BC's Indigenous Public Post-Secondary Institute

MATH-055 - Introduction to Algebra II -

MATH-055 - Introduction to Algebra II -

Course Details
The British Columbia ABE Advanced Level - Foundations Mathematics course is a further introductory algebra course intended for students who have studied little to no algebra but have a firm background in basic mathematics. This course provides students with enough algebra, geometry, and/or trigonometry to satisfy grade 11 prerequisites for some vocational, career, technical, and/or further academic programs. MATH 055 can be used as a perquisite for MATH 057. Some of the topics include algebra, linear relations and systems, functions, quadratics, geometry and trigonometry.
Part of the:
  • Available/Required in the following Programs:
  • College Readiness - Qualifying Courses
  • Course offered:
  • Spring 2024 (January - April)
  • Prerequisites : MATH 041, , Foundations and Pre-Cal Math 10, instructor permission, or advisor assessed equivalent
    Course Outline
    Instructors Qualifications: Relevant Bachelor's Degree or Equivalent
    Office Hours: 1.5 Per week
    Contact Hours: 90
    Student Evaluation
    Assignments/Chapter tests/Midterms 50-70%, Final 30-50%, Total 100%. Grading procedures follow NVIT policy.
    Learning Outcomes: It is expected that learners will use various problem solving strategies such as:
  • guess and check;
  • look for a pattern;
  • make a systematic list;
  • draw or model;
  • eliminate possibilities;
  • simplify the original problem;
  • work backward; and
  • develop alternative approaches.

  • Basic Algebra
    It is expected that learners should be able to:
  • use the terms rational, irrational, and integer to classify numbers;
  • use order of operations with real numbers;
  • solve first degree equations and inequalities;
  • solve word problems by translating them into mathematical equations; and
  • solve simple formulae for a given variable.

  • Rates
    It is expected that learners should be able to:
  • interpret rates in a given context, such as the arts, business, and health sciences;
  • solve rate problems using proportions;
  • determine unit rates;
  • convert units by dimensional analysis (multiplying by one); and
  • solve a contextual problem that involves rate or unit rates.

  • Linear Relations
    It is expected that learners should be able to:
  • write linear equations in slope-intercept form;
  • graph linear equations using a table of values;
  • graph linear equations using the y-intercept and slope and using x- and y-intercepts;
  • given a graph, find the slope of the line;
  • draw a graph to represent a rate;
  • interpret slope as an average rate of change;
  • interpret domain and range from a graph;
  • solve problems that involve linear relations;
  • use function notation; and
  • determine whether a relation is a function.

  • Systems of Linear Equations and Inequalities
    It is expected that learners should be able to:
  • solve a system of first degree equations in two unknowns by graphing, substitution and/or elimination;
  • solve practical problems that can be solved using a system of equations;
  • graph a linear inequality in two variables;
  • graph the solution for a system of linear inequalities in two variables; and
  • use the graph to solve optimization problems.

  • Quadratic Functions
    It is expected that learners should be able to:
  • factor (GCF, difference of squares, trinomials of the form ax2 + bc + c with a = 1 only);
  • solve quadratic equations by factoring or using the quadratic formula;
  • identify, from a graph, the vertex, intercepts, domain, range, and axis of symmetry;
  • determine the vertex using the vertex formula;
  • determine whether the y-coordinate of the vertex is a maximum or minimum;
  • graph a quadratic function using the vertex, intercepts, or a table of values; and
  • solve problems that involve the characteristics of a quadratic function.

  • Geometry
    It is expected that learners should be able to:
  • classify and distinguish among acute, right, obtuse, straight, reflex, complementary; supplementary, and vertically opposite angles;
  • generalize, using inductive reasoning, the angle relationships created when parallel lines are cut by a transversal and the angle sum property of a triangle;
  • use deductive reasoning to determine the measures of angles in a diagram that involve parallel lines, angles and triangles;
  • measure angles with a protractor;
  • classify triangles according to sides and angles;
  • explain the difference between similar and congruent shapes; and
  • solve problems that involve similar triangles.

  • Trigonometry
    It is expected that learners should be able to:
  • solve problems involving right triangles, using sine, cosine, or tangent ratios, the angle sum property of triangles and the Pythagorean Theorem;
  • solve triangles using Law of Cosines or Law of Sines, excluding the Ambiguous Case; and
  • solve contextual problems involving Law of Cosines or Law of Sines.

    Learners must complete a minimum of three of the following five options:

    Financial Math
    It is expected that learners should be able to:
  • solve consumer problems involving percentage (sales tax, discounts, etc.);
  • determine and or compare wages in various situations;
  • solve simple and compound interest problems; and
  • solve problems involving different forms of credit.

  • Measurement
    It is expected that learners should be able to:
  • draw a scale diagram of a 2-D shape;
  • solve problems involving scale diagrams of 2-D shapes and 3-D objects;
  • use proportions to determine the scale factor or a missing dimension of a 2-D shape or 3-D object;
  • determine from a scale diagram the area of 2-D shapes and the volume of 3-D objects; and
  • determine the effect of a change in scale factor on area and volume.

  • Statistics
    It is expected that learners should be able to:
  • determine and interpret the mean, median, mode, range and standard deviation of a set of data;
  • represent data graphically;
  • interpret and analyze graphs and identify bias;
  • understand how the normal curve can be used to describe a normally distributed population;
  • calculate z-scores; and
  • solve problems that involve standard deviation and normal distribution.

  • Logical Reasoning
    It is expected that learners should be able to:
  • make conjectures by observing patterns;
  • find a counterexample to disprove a given conjecture;
  • determine if a given argument is valid, and justify the reasoning;
  • compare, using examples, inductive and deductive reasoning;
  • prove a conjecture, using deductive reasoning; and
  • use problem solving strategies to solve problems or play games.

  • E) Project
    Possible topics might include the following:
  • create a variation on a puzzle or a game;
  • research a historical event or person involving math;
  • research an area of interest that involves math; and
  • collect and interpret data, using statistical methods.
  • Text and Materials:
  • Elayn Martin-Gay. Pre-algebra & Introductory Algebra. Current Edition. Montreal. Pearson.
  • Other Resources:
    Transfer Credits: For more information visit: www.bctransferguide.ca
    Other Information: Education Council approved February 2013.
    Current Course Offerings:
    MATH-055-01     08 Jan 2024 - 19 Apr 2024