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.