{"id":343,"date":"2023-07-16T18:15:45","date_gmt":"2023-07-16T22:15:45","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-advanced-level-developmental\/"},"modified":"2023-07-17T14:01:44","modified_gmt":"2023-07-17T18:01:44","slug":"mathematics-advanced-level-developmental","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-advanced-level-developmental\/","title":{"raw":"Mathematics: Advanced Level\u2014Developmental","rendered":"Mathematics: Advanced Level\u2014Developmental"},"content":{"raw":"<h3>Mathematics: Advanced Level\u2014Developmental<\/h3>\r\n\r\n<hr>\r\n\r\n<h5>Goal Statement<\/h5>\r\nThe goal of Advanced 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.\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>write fractions as decimals and repeating decimals as fractions<\/li>\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 with rational radicands and distinguish between exact answers and approximate answers<\/li>\r\n \t<li>simplify, add, subtract, multiply and divide square roots<\/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 when other variables are known<\/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 that can be solved using a first degree equation<\/li>\r\n<\/ul>\r\n<h6>3. Polynomials<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>distinguish between monomials, binomials, trinomials and other polynomials (in one variable only)<\/li>\r\n \t<li>apply the laws of exponents to variable expressions with integral exponents<\/li>\r\n \t<li>evaluate polynomials by substitution<\/li>\r\n \t<li>add, subtract, and multiply polynomials<\/li>\r\n \t<li>factor polynomials by removing the largest common factor<\/li>\r\n \t<li>factor binomials of the form a\u00b2x\u00b2 \u2013 b\u00b2y\u00b2 and trinomials of the form x\u00b2 + bx + c<\/li>\r\n \t<li>solve quadratic equations using the law of zero products<\/li>\r\n<\/ul>\r\n<em>Optional <\/em><em>Outcomes:<\/em>\r\n<ul>\r\n \t<li>factor trinomials of the form ax\u00b2 + bx + c<\/li>\r\n<\/ul>\r\n<h6>4. Rational Expressions and Equations<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>simplify, by factoring, rational expressions consisting of polynomial numerators and either monomial, binomial, or trinomial denominators<\/li>\r\n \t<li>determine values for which a rational expression is undefined<\/li>\r\n \t<li>multiply and divide rational expressions<\/li>\r\n \t<li>add and subtract rational expressions consisting of monomial and\/or binomial denominators<\/li>\r\n \t<li>solve simple rational equations and check solutions<\/li>\r\n<\/ul>\r\n<h6>5. Linear Equations<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>graph a linear equation including the forms <em>x<\/em> = a and <em>y<\/em> = b<\/li>\r\n \t<li>given a linear equation or its graph, determine its\r\n<ul>\r\n \t<li>slope<\/li>\r\n \t<li><em>x<\/em>- and <em>y<\/em>-intercepts<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>determine the equation of a line, <em>y<\/em> = m<em>x<\/em> + b, given\r\n<ul>\r\n \t<li>its graph<\/li>\r\n \t<li>its slope and a point on the line<\/li>\r\n \t<li>two points on the line<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h6>6. Systems of Linear Equations<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve a system of first degree equations in two unknowns by graphing, substitution, and elimination methods<\/li>\r\n \t<li>solve practical problems that can be solved using a system of equations<\/li>\r\n<\/ul>\r\n<h6>7. Radical Expressions and Equations<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>simplify square roots with variable radicands<\/li>\r\n \t<li>add, subtract, multiply and divide square roots with variable radicands<\/li>\r\n \t<li>solve equations with one square root containing a polynomial radicand and check for extraneous solutions<\/li>\r\n<\/ul>\r\n<h6>8. 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<em style=\"text-align: initial;font-size: 14pt\">Optional <\/em><em style=\"text-align: initial;font-size: 14pt\">Outcomes:<\/em>\r\n<ul>\r\n \t<li>evaluate sine and cosine for angles from 0\u00ba to 180\u00ba<\/li>\r\n \t<li>solve triangles using the Law of Cosines or the Law of Sines, excluding the ambiguous case<\/li>\r\n<\/ul>\r\n<h6>9. Optional Learning Outcomes<\/h6>\r\nStudents must complete one of the following four optional topics:\r\n<h6>A. The Quadratic Equation<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve quadratic equations by factoring<\/li>\r\n \t<li>solve equations of the form <em>x<\/em>\u00b2 + b<em>x<\/em> + c = 0 by completing the