Exam Review Topics

Jacobs Final Exam Review

For the Final Exam, you should be prepared to solve problems involving any and all of the following skills:

Chapter 2 – Number Sequences

• Identify arithmetic, geometric, square and cubic sequences
• Complete arithmetic, geometric, square and cubic sequences with missing terms
• Write a rule (or expressions) for large terms of arithmetic and geometric sequences
• Recognize the common difference for arithmetic sequences and the common ratio for geometric sequences
• Evaluate powers
• Find digital roots
• Examine a number sequence and deduce its pattern
• Understand the literal meaning of square and cube numbers (think of the pictures of dots found on clay tablets)
• List the numbers in the Fibonacci sequence
• Convert Base 10 numbers into binary, vice versa

Chapter 4 – Logarithms & Large Numbers

• Identify the names and exponential forms of the large numbers up to decillion
• Write large numbers as a power of 10
• Quickly multiply powers of ten using the law you learned
• Convert large numbers (decimal form) into scientific notation, vice versa
• Multiply & divide numbers written in scientific notation
• Find the logarithms of numbers in decimal form and scientific notation
• Compute operations with large numbers using logarithms

Chapter 7 – Methods of Counting

• Solve problems using the Fundamental Counting Principle
• Solve problems involving factorials
• Define and use correct notation for permutations and combinations
• Differentiate when to solve a problem using permutations or combinations
• Solve problems using permutations and/or combinations

Chapter 8 – The Mathematics of Chance

• Give the basic definition of probability
• Express and deduce independent from dependent events
• Convert fractions to decimals to percents and back again, as needed
• Solve problems using “basic” probability
• Solve problems involving probabilities of successive events
• Solve problems involving binomial probabilities
• Create and use (as needed) Pascal’s triangle to help in solving binomial probabilities
• Solve problems involving probabilities of complementary events

Pre-Algebra Review Unit

• Solve problems involving Order of Operations
• Evaluate exponents
• Solve problems involving rational numbers (fractions, decimals, and percents) as well as integers (signed numbers, positives/negatives)
• Translate written expressions into mathematical expressions
• Evaluate algebraic expressions by plug it in, plug it in
• Simplify variable expressions using properties and combining like terms
• Identify the Properties of Real Numbers (Commutative, Associative, Identity, Inverse, Distributive, etc.)
• Solve one-, two- and multi-step equations
• Solve a variety of word problems
• Graph a linear equation using an x/y chart
• Find the surface area and volume of a variety of shapes

Chapter 3 – Functions & Their Graphs

• Plot points on a coordinate plane
• Figure out the equations for a function based on an x-y chart
• Use an x-y chart to graph equations
• Identify the slope and x- and y-intercepts of a line
• Transform an equation from standard form to y=mx+b and vice versa
• Graph a linear function in y=mx+b form
• Find the equation of a line given a point and a slope
• Find the slope of a line given two points
• Find the equation of a line given two points
• Formulas to know: point-slope, point-point