Objectives List. Important Students should expect test questions that require a synthesis of these objectives.

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1 MATH of One Variable, Part I Textbook 1: : Algebra and Trigonometry for ET. 4 th edition by Brent, Muller Textbook 2:. Early Transcendentals, 3 rd edition by Briggs, Cochran, Gillett, Schulz s List Important Students should expect test questions that require a synthesis of these objectives. JIT Section 1.1: Multiplying and Dividing Fractions Multiply and Divide Fractions. AR 1.2, AR 1.4, AR 1.5, AR 1.6, AR 1.7, AR 5.1, AR 5.3 8, 9, 10, 11, 12, 13, 14 JIT Section 1.2: Adding and Subtracting Fractions Add and Subtract Fractions. AR 1.12, AR 1.14, AR 1.15, AR 5.10, AR 5.11, AR 5.13, AR 5.15, AR 5.26, AR 5.28, AR 5.31, , , 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 JIT Section 1.3: Parentheses Use order of operations to simplify expressions with parentheses and exponents. AR 1.21, AR 1.22, AR 1.24, AR 1.29, 8, 9, 10, 12, 13, 14 JIT Sections 1.4: Exponents Understand and utilize the laws of exponents for integer exponents. AR 2.4, AR 2.6, AR 2.8, AR 2.9, AR , 9, 11, 12, 13, 14, 15, 16, 19, 21

2 JIT Section 1.5: Roots Understand and utilize the laws of exponents for fractional exponents. AR 2.11, AR 2.13, AR 2.16, AR 2.18, AR 2.19, AR 2.20, AR 2.22, AR 2.25, AR 2.26, AR 2.28, AR 2.29, AR 2.30, AR 2.31, AR 2.34, AR 2.35, AR , 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 JIT Section 1.8: Intervals Use interval notation to describe a set of numbers. AR 1.32, AR 1.34, AR 1.35, AR 1.36, AR 3.60, AR 3.61, AR , 2, 3, 4, 5 JIT Section 4.1: Function Introduction Understand and use function notation and presentation. AR 6.10, AR 6.11, AR 6.29, AR 6.31, AR 6.32, AR 6.33, AR 6.34, AR 6.36, AR 6.39, Understand and use the absolute value function. AR 6.17, AR 6.22, Find the domain and range of a given function. AR 6.13, AR 6.14, AR 6.15, AR 6.18, AR 6.19, AR 6.21, AR , 1.1.2, 1.1.7, , , , AR 5.57, AR 5.58, AR , 2, 5, 6 3, 4 7, 8, , 1.1.6, 1.1.7, 1.1.8, 1.1.9, , , ,

3 JIT Section 4.2: Lines and Their Equations Understand slope and graph linear equations. AR 3.18, AR 3.20, AR 3.21, AR 3.29, , 2, 3, 4, 5, 10 Find equation of a line given slope and point. AR 3.11, , Given two points, find the equation of the line that AR 3.8, AR 3.9, passes through them , Understand slope relationships for parallel and perpendicular lines. Graph piecewise linear functions or write equation given graph. AR 3.13, AR 3.15, AR , , , , 9, , , , , , 12, 13, 15, 17, , , , , JIT Section 4.3: Power Functions Determine if a given function is even (symmetric across the y-axis), odd (symmetric with respect to the origin), or neither , , , Plot the graphs of y=x^2, y=x^3, y=1/x, y=1/x^2, y=x^(1/2), y=x^(1/3), y=abs(x) 8, 9, 10, 11 Know and use the domain and range of above , , , , , , , , JIT Section 4.4: Shifting Up and Down Plot a vertical shift of a basic functions. AR 7.2 8, 9 JIT Section 4.5: Shifting Left or Right Plot a horizontal shift of a basic function. AR 7.5, AR 7.7, AR 7.8 1, 2, 3a,b, 4, 5, 6

4 JIT Section 4.6: Translation Translate a basic function. AR 7.6, , AR7.14, AR 7.21, Graph a translated and/or reflected function. AR 7.12, AR 7.24, Write the equation for a translated and/or reflected AR 7.17, AR 7.18, function. AR 7.19, AR 7.20, , :10 4.6: 9, , 1.2.9, , , JIT Section 4.7: Intersection of Curves and Simultaneous Solutions Solve two equations in two variables by various methods but mostly graphing. AR 3.30, AR 3.32, AR 3.33, AT 3.34, AR 3.35, AR 3.37, , 2, 3, 5, 6, JIT 5.1: Angles Convert from degrees to radians. AR 9.1, AR 9.2, , 2 Convert from radians to degrees. AR 9.5, AR 9.7 3, 4, 5, 6 JIT Section 5.2: Definition of sinq and cosq Calculate the sine of a given angle. AR 9.38, , 2, Calculate the cosine of a given angle. AR 9.31, AR 9.32, (1, 2, 3,) , Know and use basic Pythagorean Identity. 6 JIT Section 5.3: Special Angles Define the 6 trig function values for the special angles (0, p/4, p/3, p/6, p/2) for all quadrants. AR 9.36, AR 9.42, , 9, 10, 11, , , ,

