Systems of Equations in Two Variables

The exam will be based upon your homework, the material we covered in class, along with the
reading assignments. It will be in class on Thursday, April 9, and you will have sixty- five minutes
to complete it. This study guide provides an overview of what will be on the exam.

Chapter 4.1: Systems of Equations and Graphing. Students should be able to perform each
of the following tasks:
• Find a solution for a system of equations
• Use the TI to find a point of intersection (CAL 5: INTERSECT)
• Find a solution to a system of equations by graphing by hand
• Identify Consistent and Inconsistent systems
• Graphs intersect at one point vs Graphs are parallel vs. Equations have the same graph

Chapter 4.2: Systems of Equations and Substitution. Students should be able to perform
each of the following tasks:
• Use the substitution method to find a solution to a system of equations
• See To Solve a System Using Substitution on page 303

Chapter 4.3: Systems of Equations and Elimination. Students should be able to perform
each of the following tasks:
• Solve a system of equations using the elimination method
• Multiply the equation(s) by a well chosen number(s) and then add the two equations to-
gether, then use substitution

Chapter 4.4: More Applications Using Systems. Students should be able to perform each
of the following tasks:
• State the strengths and weaknesses to finding solutions using graphical, substitution, or
elimination methods
• Translate and solve mixture problems: Given a word problem, make a table that contains
the information, translate this into a system of equations and solve

Chapter 4.5: Solving Equations by Graphing. Students should be able to perform each of
the following tasks:
• Solve equations graphically using the intersect method or the zero method
The Chapter 4 Summary and Review is on page 346-7. Review Exercises are on page 348-9. The
Chapter Test is on page 350.

Chapter 5.1: Exponents and Their Properties. Students should be able to use each of the
following rules to simplify an expression:
• The Product Rule: a^m ٠ aⁿ = a^m+n
• The Quotient Rule: a^m/aⁿ = a^m-n
• The Exponent Zero: a^0 = 1 for any real number a, a ≠ 0
• The Power Rule: (a^m)ⁿ = a^mn
• Raisng a Product to a Power: (ab)ⁿ = aⁿbⁿ
• Raising a Quotient to a Power:

Chapter 5.2: Negative Exponents and Scientific Notation. Students should be able to use
each of the following rules to simplify an expression or perform the following tasks:
• Negative Exponents: a^-n =
• Factors and Negative Exponents:
• Reciprocals and Negative Exponents:
• Transform a number in decimal notation to scientific notation and vice versa
• Multiply and divide using scientific notation
• Use significant digits appropriately

Chapter 5.3: Polynomials and Polynomial Functions. Students should be able to use the
following vocabulary and perform each of the following tasks:
• Vocabulary: Term, monomial, binomial, trinomial, polynomial, degree of term, coefficient,
leading term, leading coefficient, degree of the polynomial, linear function, quadratic func-
tion, cubic function, quartic function
• Find the domain and range of a polynomial

Chapter 5.4:Addition and Subtraction of Polynomials. Students should be able to perform
each of the following tasks:
• Add and Subtract polynomials
• Find opposites of polynomials
• Find the area, perimeter, surface or volume of a 2- or 3-dimensional object

Chapter 5.5: Multiplication of Polynomials. Students should be able to perform each of the
following tasks:
• Multiply monomials
• Multiply a monomial with a polynomial
• Multiply any two polynomials

Chapter 5.6: Special Products. Students should be able to perform each of the following tasks:
• Use the FOIL method to multiply two binomials
• Use the product of a sum and difference to simplify an expression: (A+B)(A-B) = A²-B²
• Use the square of a binomial to simplify an expression: (A + B)² = A² + 2AB + B² and
(A - B)² = A² - 2AB + B²