## 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: 6)

**Total Weeks: **20

**Prerequisites:**

Intermediate MATH 030; MATH 10; successful completion of Adult Basic Education Placement Test;

OR permission of instructor

**Non- Course Prerequisites:**

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.