This page contains sample exercises from the textbook and other examples along with the key ideas. These are good practice questions to help you understand the main ideas and they are a good indication of what you might see on quizzes, the midterm or the final. However, keep in mind that there may be other types of questions!

Winter:

Chapter 6:  Algebraic Models

• Section 6.1  Linear Equations.  Key Ideas: know what it means for two variables to be linearly related, two forms of linear equations (standard and slope-intercept),  what the sign and magnitude of slope tells you, solving or rearranging linear equations, intercepts, converting word descriptions to linear models.  Questions:  odd 9-61, 67-87
• Section 6.2  Modeling with Linear Equations.  Key ideas: Build a linear model given a point and a slope or given two points, figuring out what the variables are, making predictions.  Questions:  odd 7-21, 23, 25, 27, 31, 33
• Section 6.4  Exponential Equations and Growth.  Key Ideas: understand difference between linear and exponential functions, use exponential models for growth and decay, compound interest, populations growth, using log functions to solve equations, logistic models for populations.  Questions:  odd 9-57

Chapter 7: Systems of Linear Equations

• Section 7.1  Systems of Linear Equations.  Key Ideas: 3 cases for systems with 2 linear equations, converting word problems to linear systems and solving, supply and demand questions.  Questions: odd 9-49

Chapter 8: Geometry

• Section 8.1  Lines, Angles and Circles.  Key Ideas: Euclid's five axioms, terminology and notation for lines and angles, types of angles (right, straight, acute, obtuse), parallel lines, figuring out angles in a diagram, definition of a circle, relation between angle and arc length.  Questions: odd 9-61
• Section 8.2  Polygons.  Key Ideas: Closed, simple, convex.  Polygons: types of triangles, quadrilaterals, etc.  Angles in a triangle, general polygon.   Similar polygons.  Questions: odd 9-47
• Section 8.3 Perimeter and Area.  Key Ideas: be able to find perimeter and area for basic shapes (triangles, quads, circles, etc) and use this for more complicated shapes.  Two ways to find area of a triangle.   Using Pythagoras' Theorem.  Questions: odd 5-77.
• Section 8.4  Volume and Surface Area.  Key Ideas: be able to find volume and surface area for basic shapes (boxes, spheres, cones, cylinders, shapes with constant cross-sectional area) and use for more complicated shapes.  Questions: odd 7-43. 
• Section 8.6  Geometric Symmetry and Tessellations.  Key Ideas: know the four basic rigid motions: reflections, translations, glide reflections and rotations.  Know what a symmetry of a geometric object is.  Tessellations cover the plane with copies of polygons.  Regular tessellations.  Questions: odd 4-45
• Fractals (page 504).  Key ideas: difference between fractal geometry and regular geometry, self-similarity, how to obtain fractals, koch curve, Sierpinski gasket, fractal dimension.  odd 7-23.

Chapter 12:  Counting

• Section 12.1  Introduction to Counting Methods.  Key Ideas: use different approaches like lists or tree diagrams to count.  Generalize ideas for counting.  Questions: odd 5-53
• Section 12.2  Fundamental Counting Principle.  Key ideas: fundamental counting principle, dealing with conditions.  Questions:  odd 5-39
• Section 12.3  Combinations and permutations.  Key ideas: combinations, permutations, counting, connection with Pascal's triangle, solving counting problems.  Questions:  7-69

Chapter 13: Probability

• Section 13.1  Basics of Probability.  Key Ideas: what probability means, finding it from experimental data or from counting theory, what the value tells you, sample space, event, examples like genetics.  Questions: 9-33, 41-47, 59-67
• Section 13.2  Complements and Unions.  Key Ideas: the complement of an event and how to find its probability, the probability of the union of 2 events, how to tell if events are mutually exclusive.  Questions: 5-39
• Section 13.3  Conditional Probability and Intersection of Events.  Key Ideas: know what the conditional probability of an event E is given F (the notation and how to calculate), how to calculate the probability of two events both occurring (the intersection), difference between dependent and independent events, using probability trees.  Questions: 7-75
• Section 13.4  Expected Value.  Key Ideas: understand the meaning of the expected value, word problems with expected value- like lotteries, insurance, fair price.  Questions: 17, 19, 25-35

Chapter 3:  Graph Theory

• Section 3.1  Graphs, Puzzles and Map Colourings.  Key Ideas: know basic terminology about graphs (vertex, edge, connected, trace), Euler's theorem for determining if a graph is traceable, the Koenigsberg Bridge problem, Fleury's algorithm for finding a circuit, the 4 colour problem for map colouring.  Questions:  9-23, 27-35, 41-49

Fall:

