Secondary Mathematics - First Year - Elementary Algebra1: Measurement - Measurement and the use of measuring devices, conversion of units of measurement and solving real life problems
- Illustrate the development of measurement from the primitive to the present international system of units.
- Measure quantities.
- length.
- weight.
- volume.
- temperature.
- time.
- angle.
- Express relationships between two quantities using ratios.
- Convert measurements from one unit to another.
- Solve problems involving measurement.
2: Real Number System - Describe the real number system: integers, rational numbers, irrational numbers, real numbers
- Describe opposite quantities in real life.
- Determine the absolute value of a number.
- Solve simple absolute value equations using the number line.
- Perform fundamental operations on integers:
- addition.
- subtraction.
- multiplication.
- division.
- Illustrate the different properties:
- commutative.
- associative.
- distributive.
- identity.
- inverse.
- Solve problems involving integers
- Perform operations on dissimilar fractions and mixed forms.
- Perform operations on decimals.
- Solve problems involving fractions and decimals.
- Demonstrate knowledge and skill in solving square roots of positive rational numbers.
- Define the square root of a rational number.
- Approximate the square root of a positive rational number.
- Identify square roots which are rational and which are not rational (irrational numbers).
- If the square root of a number is not rational, determine two integers or rational numbers between which it lies.
- Give examples of other irrational numbers.
- Use knowledge related to square roots in problem-solving.
3: Algebraic Expressions - Demonstrate knowledge and skill related to simplifying and performing operations on polynomials.
- Define constants, variables, algebraic expressions.
- Simplify numerical expressions involving exponents and grouping symbols.
- Translate verbal phrases to mathematical expressions and vice versa.
- Evaluate mathematical expressions for given values of the variable(s) involved.
- Simplify algebraic expressions using the laws on exponents.
- aman=am+n
- (ab)m=ambm
- (am)n=amn
- (a/b)m=am/bm
- am/an=am-n, where m - n is a positive number if m is greater than n, m - n is a negative number if m is less than n
- Express numbers in scientific notation.
- Define polynomials.
- Classify algebraic expressions as polynomials and non-polynomials.
- 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.
- Solve problems involving polynomials.
4: First Degree Equations and Inequalities In One Variable - Demonstrate knowledge and skill in transforming and solving first degree equations and inequations in one variable.
- 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 using:
- number line.
- replacement set.
- inspection.
- Determine the solution set of first degree inequations 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.
- Solve problems using first degree equations and inequalities in one variable (e.g. relations among numbers, geometry, business, uniform motion, money problems, etc.).
5: Linear Equations in Two Variables - Demonstrate knowledge and skill related to linear equations in two variables and their application to real life problems.
- Describe the Cartesian Coordinate Plane (x-axis, y-axis, quadrant, origin).
- Given a point on the coordinate plane, give its coordinates.
- Given a pair of coordinates, plot the point.
- Given the coordinates of a point, determine the quadrant where it is located.
- Identify a linear equation in two variables: Ax+By=C.
- Construct a table of values for x and y given a linear equation in two variables, Ax+By=C.
- Draw the graph of Ax+By=C based on a table of values for x and y.
- Define features of a graph.
- x and y intercepts
- slope
- domain
- range
- Determine the following properties of the graph of a linear equation Ax + By = C:
- slope
- intercepts
- domain
- range
- trend (increasing or decreasing)
- Given a linear equation Ax + By = C, rewrite in the form y = mx + b, and vice versa.
- Draw 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
- Obtain the equation of a line given the following:
- slope intercept form
- the intercepts
- any two points
- the slope and a point
- Use linear equations in two variables to solve problems.
6: Special Products and Factoring - Demonstrate knowledge and skill in finding special products and factors of certain polynomials.
- 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
- Given the factors, find the special product.
- 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
- Given a polynomial, factor completely.
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