{"id":345,"date":"2023-07-16T18:15:46","date_gmt":"2023-07-16T22:15:46","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-advanced-level-foundations\/"},"modified":"2025-06-04T17:33:06","modified_gmt":"2025-06-04T21:33:06","slug":"mathematics-advanced-level-foundations","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-advanced-level-foundations\/","title":{"raw":"Mathematics: Advanced Level\u2014Foundations","rendered":"Mathematics: Advanced Level\u2014Foundations"},"content":{"raw":"<h3>Mathematics: Advanced Level\u2014Foundations<\/h3>\r\n\r\n<hr \/>\r\n\r\n<h5>Learning Outcomes<\/h5>\r\nIt is expected that learners will use various problem-solving strategies throughout the course\r\n<ul>\r\n \t<li>guess and check<\/li>\r\n \t<li>look for a pattern<\/li>\r\n \t<li>make a systematic list<\/li>\r\n \t<li>draw or model<\/li>\r\n \t<li>eliminate possibilities<\/li>\r\n \t<li>simplify the original problem<\/li>\r\n \t<li>work backward<\/li>\r\n \t<li>develop alternative approaches<\/li>\r\n<\/ul>\r\n<h5>CORE LEARNING OUTCOMES<\/h5>\r\n<h6>1. Skills Review<\/h6>\r\nIt is recommended that a review of the following skills be implemented throughout the course as needed, but are not required.\r\n<h6 style=\"padding-left: 40px\">A. Basic Algebra<\/h6>\r\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\r\n\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul>\r\n \t<li>use the terms rational, irrational, and integer to classify numbers<\/li>\r\n \t<li>use order of operations with real numbers<\/li>\r\n \t<li>solve first degree equations and inequalities<\/li>\r\n \t<li>solve word problems by translating them into mathematical equations<\/li>\r\n \t<li>solve simple formulae for a given variable<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h6 style=\"padding-left: 40px\">B. Linear Relations<\/h6>\r\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\r\n\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul>\r\n \t<li>write linear equations in slope-intercept form<\/li>\r\n \t<li>graph linear equations using a table of values<\/li>\r\n \t<li>graph linear equations using the y-intercept and slope and using x- and y-intercepts<\/li>\r\n \t<li>given a graph, find the slope of the line<\/li>\r\n \t<li>draw a graph to represent a rate<\/li>\r\n \t<li>interpret slope as an average rate of change<\/li>\r\n \t<li>interpret domain and range from a graph<\/li>\r\n \t<li>solve problems that involve linear relations<\/li>\r\n \t<li>use function notation<\/li>\r\n \t<li>determine whether a relation is a function<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h6 style=\"padding-left: 40px\">C. Systems of Linear Equations<\/h6>\r\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\r\n\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul>\r\n \t<li>solve a system of first-degree equations in two unknowns by graphing, substitution and\/or elimination<\/li>\r\n \t<li>solve practical problems using a system of equations<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h6 style=\"padding-left: 40px\">D. Right Triangle Trigonometry<\/h6>\r\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\r\n\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul>\r\n \t<li>solve problems involving right triangles, using sine, cosine, or tangent ratios, the angle sum property of triangles and the Pythagorean Theorem<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h6>2. Rates<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>interpret rates in a given context, such as the arts, business, and health sciences<\/li>\r\n \t<li>solve rate problems using proportions<\/li>\r\n \t<li>determine unit rates<\/li>\r\n \t<li>convert units by dimensional analysis (multiplying by one)<\/li>\r\n \t<li>solve a contextual problem that involves rate or unit rates<\/li>\r\n<\/ul>\r\n<h6>3. Systems of Linear Inequalities<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>graph a linear inequality in two variables<\/li>\r\n \t<li>graph the solution for a system of linear inequalities in two variables<\/li>\r\n \t<li>use the graph to solve optimization problems<\/li>\r\n<\/ul>\r\n<h6>4. Quadratic Functions<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>factor (GCF, difference of squares, trinomials of the form x<sup>2<\/sup> + bx + c)<\/li>\r\n \t<li>solve quadratic equations by factoring or using the