square<\/li>\r\n \t<li>solve quadratic equations by using the quadratic formula<\/li>\r\n \t<li>graph <em>y<\/em> = a<em>x<\/em>\u00b2 + b<em>x<\/em> + c and determine its<\/li>\r\n \t<li><em>x<\/em>- and <em>y<\/em>-intercepts<\/li>\r\n \t<li>vertex<\/li>\r\n \t<li>solve practical problems that can be solved using a quadratic equation<\/li>\r\n<\/ul>\r\n<h6>B. Statistics<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>determine the mean, median, mode, range and standard deviation of a set of data<\/li>\r\n \t<li>represent data graphically using broken line graphs and bar graphs<\/li>\r\n \t<li>understand how the normal curve can be used to describe a normally distributed population<\/li>\r\n \t<li>calculate z-scores and determine areas under the normal curve<\/li>\r\n \t<li>use areas under the normal curve to analyze data in terms of the probability of various events<\/li>\r\n<\/ul>\r\n<h6>C. Financial Mathematics<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve simple interest problems using the formula, <em>i<\/em> <em>= prt<\/em> (for any variable)<\/li>\r\n \t<li>solve compound interest problems for <em>A <\/em>or <em>P <\/em>using [latex]A=P\\left ( 1+\\frac{r}{n} \\right )^{nt}[\/latex]<\/li>\r\n \t<li>find the effective interest rate using [latex]E.R.=\\left ( 1+\\frac{r}{n} \\right )^{n}-1[\/latex]<\/li>\r\n \t<li>solve annuity problems using [latex]A=\\tfrac{nP[\\left ( 1+\\frac{r}{n} \\right )^{n}-1]}{r}[\/latex]&nbsp; (for <em>A<\/em> or <em>P<\/em> only)<\/li>\r\n \t<li>find periodic payment using&nbsp; &nbsp; [latex]P=\\frac{A(\\frac{r}{n})}{1-\\left ( 1+\\frac{r}{n} \\right )^{-nt}}[\/latex]<\/li>\r\n \t<li>determine the finance charge on a loan<\/li>\r\n \t<li>determine the interest rate on a loan using tables or appropriate technology<\/li>\r\n<\/ul>\r\n<h6>D. Geometry<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>classify triangles according to angles and sides<\/li>\r\n \t<li>use the properties of triangles to determine the measure of sides and angles<\/li>\r\n \t<li>determine the measure and\/or congruence of angles given a transversal and two parallel lines<\/li>\r\n \t<li>use the triangle congruence theorems in simple guided proofs<\/li>\r\n<\/ul>\r\n","rendered":"<h3>Mathematics: Advanced Level\u2014Developmental<\/h3>\n<hr \/>\n<h5>Goal Statement<\/h5>\n<p>The goal of Advanced 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.<\/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>write fractions as decimals and repeating decimals as fractions<\/li>\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 with rational radicands and distinguish between exact answers and approximate answers<\/li>\n<li>simplify, add, subtract, multiply and divide square roots<\/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 when other variables are known<\/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 that can be solved using a first degree equation<\/li>\n<\/ul>\n<h6>3. Polynomials<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>distinguish between monomials, binomials, trinomials and other polynomials (in one variable only)<\/li>\n<li>apply the laws of exponents to variable expressions with integral exponents<\/li>\n<li>evaluate polynomials by substitution<\/li>\n<li>add, subtract, and multiply polynomials<\/li>\n<li>factor polynomials by removing the largest common factor<\/li>\n<li>factor binomials of the form a\u00b2x\u00b2 \u2013 b\u00b2y\u00b2 and trinomials of the form x\u00b2 + bx + c<\/li>\n<li>solve quadratic equations using the law of zero products<\/li>\n<\/ul>\n<p><em>Optional <\/em><em>Outcomes:<\/em><\/p>\n<ul>\n<li>factor trinomials of the form ax\u00b2 + bx + c<\/li>\n<\/ul>\n<h6>4. Rational Expressions and Equations<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>simplify, by factoring, rational expressions consisting of polynomial numerators and either monomial, binomial, or trinomial denominators<\/li>\n<li>determine values for which a rational expression is undefined<\/li>\n<li>multiply and divide rational expressions<\/li>\n<li>add and subtract rational expressions consisting of monomial and\/or binomial denominators<\/li>\n<li>solve simple rational equations and check solutions<\/li>\n<\/ul>\n<h6>5. Linear Equations<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>graph a linear equation including the forms <em>x<\/em> = a and <em>y<\/em> = b<\/li>\n<li>given a linear equation or its graph, determine its\n<ul>\n<li>slope<\/li>\n<li><em>x<\/em>&#8211; and <em>y<\/em>-intercepts<\/li>\n<\/ul>\n<\/li>\n<li>determine the equation of