{"id":346,"date":"2023-07-16T18:15:46","date_gmt":"2023-07-16T22:15:46","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-advanced-level-business-technical\/"},"modified":"2025-06-04T17:32:15","modified_gmt":"2025-06-04T21:32:15","slug":"mathematics-advanced-level-business-technical","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-advanced-level-business-technical\/","title":{"raw":"Mathematics: Advanced Level\u2014Business\/Technical","rendered":"Mathematics: Advanced Level\u2014Business\/Technical"},"content":{"raw":"<h3>Mathematics: Advanced Level\u2014Business\/Technical<\/h3>\r\n\r\n<hr \/>\r\n\r\n<h5>Goal Statement<\/h5>\r\nThe goal of Advanced Business\/Technical Mathematics is to provide the student with practical applications useful in future vocational training, careers, or personal life.\r\n<h5>Learning Outcomes<\/h5>\r\n<h6>1. Operations with Real Numbers<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>add, subtract, multiply and divide rational numbers<\/li>\r\n \t<li>evaluate powers with rational bases and integer exponents<\/li>\r\n \t<li>demonstrate the order of operations with rational numbers<\/li>\r\n \t<li>evaluate radicals and distinguish between exact answers and approximate answers<\/li>\r\n \t<li>write numbers in scientific notation, convert from scientific notation to standard notation, and multiply and divide numbers expressed in scientific notation<\/li>\r\n \t<li>use a scientific calculator<\/li>\r\n<\/ul>\r\n<h6>2. First-Degree Equations and Inequalities<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve first-degree equations, in one variable, including those involving parentheses<\/li>\r\n \t<li>solve formulas for a given variable<\/li>\r\n \t<li>solve first-degree inequalities in one variable<\/li>\r\n \t<li>solve practical problems using a first-degree equation<\/li>\r\n<\/ul>\r\n<h6>3. Equations and their Graphs<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>plot points on a coordinate system<\/li>\r\n \t<li>use ordered pairs to name points on the coordinate system<\/li>\r\n \t<li>determine whether a given point is a solution to an equation in two variables<\/li>\r\n<\/ul>\r\n<strong>Optional Topics<\/strong>\r\n<ul>\r\n \t<li>recognize and create any of the graphs of the following relations:\r\n<ul>\r\n \t<li><em>y<\/em> = a<em>x<\/em> + b (linear)<\/li>\r\n \t<li><em>y<\/em> = a<em>x<\/em>\u00b2 + b<em>x<\/em> + c (quadratic)<\/li>\r\n \t<li><em>y<\/em> = a\/<em>x <\/em>(reciprocal)<\/li>\r\n \t<li><em>y<\/em> = a(b<em>x<\/em>)<sup>\u00bd<\/sup> (square root)<\/li>\r\n \t<li><em>y<\/em> = a(b<em>x<\/em>)<sup>c<\/sup> (exponential) where a, b, c are real numbers<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li>given the graph of an equation, determine the following, where appropriate:\r\n<ul>\r\n \t<li><em>x<\/em>- and <em>y<\/em>-intercepts<\/li>\r\n \t<li>vertex<\/li>\r\n \t<li>slope<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h5>Optional Learning Outcomes<\/h5>\r\nLearners must complete a minimum of three of the following:\r\n<h6>A. Systems of Equations<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve systems of linear equations in two variables graphically and\/or algebraically<\/li>\r\n \t<li>solve practical problems<\/li>\r\n<\/ul>\r\n<h6>B. Consumer Mathematics<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve consumer problems involving unit prices, wages earned in various situations, taxation, simple and compound interests, and exchange rates<\/li>\r\n \t<li>solve budget problems<\/li>\r\n \t<li>solve investment and credit problems involving interest<\/li>\r\n<\/ul>\r\n<h6>C. Finance<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve problems involving compound interest<\/li>\r\n \t<li>find the effective interest rate<\/li>\r\n \t<li>solve annuity problems<\/li>\r\n \t<li>solve loan, mortgage, and borrowing problems<\/li>\r\n \t<li>determine the finance charge on a loan<\/li>\r\n<\/ul>\r\n<h6>D. Data Analysis I<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>determine the mean, median, mode and range from a set of data<\/li>\r\n \t<li>interpret and\/or construct frequency tables, broken line graphs, bar graphs, histograms, stem-plots and other visual representations from a set of data<\/li>\r\n \t<li>design a simple statistical experiment, collect the data, analyze and communicate the results<\/li>\r\n<\/ul>\r\n<h6>E. Data Analysis II<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>find quartiles and the percentile represented by a given data value<\/li>\r\n \t<li>calculate the standard deviation of a set of data using appropriate technology<\/li>\r\n \t<li>use z-scores to analyze normally distributed data<\/li>\r\n<\/ul>\r\n<h6>F. Geometry<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>use