The goal of Advanced level Developmental Mathematics is to provide students with sufficient algebra, geometry, and trigonometry to satisfy grade 11 prerequisites for some vocational, career, technical, and/or further academic programs. This course satisfies the mathematics requirement for the BC Adult Graduation Diploma.
Hours: 120 (Lecture Hours: 120)
Total Weeks: 20
Prerequisites:
“C” or higher in MATH030 or MATH10 or equivalent or Advanced Level Placement on the CCP Math Assessment
Non- Course Prerequisites:
None
Co-requisite Statement:
None
Course Content:
Operations with Real Numbers
- Writing fractions as decimals and repeating decimals as fractions
- Adding, subtracting, multiplying and dividing rational numbers
- Evaluating powers with rational bases and integer exponents
- Order of operations with rational numbers
- Evaluating radicals with rational radicals and distinguishing between exact answer and approximate answers
- Simplifying, adding, subtracting, multiplying and dividing square roots
First Degree Equations and Inequalities
- First degree equations, including those involving parentheses
- formulas for a given variable when other variables are known
- formulas for given variable
- first degree inequalities in one variable
Polynomials
- monomials, binomials, trinomials, and other polynomials
- the laws of exponents to variable expressions with integral exponents
- adding, subtracting, and multiplying polynomials
- factoring polynomials by removing the largest common factor
- factoring binomials of the form a2x2 - b2y2 and trinomials of the form x2 + bx + c
- quadratic equations using the law of zero products
Optional: factoring trinomials of the form ax2 + bc + c
Rational Expressions
- simplifying, by factoring, rational expressions
- determining values for which a rational expression is undefined
- multiplying and dividing rational expressions
- adding and subtracting rational expressions consisting of monomial and/or binomial denominators
- solving simple rational equations and check solutions
Linear Equations
- graphing linear equations including the forms x = a and y = b
- determining slope and x and y intercepts when given a linear equation or its graph
- determining the equation of a line, y = mx + b, given its graph, given its slope and a point on the line, and given two points on the line
Systems of Linear Equations
- solving a system of first degree equations in two unknowns by graphing, substitution and elimination methods
- using a system of equations to solve practical problems
Radical Expressions
- simplifying, adding, subtracting, multiplying and dividing square roots with variable radicand
- solving equations with one square root containing a polynomial radicand and check for extraneous solutions
Trigonometry
- solving right triangles using one or more of the:
sine ratio
cosine ratio
tangent ratio
Pythagorean theorem
Angle sum property of triangles
Optional: evaluating sine and cosine for angles from 0 degrees to 180 degrees
Optional: solving triangles using the Law of Cosines or the Law of Sines, excluding the ambiguous case
Optional Course Content (one of the following must be completed):
The Quadratic Equation
- solving quadratic equations by factoring
- solving equations of the form x2 = bx = c = 0 by completing the square
- solving quadratic equations by using the quadratic formula
- graphing y = ax2 + bx + c and determining its x/y intercepts and vertex
- solving practical problems that can be solved using a quadratic equation
Statistics
- determining the mean, median, mode, range and standard deviation of a set of data
- representing data graphically using broken line graphs and bar graphs
- how the normal curve can be used to describe a normally distributed population
- calculating Z - scores and determine areas under the normal curve
- using areas under the normal curve to analyze data in terms of the probability of various events
Financial Mathematics
- simple interest problems
- compound interest problems
- calculating interest rates
- annuity problems
- periodic payment problems
- determining the finance charge on a loan
- determining the interest rate on a loan using tables or appropriate technology
Geometry
- classification of triangles according to angles and sides
- using the properties of triangles to determine the measure of sides and angles
- determining the measure and/or congruence of angles given a transversal and two parallel lines
- triangle congruence theorems in simple guided proofs
Learning Outcomes:
Operations with Real Numbers
- Write fractions as decimals and repeating decimals as fractions
- Add, subtract, multiply and divide rational numbers
- Evaluate powers with rational bases and integer exponents
- Demonstrate order of operations with rational numbers
- Evaluate radicals with rational radicands and distinguish between exact answer and approximate answers
- Simplify, add, subtract, multiply and divide square roots
First Degree Equations and Inequalities
- Solve first degree equations, in one variable, including those involving parentheses
- Solve formulas for a given variable when other variables are known
- Solve formulas for a given variable
- Solve first degree inequalities in one variable
- Solve practical problems that can be solved using a first degree equation
Polynomials
- Distinguish between monomials, binomials, trinomials, and other polynomials (in one variable only)
- Apply the laws of exponents to variable expressions with integral exponents
- Evaluate polynomials by substitution
- Add, subtract, and multiply polynomials
- Factor polynomials by removing the largest common factor
- Factor binomials of the form a2x2 - b2y2 and trinomials of the form x2 + bx + c
- Solve quadratic equations using the law of zero products
Optional: factor trinomials of the form ax2 + bc + c
Rational Expressions
- Simplify, by factoring, rational expressions consisting of polynomial numerators and either monomial, binomial or trinomial denominators
- Determine values for which a rational expression is undefined
- Multiply and divide rational expressions
- Add and subtract rational expressions consisting of monomial and/or binomial denominators
- Solve simple rational equations and check solutions
Linear Equations
- Graph a linear equations including the forms x = a and y = b
- Given a linear equation or its graph, determining its slope and x and y intercepts
- Determine the equation of a line, y = mx + b, given its graph, given its slope and a point on the line, and given two points on the line
Systems of Linear Equations
- Solve a system of first degree equations in two unknowns by graphing, substitution and elimination methods
- Solve practical problems that can be solved using a system of equations
Radical Expressions
- Simplify square roots with variable radicand
- Add, subtract, multiply and divide square roots with variable radicands
- Solve equations with one square root containing a polynomial radicand and check for extraneous solutions
Trigonometry
- Solve right triangles using one or more of the:
sine ratio
cosine ratio
tangent ratio
Pythagorean theorem
Angle sum property of triangles
Optional: evaluate sine and cosine for angles from 0 degrees to 180 degrees
Optional: solve triangles using the Law of Cosines or the Law of Sines, excluding the ambiguous case
Optional Learning Outcome (one of the following must be completed):
The Quadratic Equation
- Solve quadratic equations by factoring
- Solve equations of the form x2 = bx = c = 0 by completing the square
- Solve quadratic equations by using the quadratic formula
- Graph y = ax2 + bx + c and determining its x/y intercepts and vertex
- Solve practical problems that can be solved using a quadratic equation
Statistics
- Determine the mean, median, mode, range and standard deviation of a set of data
- Represent data graphically using broken line graphs and bar graphs
- Understand how the normal curve can be used to describe a normally distributed population
- Calculate Z - scores and determine areas under the normal curve
- Use areas under the normal curve to analyze data in terms of the probability of various events
Financial Mathematics
- Solve simple interest problems
- Solve compound interest problems
- Find the effective interest rate using E.R. = (1 + r/n)n-1
- Solve annuity problems
- Find periodic payment
- Determine the finance charge on a loan
- Determine the interest rate on a loan using tables or appropriate technology
Geometry
- Classify triangles according to angles and sides
- Use the properties of triangles to determine the measure of sides and angles
- Determine the measure and/or congruence of angles given a transversal and two parallel lines
- Use triangle congruence theorems in simple guided proofs
Grading System: Letters
Passing Grade: D (50%)
Percentage of Individual Work: 100
Textbooks: Textbooks are subject to change. Please contact the bookstore at your local campus for current book lists.