## MATH 043 - Advanced Level Developmental Mathematics

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
- 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
- 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):
- solving quadratic equations by factoring
- solving equations of the form x2 = bx = c = 0 by completing the square
- 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
- 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
- Simplify square roots with variable radicand
- 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):
- Solve quadratic equations by factoring
- Solve equations of the form x2 = bx = c = 0 by completing the square
- 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