Download General AND Specific Competencies in Mathematics II

General AND Specific Competencies in Mathematics II
(Intermediate Algebra)
A. Systems of Linear Equations and Inequalities
1. Demonstrate knowledge and skill in solving systems of linear equations in two variables and
apply these in solving problems
1. define a system of linear equations in two variables
2. solve systems of linear equations in two variables
1.2.1 given a pair of linear equations in two variables, identify those whose graphs
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intersect
coincide
are parallel
1.2.2 given a system of linear equations in two variables, find the solution graphically (i.e. by drawing the
graphs and obtaining the coordinates of the intersection)
3. given a system of linear equations in two variables, find the solution graphically:
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by elimination
by substitution
5. use systems of linear equations to solve problems (e.g. number relations, uniform motion,
geometric relations, mixture, investment, work)
2. Demonstrate knowledge and skill in solving a system of linear inequalities by graphing
1. define a system of linear inequalities
2. translate certain situations in real life to linear inequalities
3. draw the graph of a linear inequality in two variables
4. represent the solution set of a system of linear inequalities by graphing
B. Quadratic Equations
1. Demonstrate knowledge and skill in solving quadratic equations and
ability to apply in solving problems
1. distinguish a quadratic equation from a linear equation
2. find the solution set of a quadratic equation
1. determine the solution set of a quadratic equation by algebraic methods:
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factoring
quadratic formula
completing the square
2. derive the quadratic formula
3. solve rational equations which can be reduced to quadratic equations
4. use quadratic equations to solve problems
C. Rational Algebraic Expressions
1. Demonstrate knowledge and skill in simplifying and performing operations on
rational algebraic expressions and apply these in solving problems
1. define:
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rational algebraic expression
domain of a rational algebraic expression
2. translate verbal expressions into rational algebraic expressions
3. simplify rational algebraic expressions(reduce to lowest terms)
4. perform operations on rational algebraic expressions
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addition
subtraction
multiplication
division
5. simplify complex rational algebraic expressions
6. solve rational equations and check for extraneous solutions
7. solve problems involving rational algebraic expressions
D. Variation
1. Demonstrate knowledge of variation
relationships and apply these in solving
problems
1. identify relationships in real life that are:
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direct variation
direct square variations
inverse variations
joint variations
2. represent the following relationships as equations:
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“_____ is directly proportional to _____”
“_____ is inversely proportional to _____”
“_____ varies directly as _____”
“_____ varies directly as the square of _____”
“_____ varies inversely as _____”
3. solve equations on:
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direct variations
direct square variation
inverse variation
joint variation
E. Integral Exponents
1. Demonstrate knowledge and skill in simplifying expressions with integral exponents and apply
these in the solution of problems
1. demonstrate understanding of expressions with:
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positive exponents
negative exponents
zero exponents
2. evaluate numerical expressions involving integral exponents
3. rewrite algebraic expressions with zero and negative exponents
4. solve problems involving expressions with exponents
F. Radical Expressions
1. Demonstrate knowledge and skill in simplifying, performing operations and solving equations and
problems involving radical expressions
1.1 identify expressions which are perfect squares or perfect cubes
2. find the square root or cube root of expressions
3. given a number in the form where x is not a perfect nth root, name two rational numbers
between which it lies
4. use laws of exponents to simplify expressions containing rational exponents
5. rewrite expressions with rational exponents as radical expressions and vice versa
6. simplify the radical expression in such a way that the radicand contains no perfect nth
root
7. rationalize a fraction whose denominator contains square roots
8. perform operations on radical expressions
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addition
subtraction
multiplication
division
9. solve radical equations
10. solve problems involving radical equations
G. Searching for Patterns in Sequences, Arithmetic, Geometric and Others
1. Demonstrate knowledge and skill related to arithmetic sequence and apply these in solving
problems
1. list the next few terms of a sequence given several consecutive terms
2. derive, by pattern-searching, a mathematical expression (rule) for generating the
sequence
3. describe an arithmetic sequence by any of the following ways:
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giving the first few terms
giving the formula for the nth term
drawing the graph
4. given the first few terms of an arithmetic sequence, find the:
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common difference
nth term
5. given two terms of an arithmetic sequence, find: the first term; the common difference or
a specified nth term
6. solve problems involving arithmetic means
7. derive the formula for the sum of the n terms of an arithmetic sequence
8. define the sum of an arithmetic sequence
9. solve problems involving arithmetic sequences
2. Demonstrate knowledge and skill related to geometric sequence and apply these in solving
problems
1. describe a geometric sequence in any of the following ways:
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giving the first few terms of the sequence
giving the formula for the nth term
drawing the graph
2. given the first few terms of a geometric sequence, find the:
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common ratio
nth term
3. given two specified terms of a geometric sequence, find the:
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first term
common ratio
4. solve problems involving geometric means
5. derive the formula for the sum of the terms of a geometric sequence
6. find the sum of the terms of a geometric sequence
7. derive the formula for an infinite geometric series
8. solve problems involving geometric sequences
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