Mathematics: Advanced Level—Foundations

Learning Outcomes

It is expected that learners will use various problem solving strategies throughout the course

• guess and check
• look for a pattern
• make a systematic list
• draw or model
• eliminate possibilities
• simplify the original problem
• work backward
• develop alternative approaches.

CORE LEARNING OUTCOMES

1. Skills Review

It is recommended that a review of the following skills be implemented throughout the course as needed, but are not required.

A. Basic Algebra

It is expected that learners will 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
  • solve simple formulae for a given variable

B. Linear Relations

It is expected that learners will 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
  • determine whether a relation is a function

C. Systems of Linear Equations

It is expected that learners will 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

D. Right Triangle Trigonometry

It is expected that learners will be able to:

• • solve problems involving right triangles, using sine, cosine, or tangent ratios, the angle sum property of triangles and the Pythagorean Theorem

2. Rates

It is expected that learners will 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)
• solve a contextual problem that involves rate or unit rates

3. Systems of Linear Inequalities

It is expected that learners will be able to:

• graph a linear inequality in two variables
• graph the solution for a system of linear inequalities in two variables
• use the graph to solve optimization problems.

4. Quadratic Functions

It is expected that learners will be able to:

• factor (GCF, difference of squares, trinomials of the form ax2 + bx + 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
• solve problems that involve the characteristics of a quadratic function

5. Geometry

It is expected that learners will be able to:

• classify and distinguish among acute, right, obtuse, straight, reflex, complementary and 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 involves 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
• solve problems that involve similar triangles
• derive proofs that involve the properties of angles and triangles

6. Statistics

It is expected that learners will 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
• solve problems that involve standard deviation and normal distribution
• interpret statistical data using: confidence intervals, confidence levels, and margin of error

7. Trigonometry

It is expected that learners will be able to:

• solve triangles using Law of Cosines or Law of Sines, excluding the Ambiguous Case.
• solve contextual problems involving Law of Cosines or Law of Sines

8. Measurement

It is expected that learners will 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
• determine the effect of a change in scale factor on area and volume

9. Logical Reasoning

It is expected that learners will 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
• use problem solving strategies to solve problems or play games
• analyze and prove conjectures, using inductive and deductive reasoning, to solve problems

OPTIONAL LEARNING OUTCOMES

Learners may wish to complete either A, B, or C but these outcomes are not required.

A. Financial Math

It is expected that learners will 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
• solve problems involving different forms of credit

B. Permutations, Combinations, and Simple Probability

It is expected that learners will be able to:

• evaluate factorial notation
• evaluate permutation and combination notation
• solve related applied problems
• compute the probability of a simple event
• distinguish between experimental and theoretical probability

C.Project

Possible topics might include:

• 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
• Collect and interpret data, using statistical methods