quadratic formula<\/li>\r\n \t<li>identify, from a graph, the vertex, intercepts, domain, range, and axis of symmetry<\/li>\r\n \t<li>determine the vertex using the vertex formula<\/li>\r\n \t<li>determine whether the y-coordinate of the vertex is a maximum or minimum<\/li>\r\n \t<li>graph a quadratic function using the vertex, intercepts, or a table of values<\/li>\r\n \t<li>solve problems that involve the characteristics of a quadratic function<\/li>\r\n<\/ul>\r\n<h6>5. Geometry<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>classify and distinguish among acute, right, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles<\/li>\r\n \t<li>generalize, using inductive reasoning, the angle relationships created when parallel lines are cut by a transversal and the angle sum property of a triangle<\/li>\r\n \t<li>use deductive reasoning to determine the measures of angles in a diagram that involves parallel lines, angles and triangles<\/li>\r\n \t<li>measure angles with a protractor<\/li>\r\n \t<li>classify triangles according to sides and angles<\/li>\r\n \t<li>explain the difference between similar and congruent shapes<\/li>\r\n \t<li>solve problems that involve similar triangles<\/li>\r\n \t<li>derive proofs that involve the properties of angles and triangles<\/li>\r\n<\/ul>\r\n<h6>6. Statistics<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>determine and interpret the mean, median, mode, range and standard deviation of a set of data<\/li>\r\n \t<li>represent data graphically<\/li>\r\n \t<li>interpret and analyze graphs and identify bias<\/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<\/li>\r\n \t<li>solve problems that involve standard deviation and normal distribution<\/li>\r\n \t<li>interpret statistical data using: confidence intervals, confidence levels, and margin of error<\/li>\r\n<\/ul>\r\n<h6>7. Trigonometry<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve triangles using Law of Cosines and Law of Sines, excluding the Ambiguous Case<\/li>\r\n \t<li>solve contextual problems involving Law of Cosines and Law of Sines<\/li>\r\n<\/ul>\r\n<h6>8. Measurement<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>draw a scale diagram of a 2-D shape<\/li>\r\n \t<li>solve problems involving scale diagrams of 2-D shapes and 3-D objects<\/li>\r\n \t<li>use proportions to determine the scale factor or a missing dimension of a 2-D shape or 3-D object<\/li>\r\n \t<li>determine from a scale diagram the area of 2-D shapes and the volume of 3-D objects<\/li>\r\n \t<li>determine the effect of a change in scale factor on area and volume<\/li>\r\n<\/ul>\r\n<h6>9. Logical Reasoning<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>make conjectures by observing patterns<\/li>\r\n \t<li>find a counterexample to disprove a given conjecture<\/li>\r\n \t<li>determine if a given argument is valid, and justify the reasoning<\/li>\r\n \t<li>compare, using examples, inductive and deductive reasoning<\/li>\r\n \t<li>prove a conjecture, using deductive reasoning<\/li>\r\n \t<li>use problem-solving strategies to solve problems or play games<\/li>\r\n \t<li>analyze and prove conjectures, using inductive and deductive reasoning, to solve problems<\/li>\r\n<\/ul>\r\n<h5>OPTIONAL LEARNING OUTCOMES<\/h5>\r\nLearners may wish to complete either A, B, or C but these outcomes are not required.\r\n<h6>A. Financial Math<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>solve consumer problems involving percentage (sales tax, discounts, etc.)<\/li>\r\n \t<li>determine and compare wages in various situations<\/li>\r\n \t<li>solve simple and compound interest problems<\/li>\r\n \t<li>solve problems involving different forms of credit<\/li>\r\n<\/ul>\r\n<h6>B. Permutations, Combinations, and Simple Probability<\/h6>\r\nIt is expected that learners will be able to:\r\n<ul>\r\n \t<li>evaluate factorial notation<\/li>\r\n \t<li>evaluate permutation and combination notation<\/li>\r\n \t<li>solve related applied problems<\/li>\r\n \t<li>compute the probability of a simple event<\/li>\r\n \t<li>distinguish between experimental and theoretical probability<\/li>\r\n<\/ul>\r\n<h6>C. Project<\/h6>\r\nPossible topics might include:\r\n<ul>\r\n \t<li>create a variation on a puzzle or a game<\/li>\r\n \t<li>research a historical event or person involving math<\/li>\r\n \t<li>research an area of interest that involves