any of the following angle properties to determine an angle in a drawing:\r\n<ul>\r\n \t<li>vertically opposite angles<\/li>\r\n \t<li>corresponding angles, alternate interior angles, and angles on the same side of the transversal<\/li>\r\n \t<li>angles on a line<\/li>\r\n \t<li>angles on a point<\/li>\r\n \t<li>complementary and supplementary angles<\/li>\r\n \t<li>angle sum of a triangle<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>classify triangles and quadrilaterals according to their sides and angles<\/li>\r\n \t<li>draw triangles given:\r\n<ul>\r\n \t<li>three sides<\/li>\r\n \t<li>two sides and an included angle<\/li>\r\n \t<li>two angles and a side<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>draw quadrilaterals given various combinations of sides, angles, and diagonals<\/li>\r\n<\/ul>\r\n<h6>G. Trigonometry<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve right triangles using one or more of\r\n<ul>\r\n \t<li>the sine ratio<\/li>\r\n \t<li>the cosine ratio<\/li>\r\n \t<li>the tangent ratio<\/li>\r\n \t<li>the Pythagorean theorem<\/li>\r\n \t<li>the angle sum property of triangles<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<strong>Optional Topic<\/strong>\r\n<ul>\r\n \t<li>solve triangles using the Law of Sines (excluding the Ambiguous Case) and the Law of Cosines<\/li>\r\n<\/ul>\r\n<h6>H. Measurement<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>complete simple conversions<\/li>\r\n \t<li>solve problems involving composite figures, with reference to perimeter, area, volume and surface area<\/li>\r\n \t<li>calculate maximum and minimum values, using tolerances, for lengths, areas and volumes<\/li>\r\n \t<li>enlarge or reduce a dimensional object according to a specified scale<\/li>\r\n<\/ul>\r\n<h6>I. Trades Option<\/h6>\r\nIt is expected that learners will be able to solve applied problems (as related to a specific trade) using:\r\n<ul>\r\n \t<li>unit conversions<\/li>\r\n \t<li>algebra<\/li>\r\n \t<li>geometry<\/li>\r\n \t<li>right triangle trigonometry<\/li>\r\n \t<li>ratio and proportion<\/li>\r\n \t<li>percentage<\/li>\r\n<\/ul>\r\n<h6>J. Health Option<\/h6>\r\nIt is expected that learners will be able to solve applied problems (as related to the health field) using:\r\n<ul>\r\n \t<li>ratio and proportion<\/li>\r\n \t<li>unit conversion<\/li>\r\n \t<li>percentage<\/li>\r\n<\/ul>","rendered":"<h3>Mathematics: Advanced Level\u2014Business\/Technical<\/h3>\n<hr \/>\n<h5>Goal Statement<\/h5>\n<p>The goal of Advanced Business\/Technical Mathematics is to provide the student with practical applications useful in future vocational training, careers, or personal life.<\/p>\n<h5>Learning Outcomes<\/h5>\n<h6>1. Operations with Real Numbers<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>add, subtract, multiply and divide rational numbers<\/li>\n<li>evaluate powers with rational bases and integer exponents<\/li>\n<li>demonstrate the order of operations with rational numbers<\/li>\n<li>evaluate radicals and distinguish between exact answers and approximate answers<\/li>\n<li>write numbers in scientific notation, convert from scientific notation to standard notation, and multiply and divide numbers expressed in scientific notation<\/li>\n<li>use a scientific calculator<\/li>\n<\/ul>\n<h6>2. First-Degree Equations and Inequalities<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve first-degree equations, in one variable, including those involving parentheses<\/li>\n<li>solve formulas for a given variable<\/li>\n<li>solve first-degree inequalities in one variable<\/li>\n<li>solve practical problems using a first-degree equation<\/li>\n<\/ul>\n<h6>3. Equations and their Graphs<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>plot points on a coordinate system<\/li>\n<li>use ordered pairs to name points on the coordinate system<\/li>\n<li>determine whether a given point is a solution to an equation in two variables<\/li>\n<\/ul>\n<p><strong>Optional Topics<\/strong><\/p>\n<ul>\n<li>recognize and create any of the graphs of the following relations:\n<ul>\n<li><em>y<\/em> = a<em>x<\/em> + b (linear)<\/li>\n<li><em>y<\/em> = a<em>x<\/em>\u00b2 + b<em>x<\/em> + c (quadratic)<\/li>\n<li><em>y<\/em> = a\/<em>x <\/em>(reciprocal)<\/li>\n<li><em>y<\/em> = a(b<em>x<\/em>)<sup>\u00bd<\/sup> (square root)<\/li>\n<li><em>y<\/em> = a(b<em>x<\/em>)<sup>c<\/sup> (exponential) where a, b, c are real numbers<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li>given the graph of an equation, determine the following, where appropriate:\n<ul>\n<li><em>x<\/em>&#8211; and <em>y<\/em>-intercepts<\/li>\n<li>vertex<\/li>\n<li>slope<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h5>Optional Learning Outcomes<\/h5>\n<p>Learners must