Study Guide for Exam 1

This will be a closed-book exam. You will only need a pencil to take the exam.

To do well on the exam, you should be able to do the following:

Section 1.2: Exponents and Radicals

  1. Explain how exponential notation with an integer exponent is shorthand for repeated multiplication / division.
  2. Simplify expressions using the properties of integer exponents.
  3. Explain how \(n\)-th roots are related to \(n\)-th powers.
  4. Simplify expressions involving \(n\)-th roots.
  5. Explain the correspondence between \(n\)-th roots and rational exponents.
  6. Simplify expressions involving rational exponents.

Section 1.3: Algebraic Expressions

  1. Determine whether a given expression is a polynomial, and if so, specify its degree.
  2. Add and subtract polynomials.
  3. FOIL (first-outer-inner-last) products of polynomials.
  4. Pull out common factors from a polynomial expression.
  5. Factor trinomials by trial-and-error.

Section 1.4: Rational Expressions

  1. Explain how to construct a rational expression from two polynomials.
  2. Specify the domain of polynomial, radical, and rational expressions.
  3. Add, subtract, multiply, and divide rational expressions to get a rational expression in a specified form.
  4. Identify errors in an incorrect simplification of a rational expression.

Section 1.5: Equations

  1. Explain what it means for a value of a variable to “solve an equation.”
  2. List operations you can perform to each side of an equation and maintain equality.
  3. Solve a linear equation.
  4. State the quadratic formula.
  5. Solve a quadratic equation by factoring or using the quadratic formula.
  6. Perform a “check your answer” procedure after solving an equation.

Section 1.8: Inequalities.

  1. Specify what it means to solve an inequality.
  2. List the rules for manipulating inequalities.
  3. Solve linear inequalities.
  4. Solve absolute value inequalities.
  5. Perform a “check your answer” procedure after solving an inequality.
  6. Draw the solution to an inequality on the number line.

Section 1.9: The Coordinate Plane; Graphs of Equations; Circles.

  1. Draw and label the coordinate plane, including the horizontal/vertical axes and quadrants.
  2. Plot ordered pairs \((x, y)\) on the coordinate plane.
  3. Compute the distance between two points.
  4. Explain what it means for a point \((x, y)\) to satisfy an equation \(y = f(x) \).
  5. Sketch a graph of a function \(y = f(x)\) in the coordinate plane by generating a table of \(x\) and \(y = f(x)\) values.
  6. Define the \(x\)- and \(y\)-intercepts of a graph, and find them given a graph.
  7. State the equation for a circle in standard form, and identify the center and radius of a circle using the equation for the circle in standard form.