math<\/li>\r\n \t<li>collect and interpret data, using statistical methods<\/li>\r\n<\/ul>","rendered":"<h3>Mathematics: Advanced Level\u2014Foundations<\/h3>\n<hr \/>\n<h5>Learning Outcomes<\/h5>\n<p>It is expected that learners will use various problem-solving strategies throughout the course<\/p>\n<ul>\n<li>guess and check<\/li>\n<li>look for a pattern<\/li>\n<li>make a systematic list<\/li>\n<li>draw or model<\/li>\n<li>eliminate possibilities<\/li>\n<li>simplify the original problem<\/li>\n<li>work backward<\/li>\n<li>develop alternative approaches<\/li>\n<\/ul>\n<h5>CORE LEARNING OUTCOMES<\/h5>\n<h6>1. Skills Review<\/h6>\n<p>It is recommended that a review of the following skills be implemented throughout the course as needed, but are not required.<\/p>\n<h6 style=\"padding-left: 40px\">A. Basic Algebra<\/h6>\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>use the terms rational, irrational, and integer to classify numbers<\/li>\n<li>use order of operations with real numbers<\/li>\n<li>solve first degree equations and inequalities<\/li>\n<li>solve word problems by translating them into mathematical equations<\/li>\n<li>solve simple formulae for a given variable<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h6 style=\"padding-left: 40px\">B. Linear Relations<\/h6>\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>write linear equations in slope-intercept form<\/li>\n<li>graph linear equations using a table of values<\/li>\n<li>graph linear equations using the y-intercept and slope and using x- and y-intercepts<\/li>\n<li>given a graph, find the slope of the line<\/li>\n<li>draw a graph to represent a rate<\/li>\n<li>interpret slope as an average rate of change<\/li>\n<li>interpret domain and range from a graph<\/li>\n<li>solve problems that involve linear relations<\/li>\n<li>use function notation<\/li>\n<li>determine whether a relation is a function<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h6 style=\"padding-left: 40px\">C. Systems of Linear Equations<\/h6>\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>solve a system of first-degree equations in two unknowns by graphing, substitution and\/or elimination<\/li>\n<li>solve practical problems using a system of equations<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h6 style=\"padding-left: 40px\">D. Right Triangle Trigonometry<\/h6>\n<p style=\"padding-left: 40px\">It is expected that learners will be able to:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>solve problems involving right triangles, using sine, cosine, or tangent ratios, the angle sum property of triangles and the Pythagorean Theorem<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h6>2. Rates<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>interpret rates in a given context, such as the arts, business, and health sciences<\/li>\n<li>solve rate problems using proportions<\/li>\n<li>determine unit rates<\/li>\n<li>convert units by dimensional analysis (multiplying by one)<\/li>\n<li>solve a contextual problem that involves rate or unit rates<\/li>\n<\/ul>\n<h6>3. Systems of Linear Inequalities<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>graph a linear inequality in two variables<\/li>\n<li>graph the solution for a system of linear inequalities in two variables<\/li>\n<li>use the graph to solve optimization problems<\/li>\n<\/ul>\n<h6>4. Quadratic Functions<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>factor (GCF, difference of squares, trinomials of the form x<sup>2<\/sup> + bx + c)<\/li>\n<li>solve quadratic equations by factoring or using the quadratic formula<\/li>\n<li>identify, from a graph, the vertex, intercepts, domain, range, and axis of symmetry<\/li>\n<li>determine the vertex using the vertex formula<\/li>\n<li>determine whether the y-coordinate of the vertex is a maximum or minimum<\/li>\n<li>graph a quadratic function using the vertex, intercepts, or a table of values<\/li>\n<li>solve problems that involve the characteristics of a quadratic function<\/li>\n<\/ul>\n<h6>5. Geometry<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>classify and distinguish among acute, right, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles<\/li>\n<li>generalize, using inductive reasoning, the angle relationships created when parallel lines are cut by a transversal and the angle sum property of a