Mathematics 2 includes system of linear equations and inequalities, quadratic equations, rational algebraic expressions, and searching for patterns in sequences and series as applied in real life situations.

Course Objectives:

At the end of the school year, a student is expected to:

   1.  demonstrate understanding and skills in

          a.  writing equations of a line,

          b.  finding solutions of quadratic equations, system of linear equations and inequalities,

          c.  performing fundamental operations on rational expressions, radicals and exponents,

          d.  solving sequences, series and variations.

   2.  develop skills to analyze, synthesize, draw logical conclusions and consequently develop critical thinking in solving word problems.

   3.  develop  a personal style and approach in solving problems in intermediate algebra.

   4.  show appreciation of the practical applications of intermediate algebra in confronting real life problems.

Third Year

MATHEMATICS 3:  INTERMEDIATE ALGEBRA/GEOMETRY/INTRODUCTION TO TRIGONOMETRY

Amazing scientific and technological discoveries and innovations have made rapid changes in today’s life and culture.  One of the greatest tools to effect these discoveries and innovations is mathematics.

Mathematics 3 forms part of the sequential topics of High School Mathematics.  It is a continuation of the Second Year Algebra topics and an introductory subject to geometry and trigonometry.  Mathematics 3 is therefore both a deepening of algebra and a foundation  the students’ success in geometry and trigonometry in preparation for the demands of the information age.

Third Year High School Mathematics includes topics in Intermediate Algebra namely:  quadratic equations, sequences and series, and variations.  Geometry includes basic concepts in Geometry, logic of Geometry, Congruence of Triangles, perpendicularity and parallelism, quadrilaterals, and similarity.  Right triangle trigonometry is introduced to prepare the students for the computational task in Physics.

Course Objectives:

At the end of the school year, the students are expected to:

1.    demonstrate knowledge, understanding, and skills in solving quadratic equations, sequences and series, variations, and right triangles.

2.    demonstrate knowledge, understanding, and skills in both inductive and deductive reasoning by proving statements and theorems. 

3.    manifest competence and understanding of concepts and skills in geometric relations, in proving and applying theorems on congruence and similarities of triangles and quadrilaterals, and in solving right triangles.

4.    develop a habit of thinking logically and critically.

Fourth Year

Mathematics 4:   PRECALCULUS/COMBINATORICS/TRIGONOMETRY

A practical knowledge of mathematics is what everyone needs in the ever-changing and complicated modern society.  An intensive mathematical background, both technical and functional is an advantage in facing realities in life.

The Mathematics 4 Program aims at providing the students with the necessary skills and  preparation for more mathematics in college, and with some practical ideas for living a challenging life.  It includes Pre-Calculus topics such as:  Polynomial, Exponential, Logarithmic, Trigonometric and Circular Functions, Variations, Conic Sections, and Probability.

The topics on Functions and Conics prepare the students for an in-depth study on Mathematical Analysis, Engineering, and Business courses.  Combinatorics (with Probability) orients them on more serious Computer-related studies.  Generally, the topics provide them necessary skills for Physics and other sciences.  Problem-solving techniques and strategies in these various subject matters prepare them for problem situations in life.

Course Objectives:

At the end of the school year, the students are expected to:

1.    demonstrate understanding of the circle, its parts, its properties, and its relations with other plane figures.

2.    demonstrate skills in writing the equation of a conic section and in graphing conics.

3.    demonstrate understanding of trigonometric and circular functions, their properties and applications.

4.    show appreciation of the properties of operations on the set of complex numbers.

5.    demonstrate understanding of exponential function and its applications.

6.    demonstrate understanding of logarithmic function and its applications.

7.    manifest skills in manipulating expressions using the operations and properties of polynomials and polynomial functions.

8.    demonstrate skills in using permutations and combinations in real-life events.

9.    demonstrate knowledge and understanding of the probability of events and outcomes.

10. manifest proficiency in understanding and operating the keys of a scientific calculator.

11. show appreciation of the usefulness of the Pre-calculus topics to everyday life situations.