{"id":342,"date":"2023-07-16T18:15:45","date_gmt":"2023-07-16T22:15:45","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-intermediate-level-algebraic\/"},"modified":"2023-07-16T18:15:45","modified_gmt":"2023-07-16T22:15:45","slug":"mathematics-intermediate-level-algebraic","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/chapter\/mathematics-intermediate-level-algebraic\/","title":{"raw":"Mathematics: Intermediate Level\u2014Algebraic","rendered":"Mathematics: Intermediate Level\u2014Algebraic"},"content":{"raw":"\n<div class=\"mathematics:-intermediate-level\u2014algebraic\">\n<h3>Mathematics: Intermediate Level\u2014Algebraic<\/h3>\n\n<hr>\n\nEstimation is a skill that should be emphasized. Students should also be strongly encouraged to check answers and that solutions are reasonable in the context.\n<h5>Learning Outcomes<\/h5>\n<h6>1. Operations with Rational Numbers<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>write fractions as decimals and decimals as fractions<\/li>\n \t<li>add, subtract, multiply, divide, and simplify rational numbers<\/li>\n \t<li>use order of operations<\/li>\n \t<li>graph rational numbers on the number line<\/li>\n \t<li>define absolute value<\/li>\n<\/ul>\n<h6>2. Measurement<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>use the common metric units for temperature, length, area, volume\/capacity, and mass<\/li>\n \t<li>use the common Imperial or US Customary units for temperature, length, area, volume\/ capacity, and force<\/li>\n \t<li>convert between and within metric and Imperial or US Customary units using tables and\/or calculators<\/li>\n \t<li>use proportional reasoning for conversions<\/li>\n<\/ul>\n<h6>3. Perimeter, Area, and Volume<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures using formulas<\/li>\n \t<li>find areas of the above shapes using formulas<\/li>\n \t<li>find the surface areas of cubes, rectangular solids, right cylinders, spheres, and composite solids using formulas<\/li>\n \t<li>find the volumes of cubes, rectangular solids, right cylinders and cones, spheres, and composite solids using formulas<\/li>\n \t<li>distinguish between concepts of perimeter and area and their respective units<\/li>\n<\/ul>\n<h6>4. Ratio, Proportion and Percent<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>read, write, interpret, and compare ratios<\/li>\n \t<li>read, write and identify proportions and use them to solve problems<\/li>\n \t<li>use ratio and proportion to interpret and make scale drawings<\/li>\n \t<li>use ratio and proportion to solve problems involving similar triangles<\/li>\n \t<li>use ratio and proportion to solve problems including:\n<ul>\n \t<li>finding percent when part and whole are known<\/li>\n \t<li>finding part when percent and whole are known<\/li>\n \t<li>finding whole when part and percent are known<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h6>5. Algebra<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>explain the use of variables<\/li>\n \t<li>evaluate algebraic expressions using substitution<\/li>\n \t<li>combine like terms and remove parentheses<\/li>\n \t<li>solve first degree equations in one variable<\/li>\n \t<li>translate a problem into an equation<\/li>\n \t<li>use equations to solve problems<\/li>\n \t<li>solve simple formulas for a given variable<\/li>\n \t<li>use formulas to solve problems<\/li>\n<\/ul>\n<h6>6. Linear Equations and Graphing<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>draw a Cartesian co-ordinate system<\/li>\n \t<li>plot and name points in a Cartesian co-ordinate system<\/li>\n \t<li>given an equation in two variables:\n<ul>\n \t<li>determine if an ordered pair is a solution<\/li>\n \t<li>find ordered pairs which are solutions<\/li>\n<\/ul>\n<\/li>\n \t<li>graph equations of the form x = a and y = b,<\/li>\n \t<li>define slope and relate to grade and pitch<\/li>\n \t<li>graph linear equations using\n<ul>\n \t<li>slope and y-intercept<\/li>\n \t<li>two intercepts<\/li>\n \t<li>a table of values<\/li>\n<\/ul>\n<\/li>\n \t<li>find x- and y-intercepts<\/li>\n \t<li>determine the equation of a line, y = mx + b, given\n<ul>\n \t<li>its graph<\/li>\n \t<li>its slope and a point on the line<\/li>\n \t<li>two points on the line<\/li>\n<\/ul>\n<\/li>\n \t<li>solve problems using graphs of linear equations<\/li>\n<\/ul>\n<h6>7. Powers, Roots, and Scientific Notation<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>read and write numbers expressed as powers<\/li>\n \t<li>evaluate powers with integral exponents<\/li>\n \t<li>apply laws of exponents to simplify expressions<\/li>\n \t<li>express numbers using scientific notation<\/li>\n \t<li>convert between scientific and standard notation<\/li>\n \t<li>determine the square root of a perfect square<\/li>\n \t<li>express a square root as a mixed radical in simplest form (numerical radicands only)<\/li>\n \t<li>approximate square roots of real numbers using a calculator<\/li>\n<\/ul>\n<h6>8. Polynomials<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>distinguish between monomials, binomials, trinomials and other polynomials in one variable only<\/li>\n \t<li>apply the laws of exponents to variable expressions with integral exponents<\/li>\n \t<li>evaluate polynomials by substitution<\/li>\n \t<li>add, subtract, and multiply polynomials in one variable<\/li>\n \t<li>factor polynomials by removing the largest common factor<\/li>\n \t<li>factor binomials of the form a2<em>x<\/em>2 \u2013 b2<em>y<\/em>2<\/li>\n \t<li>factor trinomials of the form a<em>x<\/em>2 + b<em>x<\/em> + c with a = 1 ONLY<\/li>\n \t<li>divide a polynomial by a monomial<\/li>\n<\/ul>\n<h6>9. Trigonometry<\/h6>\nIt is expected that learners will be able to:\n<ul>\n \t<li>name parts of a triangle<\/li>\n \t<li>find missing side of a right triangle using the Pythagorean Theorem<\/li>\n \t<li>find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios<\/li>\n \t<li>solve problems using right angle trigonometry<\/li>\n<\/ul>\n<p class=\"import-BodyText\" style=\"margin-left: 0pt;text-indent: 18.05pt\"><\/p>\n\n<\/div>\n","rendered":"<div class=\"mathematics:-intermediate-level\u2014algebraic\">\n<h3>Mathematics: Intermediate Level\u2014Algebraic<\/h3>\n<hr \/>\n<p>Estimation is a skill that should be emphasized. Students should also be strongly encouraged to check answers and that solutions are reasonable in the context.