triangle<\/li>\n<li>use deductive reasoning to determine the measures of angles in a diagram that involves parallel lines, angles and triangles<\/li>\n<li>measure angles with a protractor<\/li>\n<li>classify triangles according to sides and angles<\/li>\n<li>explain the difference between similar and congruent shapes<\/li>\n<li>solve problems that involve similar triangles<\/li>\n<li>derive proofs that involve the properties of angles and triangles<\/li>\n<\/ul>\n<h6>6. Statistics<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>determine and interpret the mean, median, mode, range and standard deviation of a set of data<\/li>\n<li>represent data graphically<\/li>\n<li>interpret and analyze graphs and identify bias<\/li>\n<li>understand how the normal curve can be used to describe a normally distributed population<\/li>\n<li>calculate z-scores<\/li>\n<li>solve problems that involve standard deviation and normal distribution<\/li>\n<li>interpret statistical data using: confidence intervals, confidence levels, and margin of error<\/li>\n<\/ul>\n<h6>7. Trigonometry<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve triangles using Law of Cosines and Law of Sines, excluding the Ambiguous Case<\/li>\n<li>solve contextual problems involving Law of Cosines and Law of Sines<\/li>\n<\/ul>\n<h6>8. Measurement<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>draw a scale diagram of a 2-D shape<\/li>\n<li>solve problems involving scale diagrams of 2-D shapes and 3-D objects<\/li>\n<li>use proportions to determine the scale factor or a missing dimension of a 2-D shape or 3-D object<\/li>\n<li>determine from a scale diagram the area of 2-D shapes and the volume of 3-D objects<\/li>\n<li>determine the effect of a change in scale factor on area and volume<\/li>\n<\/ul>\n<h6>9. Logical Reasoning<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>make conjectures by observing patterns<\/li>\n<li>find a counterexample to disprove a given conjecture<\/li>\n<li>determine if a given argument is valid, and justify the reasoning<\/li>\n<li>compare, using examples, inductive and deductive reasoning<\/li>\n<li>prove a conjecture, using deductive reasoning<\/li>\n<li>use problem-solving strategies to solve problems or play games<\/li>\n<li>analyze and prove conjectures, using inductive and deductive reasoning, to solve problems<\/li>\n<\/ul>\n<h5>OPTIONAL LEARNING OUTCOMES<\/h5>\n<p>Learners may wish to complete either A, B, or C but these outcomes are not required.<\/p>\n<h6>A. Financial Math<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>solve consumer problems involving percentage (sales tax, discounts, etc.)<\/li>\n<li>determine and compare wages in various situations<\/li>\n<li>solve simple and compound interest problems<\/li>\n<li>solve problems involving different forms of credit<\/li>\n<\/ul>\n<h6>B. Permutations, Combinations, and Simple Probability<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>evaluate factorial notation<\/li>\n<li>evaluate permutation and combination notation<\/li>\n<li>solve related applied problems<\/li>\n<li>compute the probability of a simple event<\/li>\n<li>distinguish between experimental and theoretical probability<\/li>\n<\/ul>\n<h6>C. Project<\/h6>\n<p>Possible topics might include:<\/p>\n<ul>\n<li>create a variation on a puzzle or a game<\/li>\n<li>research a historical event or person involving math<\/li>\n<li>research an area of interest that involves math<\/li>\n<li>collect and interpret data, using statistical methods<\/li>\n<\/ul>\n","protected":false},"author":1935,"menu_order":5,"template":"","meta":{"pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-345","chapter","type-chapter","status-publish","hentry"],"part":340,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/345","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\/345\/revisions"}],"predecessor-version":[{"id":473,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/345\/revisions\/473"}],"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\/345\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/media?parent=345"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapter-type?post=345"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/contributor?post=345"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/license?post=345"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}