a line, <em>y<\/em> = m<em>x<\/em> + b, given\n<ul>\n<li>its graph<\/li>\n<li>its slope and a point on the line<\/li>\n<li>two points on the line<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h6>6. Systems of Linear Equations<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve a system of first degree equations in two unknowns by graphing, substitution, and elimination methods<\/li>\n<li>solve practical problems that can be solved using a system of equations<\/li>\n<\/ul>\n<h6>7. Radical Expressions and Equations<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>simplify square roots with variable radicands<\/li>\n<li>add, subtract, multiply and divide square roots with variable radicands<\/li>\n<li>solve equations with one square root containing a polynomial radicand and check for extraneous solutions<\/li>\n<\/ul>\n<h6>8. 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><em style=\"text-align: initial;font-size: 14pt\">Optional <\/em><em style=\"text-align: initial;font-size: 14pt\">Outcomes:<\/em><\/p>\n<ul>\n<li>evaluate sine and cosine for angles from 0\u00ba to 180\u00ba<\/li>\n<li>solve triangles using the Law of Cosines or the Law of Sines, excluding the ambiguous case<\/li>\n<\/ul>\n<h6>9. Optional Learning Outcomes<\/h6>\n<p>Students must complete one of the following four optional topics:<\/p>\n<h6>A. The Quadratic Equation<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve quadratic equations by factoring<\/li>\n<li>solve equations of the form <em>x<\/em>\u00b2 + b<em>x<\/em> + c = 0 by completing the square<\/li>\n<li>solve quadratic equations by using the quadratic formula<\/li>\n<li>graph <em>y<\/em> = a<em>x<\/em>\u00b2 + b<em>x<\/em> + c and determine its<\/li>\n<li><em>x<\/em>&#8211; and <em>y<\/em>-intercepts<\/li>\n<li>vertex<\/li>\n<li>solve practical problems that can be solved using a quadratic equation<\/li>\n<\/ul>\n<h6>B. Statistics<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>determine the mean, median, mode, range and standard deviation of a set of data<\/li>\n<li>represent data graphically using broken line graphs and bar graphs<\/li>\n<li>understand how the normal curve can be used to describe a normally distributed population<\/li>\n<li>calculate z-scores and determine areas under the normal curve<\/li>\n<li>use areas under the normal curve to analyze data in terms of the probability of various events<\/li>\n<\/ul>\n<h6>C. Financial Mathematics<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve simple interest problems using the formula, <em>i<\/em> <em>= prt<\/em> (for any variable)<\/li>\n<li>solve compound interest problems for <em>A <\/em>or <em>P <\/em>using [latex]A=P\\left ( 1+\\frac{r}{n} \\right )^{nt}[\/latex]<\/li>\n<li>find the effective interest rate using [latex]E.R.=\\left ( 1+\\frac{r}{n} \\right )^{n}-1[\/latex]<\/li>\n<li>solve annuity problems using [latex]A=\\tfrac{nP[\\left ( 1+\\frac{r}{n} \\right )^{n}-1]}{r}[\/latex]&nbsp; (for <em>A<\/em> or <em>P<\/em> only)<\/li>\n<li>find periodic payment using&nbsp; &nbsp; [latex]P=\\frac{A(\\frac{r}{n})}{1-\\left ( 1+\\frac{r}{n} \\right )^{-nt}}[\/latex]<\/li>\n<li>determine the finance charge on a loan<\/li>\n<li>determine the interest rate on a loan using tables or appropriate technology<\/li>\n<\/ul>\n<h6>D. Geometry<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>classify triangles according to angles and sides<\/li>\n<li>use the properties of triangles to determine the measure of sides and angles<\/li>\n<li>determine the measure and\/or congruence of angles given a transversal and two parallel lines<\/li>\n<li>use the triangle congruence theorems in simple guided proofs<\/li>\n<\/ul>\n","protected":false},"author":1935,"menu_order":3,"template":"","meta":{"pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-343","chapter","type-chapter","status-publish","hentry"],"part":340,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/343","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":2,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/343\/revisions"}],"predecessor-version":[{"id":387,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/343\/revisions\/387"}],"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\/343\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/media?parent=343"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapter-type?post=343"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/contributor?post=343"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/license?post=343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}