<\/p>\n<h5>Learning Outcomes<\/h5>\n<h6>1. Operations with Rational Numbers<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>write fractions as decimals and decimals as fractions<\/li>\n<li>add, subtract, multiply, divide, and simplify rational numbers<\/li>\n<li>use order of operations<\/li>\n<li>graph rational numbers on the number line<\/li>\n<li>define absolute value<\/li>\n<\/ul>\n<h6>2. Measurement<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>use the common metric units for temperature, length, area, volume\/capacity, and mass<\/li>\n<li>use the common Imperial or US Customary units for temperature, length, area, volume\/ capacity, and force<\/li>\n<li>convert between and within metric and Imperial or US Customary units using tables and\/or calculators<\/li>\n<li>use proportional reasoning for conversions<\/li>\n<\/ul>\n<h6>3. Perimeter, Area, and Volume<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures using formulas<\/li>\n<li>find areas of the above shapes using formulas<\/li>\n<li>find the surface areas of cubes, rectangular solids, right cylinders, spheres, and composite solids using formulas<\/li>\n<li>find the volumes of cubes, rectangular solids, right cylinders and cones, spheres, and composite solids using formulas<\/li>\n<li>distinguish between concepts of perimeter and area and their respective units<\/li>\n<\/ul>\n<h6>4. Ratio, Proportion and Percent<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>read, write, interpret, and compare ratios<\/li>\n<li>read, write and identify proportions and use them to solve problems<\/li>\n<li>use ratio and proportion to interpret and make scale drawings<\/li>\n<li>use ratio and proportion to solve problems involving similar triangles<\/li>\n<li>use ratio and proportion to solve problems including:\n<ul>\n<li>finding percent when part and whole are known<\/li>\n<li>finding part when percent and whole are known<\/li>\n<li>finding whole when part and percent are known<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h6>5. Algebra<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>explain the use of variables<\/li>\n<li>evaluate algebraic expressions using substitution<\/li>\n<li>combine like terms and remove parentheses<\/li>\n<li>solve first degree equations in one variable<\/li>\n<li>translate a problem into an equation<\/li>\n<li>use equations to solve problems<\/li>\n<li>solve simple formulas for a given variable<\/li>\n<li>use formulas to solve problems<\/li>\n<\/ul>\n<h6>6. Linear Equations and Graphing<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>draw a Cartesian co-ordinate system<\/li>\n<li>plot and name points in a Cartesian co-ordinate system<\/li>\n<li>given an equation in two variables:\n<ul>\n<li>determine if an ordered pair is a solution<\/li>\n<li>find ordered pairs which are solutions<\/li>\n<\/ul>\n<\/li>\n<li>graph equations of the form x = a and y = b,<\/li>\n<li>define slope and relate to grade and pitch<\/li>\n<li>graph linear equations using\n<ul>\n<li>slope and y-intercept<\/li>\n<li>two intercepts<\/li>\n<li>a table of values<\/li>\n<\/ul>\n<\/li>\n<li>find x- and y-intercepts<\/li>\n<li>determine the equation of a line, y = mx + 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<li>solve problems using graphs of linear equations<\/li>\n<\/ul>\n<h6>7. Powers, Roots, and Scientific Notation<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>read and write numbers expressed as powers<\/li>\n<li>evaluate powers with integral exponents<\/li>\n<li>apply laws of exponents to simplify expressions<\/li>\n<li>express numbers using scientific notation<\/li>\n<li>convert between scientific and standard notation<\/li>\n<li>determine the square root of a perfect square<\/li>\n<li>express a square root as a mixed radical in simplest form (numerical radicands only)<\/li>\n<li>approximate square roots of real numbers using a calculator<\/li>\n<\/ul>\n<h6>8. 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 in one variable<\/li>\n<li>factor polynomials by removing the largest common factor<\/li>\n<li>factor binomials of the form a2<em>x<\/em>2 \u2013 b2<em>y<\/em>2<\/li>\n<li>factor trinomials of the form a<em>x<\/em>2 + b<em>x<\/em> + c with a = 1 ONLY<\/li>\n<li>divide a polynomial by a monomial<\/li>\n<\/ul>\n<h6>9. Trigonometry<\/h6>\n<p>It is expected that learners will be able to:<\/p>\n<ul>\n<li>name parts of a triangle<\/li>\n<li>find missing side of a right triangle using the Pythagorean Theorem<\/li>\n<li>find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios<\/li>\n<li>solve problems using right angle trigonometry<\/li>\n<\/ul>\n<p class=\"import-BodyText\" style=\"margin-left: 0pt;text-indent: 18.05pt\">\n<\/div>\n","protected":false},"author":1935,"menu_order":2,"template":"","meta":{"pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-342","chapter","type-chapter","status-publish","hentry"],"part":340,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/342","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":0,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapters\/342\/revisions"}],"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\/342\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/media?parent=342"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/pressbooks\/v2\/chapter-type?post=342"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/contributor?post=342"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/abehandbook\/wp-json\/wp\/v2\/license?post=342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}