MA119 Learning Goals

There are in total learning goals. Check the goals you have mastered and click the following button to see your level of mastery.

Algebra Preliminaries

R-1. Arithmetic

  • I can simplify fractions.
  • I can perform the operations addition, subtraction, multiplication and division on real numbers using order of operations.
  • I can evaluate and simplify arithmetic expressions without the use of a calculator.

R-2. Set theory

  • I can describe a set using set builder notation.
  • I can perform operations (union, intersection and complement) on sets.
  • I can convert between interval notation, inequality notation, and graphical notation for subsets of real numbers.

R-3. Integer Exponents

  • I can demonstrate understanding properties of integral exponents and use the properties to simplify expressions with integral exponents.

R-4. Polynomial Essentials

  • I can differentiate between a “term” and a “factor” and “multiples”.
  • I can evaluate algebraic expressions.
  • I can characterize polynomials as monomials, binomials, trinomials.
  • I can identify the degree of a polynomial, and describe coefficients.
  • I can add and subtract polynomials by combining like terms.
  • I can multiply polynomials using associative, commutative, and distributive properties.
  • I can perform operations on polynomials using order of operations.
  • I can state and apply the formulas for the squares of binomials.
  • I can state and apply the formulas for the difference of squares.
  • I can state and apply the formulas for the difference of two cubes and the sum of two cubes.

R-5. Solving inequalities

  • I can use properties of inequalities to simplify, and to solve inequalities.
  • I can solve compounded inequalities and write the solution set in interval notations.

R-6. Geometry Essentials

  • I can use the Pythagorean Theorem and its converse.
  • I know and can apply geometry formulas (perimeter/circumference/area/volume) related to squares, triangles, circles, and boxes.

Operations on Algebraic Expressions

C-1. Factoring Essentials

  • I can identify a greatest common factor (GCF) and use it to factor polynomials.
  • I can apply grouping method to factor a polynomial with four term.
  • I can apply trial-error method to factor a trinomial.
  • I can factor a binomial using formulas (difference of squares, difference or sum of cubes).
  • I can factor a polynomial completely using various methods.
  • I can simplify a polynomial and then factor.
  • I can use substitution idea to factor a polynomial whose terms contains powers of another polynomial.

C-2. Rational Expressions

  • I can perform algebraic operations on rational expressions, including reducing to lowest terms, addition, subtraction, multiplication, and division.
  • I can simplify complex rational expressions.

C-3. Radicals and Rational Exponents

  • I can demonstrate understanding of n-th roots and simplify expressions involving n-th roots.
  • I can demonstrate understanding of rational exponents and simplify expressions involving rational exponents.
  • I can evaluate a n-th root using a calculator or softwares.
  • I can express a radical using rational exponents and backward.
  • I can multiply, divide and simplify radical expressions.
  • I can add and subtract radical expressions.
  • I can perform operations on radical expressions.
  • I can rationalize the denominator or numerator of a given (radical) expression.

C-4. Logarithmic Expressions

  • I can demonstrate understanding of properties of logarithms and evaluate logarithms.
  • I can use properties of logarithms to expand a logarithm and write a logarithmic expression to a single logarithm.
  • I can evaluate a logarithm using a calculator and the base change property.

Solving Equations

C-5. Absolute Value Equations

  • I can solve a simple absolute value equation.
  • I can isolate the absolute value expression in the equation and then solve the equation.
  • I can apply the idea to more general situations.

C-6. Quadratic Equations

  • I can simplify and solve quadratic equations by factoring.
  • I can simplify and solve quadratic equations by completing the square.
  • I can simplify and solve quadratic equations by using the quadratic formula.
  • I can quadratic-like polynomial equations.
  • I can model situations using quadratic equations and use the model to form conclusions.
  • I can build and solve a work problem using quadratic Equations.

C-7. Radical Equations

  • I can solve simple radical equations.
  • I can solve equations involving two radical terms.
  • I can use factoring to solve quadratic-like equations involving radicals.

C-8. Exponential Equations

  • I can solve a simple exponential equation.
  • I can solve a quadratic-like equations involving exponential expressions.
  • I can solve an equation involve radicals of exponential expressions.

C-9. Logarithmic Equations

  • I can write a logarithmic equation as an exponential equation and backward.
  • I can solve a simple logarithmic equation.
  • I can solve a quadratic-like equations involving logarithmic expressions.
  • I can solve an equation involve radicals of logarithmic expressions.
  • I can use properties of logarithms to solve exponential equations.
  • I can solve applied exponential and logarithmic equations

C-10. Systems of Linear Equations

  • I can solve systems of linear equations in two variables.
  • I can identify inconsistent systems of equations in two variables.
  • I can express the solution of a system of dependent equations in two variables.

E-1. Problem Solving Strategies

  • I can use variety of techniques from algebra to setup and solve an equation involving powers, radicals, exponentiation, and/or logarithmic.
  • I can solve problems through comparing differences, making analogies and drawing inferences.

Algebra and Geometry (Graphs) of Functions

C-11. Function Essentials

  • I can demonstrate understanding of the definition of a function and can determine when relations are functions given a graph, table or real-world situation.
  • I understand the meaning of function notation and can evaluate a function for a given input.
  • I can find the domain of a function defined by an equation or by a graph.
  • I can find the range of a function defined by an equation or by a graph.
  • I can describe a function using words, equations and graph.
  • I can create new functions from given functions by algebraic operations.
  • I can create new functions from composition.

C-12. Linear Functions

  • I can find the slope of a line passing through two points.
  • I can find the slope and intercepts of a line from its equation or graph.
  • I can identify the type of slope (negative, positive, zero, undefined) of a line given its equation or graph.
  • I can interpret the meaning of the slope given a context.
  • I can write the equation of a line in slope-intercept form.
  • I can find the point-slope form equation of a line given its slope and a point.
  • I can find an equation of a line given two distinct points (including vertical and horizontal lines).
  • I can find equations of parallel lines.
  • I can find equations of perpendicular lines.
  • I can graph a line.
  • I can use one variable to express the coordinates of a point on a line given its equation.

C-13. Quadratic Functions

  • I can find the vertex and the axis of symmetry on the graph of a quadratic function.
  • I can find the vertex and the axis of symmetry of a quadratic function using its equation.
  • I can find intercepts of a quadratic function using its graph.
  • I can find intercepts of a quadratic function using its equation.
  • I can graph a quadratic function using its equation.
  • I can find the minimum or maximum value of a quadratic function using its equation or graph.
  • I can find the values of the independent variable of a quadratic function such as the value of it dependent variable equals a given number.
  • I can find the equation of a quadratic function using its graph.

C-14. Rational Functions

  • I can find the domain of a rational function.
  • I can solve applied problems involving rational functions.

C-15. Radical Functions

  • I can find the domain of a radical function.
  • I can find the domain a rational-like function involving radicals.
  • I can graph the square root function.

C-16. Exponential Functions

  • I can evaluate exponential functions in the form \(y=ab^x\) and relate the meaning to the context of a real-world situation.
  • I can setup an exponential function for an investment and determine the account balance.

C-17. Logarithmic Functions

  • I can change an exponential equation to a logarithmic equation.
  • I can change a logarithmic equation to an exponential equation.
  • I can evaluate logarithmic expressions without using a calculator.
  • I can determine the domain of a logarithmic function.