Math 1

GENERAL AND SPECIFIC COMPETENCIES IN MATHEMATICS I (Elementary Algebra) A. Measurement 1. Demonstrate knowledge and skill in measurement and the use of measuring devices, conversion of units of measurement and solving real life problems 1.1 illustrate the development of measurement from the primitive to the present international system of units 1.2 measure: • length • weight • volume • temperature • time • angle 1.3 express relationships between two quantities using ratios 1.4 convert measurements from one unit to another 1.5 solve problems involving measurement B. Real Number System 1. Describe the real number system: integers, rational numbers, irrational numbers, real numbers 1.1 describe opposite quantities in real life 1.2 determine the absolute value of a number 1.3 solve simple absolute value equations using the number line 1.4 perform fundamental operations on integers: • addition • subtraction • multiplication • division 1.5 illustrate the different properties: • commutative • associative • distributive • identity • inverse 1.6 solve problems involving integers 1.7 perform operations on dissimilar fractions and mixed forms 1.8 perform operations on decimals 1.9 solve problems involving fractions and decimals 2. Demonstrate knowledge and skill in solving square roots of positive rational numbers

2

2.1 define the square root of a rational number 2.2 approximate the square root of a positive rational number 2.3 identify square roots which are rational and which are not rational (irrational numbers) 2.4 if the square root of a number is not rational, determine two integers or rational numbers between which it lies 2.5 give examples of other irrational numbers 2.6 use knowledge related to square roots in problem-solving C.

Algebraic Expressions 1. Demonstrate knowledge and skill related to simplifying and performing operations on polynomials 1.1 define constants, variables, algebraic expressions 1.2 simplify numerical expressions involving exponents and grouping symbols 1.3 translate verbal phrases to mathematical expressions and vice versa 1.4 evaluate mathematical expressions for given values of the variable(s) involved 1.5 simplify algebraic expressions using the laws on exponents: • aman = am+n • ( ab ) m = a mb m •

(a )

•

am a =   bm b

•

am = am−n n a

m n

= a mn

m

where

m – n is a positive number if m > n m – n is a negative number if m < n

1.6 express numbers in scientific notation 1.7 define polynomials 1.8 classify algebraic expressions as polynomials and non-polynomials 1.9 perform operations on polynomials • addition and subtraction • multiplication : polynomial by a monomial • multiplication : polynomial by another polynomial • division : polynomial by a monomial • division : polynomial by a polynomial 1.10solve problems involving polynomials

3

D. First Degree Equations and Inequalities In One Variable 1. Demonstrate knowledge and skill in transforming and solving first degree equations and inequalities in one variable 1.1 1.2 1.3

1.4 1.5 1.6 1.7 1.8

distinguish between equations and inequalities translate verbal statements involving general or unknown quantities to equations and inequalities and vice versa determine the solution set of first degree equations and inequalities using: • number line • replacement set • inspection state the different properties of equality illustrate the different properties of equality apply the properties of equality in finding the solution set of first degree equations apply the properties of inequality in finding the solution set of first degree inequalities solve problems using first degree equations and inequalities in one variable (e.g. relations among numbers, geometry, business, uniform motion, money problems, etc.)

E. Linear Equations in Two Variables 1. Demonstrate knowledge and skill related to linear equations in two variables and apply this in solving real life problems 1.1 describe the Cartesian Coordinate Plane (x-axis, y-axis, quadrant, origin) 1.2 given a point on the coordinate plane, give its coordinates 1.3 given a pair of coordinates, plot the point 1.4 given the coordinates of a point, determine the quadrant where it is located 1.5 identify a linear equation in two variables: Ax+By=C 1.6 construct a table of values for x and y given a linear equation in two variables, Ax+By=C 1.7 draw the graph of Ax+By=C based on a table of values for x and y 1.8 define: • x and y intercepts • slope • domain • range 1.9 determine the following properties of the graph of a linear equation Ax + By = C : • slope • intercepts • domain

4

• range • trend (increasing or decreasing) 1.10given a linear equation Ax + By = C, rewrite in the form y = mx + b, and vice versa 1.11draw the graph of a linear equation in two variables described by an equation using • the intercepts • any two points • the slope and a given point 1.12obtain the equation of a line given the following: • slope intercept form • the intercepts • any two points • the slope and a point 1.13use linear equations in two variables to solve problems F. Special Products and Factoring 1. Demonstrate knowledge and skill in finding special products and factors of certain polynomials 1.1 identify special products • polynomials whose terms have a common monomial factor • trinomials which are products of two binomials • trinomials which are squares of a binomial • products of the sum and difference of two quantities ( x 2 − y 2 , x3 + y 3 , x3 − y 3 ) 1.2 given the factors, find the special product 1.3 factor polynomials • polynomials whose terms have a common monomial factor • trinomials which are products of two binomials • trinomials which are squares of a binomial • products of the sum and difference of two quantities ( x 2 − y 2 , x3 + y 3 , x3 − y 3 ) 1.4 given a polynomial, factor completely

5