Department of Education

Region IV – A CALABARZON

Division of Antipolo City

SAN JOSE NATIONAL HIGH SCHOOL

GENERAL AND SPECIFIC COMPETENCIES IN MATHEMATICS IV

(Advanced Algebra, Trigonometry and Statistics)

A. Functions

1. Demonstrate knowledge and skill related to functions in general

1.1 Define a function

1.2 Differentiate a function from a mere relation

* real life relationships

* set of ordered pairs

* graph of a given set of ordered pairs

* vertical line test

* given equation

1.3 Illustrate the meaning of the functional notation f(x)

1.4 Determine the value of f(x) given a value for x

B. Linear Functions

1. Demonstrate knowledge and skill related to linear functions and apply in solving problems

1. Define the linear function f(x) = mx + b

2. Given a linear function Ax + By = C, rewrite in the form f(x) = mx + b and vice versa 3. Draw the graph of a linear function given the following: * any two points

* x and y intercepts

* slope and one point

* slope and the y-intercept

4. Given f(x) = mx + b, determine the following: * slope

* trend: increasing or decreasing

* x and y intercepts

* some points

5. Determine f(x) = mx + b given:

* slope and y-intercept

* x and y intercepts

* slope and one point

* any two points

6. Solve problems involving linear functions

C. Quadratic Functions

1. Demonstrate knowledge and skill related to quadratic functions and apply these in solving problems

1.1 Identify quadratic functions f(x) = ax2 + bx + c

1.2 Rewrite a quadratic function ax2 + bx + c in the form f(x) = a(x-h)2 + k and vice versa

1.3 Given a quadratic function, determine:

* highest or lowest point (vertex)

* axis of symmetry

* direction or opening of the graph

1.4 Draw the graph of a quadratic function using the:

* vertex

* axis of symmetry

* direction of opening of the graph

* given points

1.5 Analyze the effects on the graph of changes in a, h and k in f(x)= a(x-h)2 + k

1.6 Determine the “zeros of a quadratic function” by relating this to “roots of a quadratic equation”

1.7 Find the roots of a quadratic equation by:

* factoring

* quadratic formula

* completing the square

1.8 Derive the quadratic function given:

* zeros of the function

* table of values

* graph

1.9 Solve problems involving quadratic functions and equations D. Polynomial Functions

1. Demonstrate knowledge and skill related to polynomial functions

1.1 Identify a polynomial function from a given set of relations

1.2 Determine the degree of a given polynomial function

1.3 Find the quotient of polynomials by:

* algorithm

* synthetic division

1.4 Find by synthetic division the quotient and the remainder when p(x) is divided by (x – c) 1.5 State and illustrate the Remainder Theorem

1.6 Find the value of p(x) for x = k by:

* synthetic division

* Remainder Theorem

1.7 Illustrate the Factor Theorem

1.8 Find the zeros of polynomial functions of degree greater than 2 by: * Factor Theorem

* factoring

* synthetic division

* depressed equations

1.9 Draw the graph of polynomial functions of degree greater than 2 (use graphing calculator if available) E. Exponential and Logarithmic Functions

1. Demonstrate knowledge and skill related to exponential functions 1.1 Identify certain relationships in real life which are exponential (e.g....

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