Chapter 1: Problem Solving and Set Theory

• Section 1.1 Problem solving.  Key ideas: knowing that there are different ways to solve a problem, the 4 steps of problem solving (understand the question, devise a plan, carry out plan, verify answer), looking for patterns, predicting next number in a sequence (sometimes more than one right answer- just make sure to explain your reasoning), Gauss's method of finding sums (1 + 2 + ... + n = n(n+1)/2 etc), Pascal's triangle- know how to fill out, know a few facts about Pascal, know how to use the triangle to find the number of ways to choose objects (like the pizza question).  There are other problem-solving strategies in the book that we didn't go over in class.  Make sure to read these examples to see other approaches.  Questions from the book: 13, 15, 19, 21, 25, 27, 33, 35, 61, 63, 69
• Section 1.2  Estimation.  Key Ideas: how to round numbers off to make estimates, using compatible numbers, examples like estimating a grocery bill.  We will not cover this material in class, but you are responsible for reading it.  If you can do the sample exercises from the book then you should be fine.  There are also some on the first assignment (and you can see similar examples if you aren't sure what to do).  Questions from the book: 8, 13, 15, 17, 19, 21, 23, 29, 33, 35, 39, 43, 45, 51, 53
• Section 1.3  The Language of Sets.  Key Ideas: ways to specify a set (listing and set-builder notation), what it means for a set to be well-defined, set notation (empty set, element of, not an element of), the cardinal number of a set.  Questions from the book: 7, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 33, 35, 37, 43, 49, 51, 55, 59, 61, 65, 67, 73, 75, 79
• Section 1.4  Comparing sets.  Key Ideas: what does it mean for a set to be a subset of another set, when are two sets equal, when two sets are equivalent, number of subsets of a set.  Questions: 11, 13, 15, 17, 21, 23, 25, 27, 31, 33, 35, 37, 39, 59, 61, 63
• Section 1.5  Set Operations.  Key Ideas: know how to do union, intersection, complement and difference, use Venn diagrams.  Questions: 1, 3, 7, 11, 13, 15, 17, 19, 21, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75 
• Section 1.6 Survey Problems.  Key Ideas: know how to convert a word problem to a Venn diagram and get info from the diagram.  Questions:  7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35

Chapter 2: Logic

• Section 2.1  Inductive and Deductive Reasoning.  Key ideas: know what the difference between inductive and deductive reasoning is, be able to give examples using each type of reasoning.  Questions:  7, 9, 11, 17, 19, 25, 31, 39, 45, 51
• Section 2.2  Statements, Connectives and Quantifiers.  Key ideas: know what a statement is, know how to tell if a statement is simple or compound, different connectives (not, and, or, if...then, if and only if), symbols for connectives, universal quantifier (all, every, always), existential quantifier (some, sometimes, there is at least one), negation of quantified statements.  Questions:  1, 3, 5, 7, 11, 13, 15, 17, 21, 23, 25, 27, 29, 37, 39, 41, 43, 45, 47, 49, 63, 65, 67, 69
• Section 2.3  Truth Tables.  Key ideas: know how to do truth tables for the five types of connective statements, know how many rows there should be based on the number of simple statements in the compound statement, be able to fill out table for more complicated statements, DeMorgan's laws for logic.  Questions:  1, 5, 7, 9, 11, 13, 15, 21-28, 29, 36, 37, 39, 41, 43, 49, 51, 53, 55, 57, 61, 63, 65
• Section 2.4 The Conditional and Biconditional.  Key Ideas: know what conditional and biconditional statements look like, and their corresponding truth tables.  You also need to know what the converse, inverse and contrapositive of a conditional statement are, and which ones are logically equivalent.  Questions:  5, all odd 9-43
• Section 2.5  Verifying Arguments.  Key Ideas: be able to write arguments symbolically, know how to determine if an argument is valid or invalid, standard arguments (don't need to memorize name, but know that they are valid: law of detachment, law of contraposition, law of syllogism, disjunctive syllogism), standard invalid arguments (fallacy of converse, fallacy of inverse).  Questions: odd 11-47

Chapter 4:  Numeration Systems

• Section 4.1  The Evolution of Number Systems.  Key Ideas: different types of number systems (simple grouping, multiplicative), historical examples (Egyptian, Roman, Chinese), know the symbols for Roman, be able to convert between different systems.  Questions: 5, 6, odd 9-73, 77, 79, 83, 85
• Section 4.2   Place Value Systems.  Key Ideas: Place value systems (ex. Babylonian, know symbols), expanded form of numbers.  Questions:  5, 9, 13, 17, 19, 29, 31, 33
• Section 4.3  Calculating in Other Bases.  Key Ideas:  different bases (converting, doing addition and subtraction).  Questions:  odd 9-63, 73 (just octal), 79, 89

Chapter 5:  Number Theory and the Real Number System

• Section 5.1  Number Theory.  Key Ideas: definition of prime/composite, how many primes are there, Mersenne primes (not in the book), Sieve of Eratosthenes, divisibility tests, factoring, prime factors, GCD, LCM, using GCD and LCM to solve problems.  Questions:  odd 9- 63, 73, 75, 77, 79
• Section 5.2  Integers.  Key Ideas: rules for adding, subtracting, multiplying and dividing integers.  Questions: odd 7-93
• Section 5.3  The Rational Numbers.  Key Ideas: determining when two fractions are equal, arithmetic of fractions, word problems with fractions, converting fractions to decimals and decimals to fractions.  Questions: odd 9-115
• Section  5.4  The Real Number System.  Key Ideas: what irrational numbers look like (infinite non-repeating decimals), working with radical expressions, properties of number systems (closed, commutative, associative, identity, inverse, distributive).  Questions: odd 9-89

Last updated April 9, 2008.