## MATHEMATICS

**Description: This Licensure of test consists of 200 items covering topics from these 10 subjects areas:**

- Arithmetic and Number Theory
- Basic and Advanced Algebra
- Plane Geometry
- Circular and Trigonometric Functions
- Probability and Statistics
- Analytic Geometry
- Business Mathematics
- Calculus (Basic)

**A. OBJECTIVES EXPECTATIONS:**

The Licensure Examinee should be able to:

- Show a working knowledge of basic terms and concepts in arithmetic, algebra, geometry, trigonometry, analytics, calculus, probability and statistics
- Solve, evaluate, and manipulate symbolic and numerical problems in the above mathematics areas by applying fundamental rules, principles and process.
- Solve verbal problems in each of the above mathematical areas
- Interpret graphic, symbolic and word problems
- Show ability to apply theories and principles of teaching and learning to mathematics teaching

**B. BASIC CONTENT OUTLINE FOR MATHEMATICS MAJOR**

**1. Arithmetic and Number Theory (0% – 40 items)**

1.1 Operation on signed numbers

1.2 Least Common Multiples, Greatest Common Factor

1.3 Divisibility Rules

1.4 Ratio an Proportion

1.5 Percentage, Rate and Base

1.6 Measurement and units of measure

**2. Basic and Advanced Algebra (25%- 50 items)**

2.1 Algebraic operations and process

2.2 Laws of exponents for multiplication and division of algebraic expressions

2.3 Operations with monomials and polynomials

2.4 Relations, functions and their zeros (linear and quadratic)

2.4.1 Definition of domain and range

2.4.2 Linear equations

2.4.3 Quadratic equations

2.4.4 Systems of equations

2.4.5 Radical equations

2.5 Special products and factors

2.6 Operations on rational expressions

2.7 Operations on radical expressions

2.7.1 Evaluating powers

2.7.2 Negative and Fractional exponents

2.7.3 Imaginary and complex numbers

2.8 Exponential and logarithmic functions

2.9 Inequalities: linear, quadratic and systems

2.10 Arithmetic and geometric sequences and series

2.11 Variation

2.11.1 Direct variation

2.11.2 Inverse variation

2.11.3 Joint variation

2.12 Polynomial functions of higher degree

2.12.1 Synthetic division

2.12.2 The Remainder Theorem, Rational Root Theorem and the Factor Theorem

**3. Plane Geometry – (15%-30)**

3.1 Coordinate geometry

3.1.1 The length of a line

3.1.2 The midpoint of a line

3.1.3 Graph of a linear equation

3.1.4 The equation of a straight line

3.1.5 Parallel and perpendicular lines

3.2 Angles and straight lines

3.2.1 Types and measures of angles (complementary, supplementary, linear pair)

3.2.2 Dividing a vertical line into a number of equal parts

3.2.3 Construction of perpendicular & parallel lines and their properties

3.2.4 Angle bisection

3.3 Triangles

3.3.1 Types of triangles, their properties

3.3.2 Pythagora’s Theorem

3.4 Quadrilaterals and Other Polygons

3.4.1 Properties of rectangles, squares, rhombi, trapezoids

3.4.2 Sum of the interior angles of a polygon

3.4.3 Sum of exterior angles of a convex polygon

3.4.4 Symmetry of regular polygons

3.5 The Circle

3.5.1 Circles and circle concepts

3.5.2 Central angles and arcs

3.5.3 Chords, tangents and secants

3.5.4 Sectors and segments

3.5.5 Measures of angles formed in, on and outside a circle

3.6 Triangle Congruence

3.6.1 Corresponding parts of triangle

3.6.2 SAS, SSS, SAA, and ASA Theorems

3.6.3 Proving triangles congruent

3.7 Similarity and Proportionality

3.7.1 Properties of proportions

3.7.2 Proportional segments

3.7.3 Basic proportionality & related theorems

3.7.4 Special angles/triangles

**4. Circular and Trigonometric Functions (10%-20 items)**

4.1 Circular functions

4.2 Trigonometric ratios of reference angles

4.3 Graphs of circular functions

4.4 Degree-radian conversion

4.5 The eight basic trigonometric identities

4.6 Proving identities

4.7 The Pythagorean identities

4.8 Sine and cosine laws

4.9 Solution of triangles

**5. Probability and Statistics (10%- 20 items)**

5.1 Counting Techniques

5.1.1 Theoretical and Experimental Probability

5.2 Probability of Events

5.2.1 Permutation

5.2.2 Independent & dependent events

5.2.3 Mutually exclusive and non-mutually exclusive events

5.3 Graph reading and interpretation

5.4 Computing measures of average mean (mean, median, mode)

5.5 Computing measures of variability

5.5.1 Range and Interquartile Range

5.5.2 Average deviation

5.5.3 Standard deviation

5.6 Correlation and Regression

5.6.1 Pearson r and Spearman rho

5.6.2 The regression line

5.6.3 Linear regression

5.7 Statistical Inference

5.7.1 Normal curve

5.7.2 Null Hypothesis

5.7.3 Levels of Significance

5.8 Common Test of Significance (t, F, Z, x2)

**6. Analytic Geometry ( 10% – 20 items)**

6.1 Slope of a line

6.2 Equations of lines: tangents & normal

6.2.1 Point slope form

6.2.2 Slope intercept form

6.2.3 Parallel and perpendicular lines

6.2.4 Midpoint of a line

6.2.5 Distance formula

6.3 Equations and graphs

**7. Business Mathematics (5% – 10 items)**

7.1 Discounts: commission

7.2 Simple and compound interest

**8. Calculus (Basic) (5%-10 items)**

Steve

June 22, 2017 at 6:17 pmAng TOS po ba na nasa taas ay for September 2017 LET?

juan dela crus

December 3, 2016 at 3:37 pmkompleto po ba itong coverage for biology? parang kakaunti? slamat

Sundoval Cortez

May 19, 2016 at 7:37 pmNo further outline for Biological Sciences?

Mark Flores Lillo

April 23, 2016 at 10:54 amHi may I ask. Yung Course Outline ba for Bio major ay complete?

jj

September 11, 2015 at 11:23 amis this the final TOS?

Felix Urot

June 19, 2015 at 1:38 pmThank you, I hope this is the Final TOS. and no more changes because this is what I’m biting on.

ELMER B. GARROVILLAS

March 30, 2015 at 9:04 pmpls. put the real answere oe the key to correction to know the correct answere

TeacherPH

March 30, 2015 at 9:26 pmHi Sir, lahat po ng online reviewer sa teacherph ay may mga tamang sagot.. kailangan niyo lang pong tapusin yung exam para makita ito. Maraming Salamat!

janile

March 26, 2015 at 11:18 amthankyou for all the guidlines you share with us it will help us to our exam.

Evangeline Sumaling Bascos

March 22, 2015 at 4:32 amthank you for the guidelines. more power and god speed!