complete a minimum of three of the following:<\/p>\n<h6>A. Systems of Equations<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve systems of linear equations in two variables graphically and\/or algebraically<\/li>\n<li>solve practical problems<\/li>\n<\/ul>\n<h6>B. Consumer Mathematics<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve consumer problems involving unit prices, wages earned in various situations, taxation, simple and compound interests, and exchange rates<\/li>\n<li>solve budget problems<\/li>\n<li>solve investment and credit problems involving interest<\/li>\n<\/ul>\n<h6>C. Finance<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve problems involving compound interest<\/li>\n<li>find the effective interest rate<\/li>\n<li>solve annuity problems<\/li>\n<li>solve loan, mortgage, and borrowing problems<\/li>\n<li>determine the finance charge on a loan<\/li>\n<\/ul>\n<h6>D. Data Analysis I<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>determine the mean, median, mode and range from a set of data<\/li>\n<li>interpret and\/or construct frequency tables, broken line graphs, bar graphs, histograms, stem-plots and other visual representations from a set of data<\/li>\n<li>design a simple statistical experiment, collect the data, analyze and communicate the results<\/li>\n<\/ul>\n<h6>E. Data Analysis II<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>find quartiles and the percentile represented by a given data value<\/li>\n<li>calculate the standard deviation of a set of data using appropriate technology<\/li>\n<li>use z-scores to analyze normally distributed data<\/li>\n<\/ul>\n<h6>F. Geometry<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>use any of the following angle properties to determine an angle in a drawing:\n<ul>\n<li>vertically opposite angles<\/li>\n<li>corresponding angles, alternate interior angles, and angles on the same side of the transversal<\/li>\n<li>angles on a line<\/li>\n<li>angles on a point<\/li>\n<li>complementary and supplementary angles<\/li>\n<li>angle sum of a triangle<\/li>\n<\/ul>\n<\/li>\n<li>classify triangles and quadrilaterals according to their sides and angles<\/li>\n<li>draw triangles given:\n<ul>\n<li>three sides<\/li>\n<li>two sides and an included angle<\/li>\n<li>two angles and a side<\/li>\n<\/ul>\n<\/li>\n<li>draw quadrilaterals given various combinations of sides, angles, and diagonals<\/li>\n<\/ul>\n<h6>G. Trigonometry<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve right triangles using one or more of\n<ul>\n<li>the sine ratio<\/li>\n<li>the cosine ratio<\/li>\n<li>the tangent ratio<\/li>\n<li>the Pythagorean theorem<\/li>\n<li>the angle sum property of triangles<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Optional Topic<\/strong><\/p>\n<ul>\n<li>solve triangles using the Law of Sines (excluding the Ambiguous Case) and the Law of Cosines<\/li>\n<\/ul>\n<h6>H. Measurement<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>complete simple conversions<\/li>\n<li>solve problems involving composite figures, with reference to perimeter, area, volume and surface area<\/li>\n<li>calculate maximum and minimum values, using tolerances, for lengths, areas and volumes<\/li>\n<li>enlarge or reduce a dimensional object according to a specified scale<\/li>\n<\/ul>\n<h6>I. Trades Option<\/h6>\n<p>It is expected that learners will be able to solve applied problems (as related to a specific trade) using:<\/p>\n<ul>\n<li>unit conversions<\/li>\n<li>algebra<\/li>\n<li>geometry<\/li>\n<li>right triangle trigonometry<\/li>\n<li>ratio and proportion<\/li>\n<li>percentage<\/li>\n<\/ul>\n<h6>J. Health Option<\/h6>\n<p>It is expected that learners will be able to solve applied problems (as related to the health field) using:<\/p>\n<ul>\n<li>ratio and proportion<\/li>\n<li>unit conversion<\/li>\n<li>percentage<\/li>\n<\/ul>\n","protected":false},"author":1935,"menu_order":6,"template":"","meta":{"pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-346","chapter","type-chapter","status-publish","hentry"],"part":340,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/users\/1935"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/346\/revisions"}],"predecessor-version":[{"id":472,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/346\/revisions\/472"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/parts\/340"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/346\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/media?parent=346"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapter-type?post=346"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/contributor?post=346"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/license?post=346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}