Secondary Mathematics - Second Year - Intermediate AlgebraSystems of Linear Equations and Inequalities 1: Solving Systems of Linear Equations and Inequalities in two variables - Define a system of linear equations in two variables.
- Solve systems of linear equations in two variables
- given a pair of linear equations in two variables, identify those
whose graphs
- intersect
- coincide
- are parallel
- 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)
2: Solution Set of the Systems of Linear Equations - given a system of linear equations in two variables, find the solution:
- by elimination
- by substitution
- given a system of linear equations to solve problems (e.g. number relations,
uniform motion, geometric relations, mixture, investment, work)
3: System of Linear Inequalities - Demonstrate knowledge and skill in solving a system of linear inequalities
by graphing
- Define a system of linear inequalities.
- Translate certain situations in real life to linear
inequalities.
- Draw the graph of a linear inequality in two variables.
- Represent the solution set of a system of linear inequalities by
graphing.
Quadratic Equations 4: Quadratic Equations and Their Roots - Demonstrate knowledge and skill in solving quadratic equations.
- Distinguish a quadratic equation from a linear equation.
- Find the solution set of a quadratic equation.
- determine the solution set of a quadratic equation
ax2+bx+c = 0 by algebraic methods:
- factoring
- quadratic formula
- completing the square
- derive the quadratic formula
- solve rational equations which can be reduced to quadratic
equations
- use quadratic equations to solve problems
Rational Algebraic Expressions 5: Simplifying Rational Algebraic Expressions - Demonstrate knowledge and skill in simplifying rational algebraic
expressions.
- Define rational algebraic expressions and domain of a rational
algebraic expression
- Translate verbal expressions into rational algebraic
expressions.
- Simplify rational algebraic expressions(reduce to lowest
terms).
6: Operations on Rational Algebraic Expressions - Perform operations on rational algebraic expressions.
- addition
- subtraction
- multiplication
- division
7: Rational Expressions and Equations - Simplify complex rational algebraic expressions.
- Solve rational equations and check for extraneous solutions.
- Solve problems involving rational algebraic expressions.
Variation 8: Talking about Variation. - Demonstrate knowledge of variation relationships and apply these in solving
problems
- Identify relationships in real life that are:
- direct variation
- direct square variations
- inverse variations
- joint variations
- Represent the following relationships as equations:
- _____ is directly proportional to _____
- _____ is inversely proportional to _____
- _____ varies directly as _____
- _____ varies directly as the square of _____
- _____ varies inversely as _____
- Solve equations on:
- direct variation
- direct square variations
- inverse variations
- joint variations
Integral Exponents 9: The Integral Exponents - Demonstrate knowledge and skill in simplifying expressions with integral
exponents and apply these in the solution of problems
- Demonstrate understanding of expressions with:
- positive exponents
- negative exponents
- zero exponents
- Evaluate numerical expressions involving integral exponents.
- Rewrite algebraic expressions with zero and negative exponents.
- Solve problems involving expressions with exponents.
Expressions and Equations involving Radicals 10: Radical Expressions in General - Demonstrate knowledge and skill in simplifying radical expressions
- Identify expressions which are perfect squares or perfect
cubes.
- Find the square root or cube root of expressions.
- Given a number in the form nroot{n}{x} where x is not a perfect nth root,
name two rational numbers between which it lies.
- Use laws of exponents to simplify expressions containing rational
exponents.
- Rewrite expressions with rational exponents as radical expressions and vice
versa.
- Simplify the radical expression in such a way that the radicand contains no
perfect nth root.
- Rationalize a fraction whose denominator contains square roots.
11: Operations on Radical Expressions - Perform operations on radical expressions.
- addition
- subtraction
- multiplication
- division
- Solve radical equations.
- Solve problems involving radical equations.
Searching Patterns in Sequences — Arithmetic, Geometric and Others 12: Arithmetic Sequences - Demonstrate knowledge and skill related to arithmetic sequences and apply
these in solving problems
- List the next few terms of a sequence given several consecutive
terms.
- Derive, by pattern-searching, a mathematical expression (rule) for
generating the sequence.
- Describe an arithmetic sequence by any of the following ways:
- giving the first few terms
- giving the formula for the nth term
- drawing the graph
- given the first few terms of an arithmetic sequence, find the:
- common difference
- nth term
- Given two terms of an arithmetic sequence, find: the first term; the
common difference or a specified nth term.
- Solve problems involving arithmetic means.
- Derive the formula for the sum of the n terms of an arithmetic
sequence.
- Define the sum of an arithmetic sequence.
- Solve problems involving arithmetic sequences.
13: Geometric Sequences and Series - Demonstrate knowledge and skill related to geometric sequences and apply
these in solving problems
- Describe a geometric sequence in any of the following ways:
- giving the first few terms of the sequence
- giving the formula for the nth term
- drawing the graph
- given the first few terms of a geometric sequence, find the common
ratio and the nth term
- given two specified terms of a geometric sequence, find the first
term and common ratio
- Solve problems involving geometric means
- Derive the formula for the sum of the terms of a geometric
sequence.
- Find the sum of the terms of a geometric sequence.
- Derive the formula for an infinite geometric series.
- Solve problems involving geometric sequences.
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