Mathematics: Advanced Level—Business/Technical

Goal Statement

The goal of Advanced Business/Technical Mathematics is to provide the student with practical applications useful in future vocational training, careers, or personal life.

Learning Outcomes

1. Operations with Real Numbers

It is expected that learners will be able to:

• add, subtract, multiply and divide rational numbers
• evaluate powers with rational bases and integer exponents
• demonstrate the order of operations with rational numbers
• evaluate radicals and distinguish between exact answers and approximate answers
• write numbers in scientific notation, convert from scientific notation to standard notation, and multiply and divide numbers expressed in scientific notation
• use a scientific calculator

2. First-Degree Equations and Inequalities

It is expected that learners will be able to:

• solve first-degree equations, in one variable, including those involving parentheses
• solve formulas for a given variable
• solve first-degree inequalities in one variable
• solve practical problems using a first-degree equation

3. Equations and their Graphs

It is expected that learners will be able to:

• plot points on a coordinate system
• use ordered pairs to name points on the coordinate system
• determine whether a given point is a solution to an equation in two variables

Optional Topics

• recognize and create any of the graphs of the following relations:
  • y = ax + b (linear)
  • y = ax² + bx + c (quadratic)
  • y = a/x (reciprocal)
  • y = a(bx)^½ (square root)
  • y = a(bx)^c (exponential) where a, b, c are real numbers

• given the graph of an equation, determine the following, where appropriate:
  • x– and y-intercepts
  • vertex
  • slope

Optional Learning Outcomes

Learners must complete a minimum of three of the following:

A. Systems of Equations

It is expected that learners will be able to:

• solve systems of linear equations in two variables graphically and/or algebraically
• solve practical problems

B. Consumer Mathematics

It is expected that learners will be able to:

• solve consumer problems involving unit prices, wages earned in various situations, taxation, simple and compound interests, and exchange rates
• solve budget problems
• solve investment and credit problems involving interest

C. Finance

It is expected that learners will be able to:

• solve problems involving compound interest
• find the effective interest rate
• solve annuity problems
• solve loan, mortgage, and borrowing problems
• determine the finance charge on a loan

D. Data Analysis I

It is expected that learners will be able to:

• determine the mean, median, mode and range from a set of data
• interpret and/or construct frequency tables, broken line graphs, bar graphs, histograms, stem-plots and other visual representations  from a set of data
• design a simple statistical experiment, collect the data, analyze and communicate the results

E. Data Analysis II

It is expected that learners will be able to:

• find quartiles and the percentile represented by a given data value
• calculate the standard deviation of a set of data using appropriate technology
• use z-scores to analyze normally distributed data

F. Geometry

It is expected that learners will be able to:

• use any of the following angle properties to determine an angle in a drawing:
  • vertically opposite angles
  • corresponding angles, alternate interior angles, and angles on the same side of the transversal
  • angles on a line
  • angles on a point
  • complementary and supplementary angles
  • angle sum of a triangle
• classify triangles and quadrilaterals according to their sides and angles
• draw triangles given:
  • three sides
  • two sides and an included angle
  • two angles and a side
• draw quadrilaterals given various combinations of sides, angles, and diagonals

G. Trigonometry

It is expected that learners will be able to:

• solve right triangles using one or more of
  • the sine ratio
  • the cosine ratio
  • the tangent ratio
  • the Pythagorean theorem
  • the angle sum property of triangles

Optional Topic

• solve triangles using the Law of Sines (excluding the ambiguous case) and the Law of Cosines

H. Measurement

It is expected that learners will be able to:

• complete simple conversions
• solve problems involving composite figures, with reference to perimeter, area, volume and surface area
• calculate maximum and minimum values, using tolerances, for lengths, areas and volumes
• enlarge or reduce a dimensional object according to a specified scale

I. Trades Option

It is expected that learners will be able to solve applied problems (as related to a specific trade) using:

• unit conversions
• algebra
• geometry
• right triangle trigonometry
• ratio and proportion
• percentage

J. Health Option

It is expected that learners will be able to solve applied problems (as related to the health field) using:

• ratio and proportion
• unit conversion
• percentage