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 3467. Review Exercises are on page
3489. 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 a^{n} = a^{m+n}
• The Quotient Rule: a^{m}/a^{n} = a^{mn}
• 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} = a^{n}b^{n}
• 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 3dimensional 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)(AB)
= A^{2}B^{2}
• Use the square of a binomial to simplify an expression: (A + B)^{2} = A^{2} + 2AB
+ B^{2} and
(A  B)^{2} = A^{2}  2AB + B^{2}