5 JIT Section 5.5: The Other Trigonometric Functions Find the value of the 6 trig functions for any specific angle. Given one trigonometric function value (sin x, cos x, or tan x) and an interval, determine the other two function values. Answer conceptual questions involving trigonometric functions. AR 9.44, AR 9.45, , , AR 9.12, AR 9.13, AR 9.14, AR 9.15, AR 9.16, , , , , 2, , , JIT Section 5.4: Graphs Involving sinx and cosx Graph all 6 trig functions unshifted , , Graph a given trig function and find the period, amplitude, and phase shift for the given function. AR9.59, AR 9.63 AR 9.46, AR 9.47, AR 9.50, AR 9.51, AR 9.52, AR 9.54, AR 9.55, AR 9.60, AR 9.61, , : 4, 5, 6, : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, , JIT Section 15.1: Trigonometric Identities Use the addition, double- angle, or half-angle formulas to derive identities and/or evaluate trig functions. Use the Pythagorean Identities to derive identities and/or evaluate trig functions. AR , 7, 8, 9, 12, 13, AR 9.65, AR 9.66, AR 9.67, AR 9.69, AR 9.70, AR 9.71, AR 9.73, 1.4.7, Solve trigonometric equations , , , , , AR 9.95, AR , 15 1, 2, 3, 4, , , , , , , , , ,

6 JIT Section 10.1: Common Factors Factor an expression by pulling out a common factor. AR 4.1, AR 4.2 1, 2, 3, 4, 5, 6 JIT Section 10.2: Special Formulas Factor expressions of the form: Difference of 2 squares Sum of 2 cubes Difference of 2 cubes AR 4.30, AR 4.32, AR 4.36, AR 4.39 Factor quadratic expressions. AR 4.10, AR 4.12, AR 4.13 Factor with a combination of methods. AR 4.34, AR 4.35, AR 4.37, AR 4.38, AR 4.18, AR 4.21, AR 4.29 Simplify rational expressions with factoring. AR 5.5, AR 5.6, AR 5.7, AR 5.16, AR 5.19, AR 5.21, AR , 9, 10 11, 12, 13, 17, 18, 19 15, 16, 20 JIT Section 10.3: Grouping Factor by grouping. AR 4.5, AR 4.8, AR 4.9, AR 5.8 1, 2, 3, 4, 5, 6, 8, 9 JIT Section 10.4: The Factor Theorem and Long Division Apply the Factor Theorem and use long division to find all the factors. 1, 2, 3, 4, 6, 7, 9, 10

7 JIT Section 2.1 Completing the Square Complete the square to change the form of a quadratic. AR 4.25, AR , 2 Complete the square to help solve a quadratic. AR 4.63, AR 4.64, 3, 4 Use completing the square to help find the center and radius of a circle. AR , 8 JIT Section 10.5: Rationalizing Numerators or Denominators Using Conjugates Rationalize the numerator or denominator of a given expression. AR 5.39, AR 5.40, AR 2.39, AR 2.40, AR 2.41, AR , 2, 3, 4, 5, 6, 7 JIT Section 10.6: Extracting Factors from Radicals Extract factors from under a radical sign. Understand expressions like!x # + y # x + y and x # x AR 2.43, AR 2.44, AR , 9 JIT Section 3.1: Equations of Degree 1 AR 3.3, AR 3.6 8, 9 Solve equations of degree 1 (i.e. linear equations) in one variable. Solve equations in two variables. AR , 12, 13, 14, 15, 16, 17, 18 Do simple applications. 10, 19, 20, 21, 22

8 JIT Section 3.2: Equations of Degree 2 Solve equations of degree 2 by factoring etc. AR 4.46, AR 4.47, AR 4.52, AR 4.54 AR 4.55, AR 4.56, AR4.58, AR 4.59, AR 4.61 Solve equations of degree 2 with quadratic formulas. AR 4.69, AR 4.71, AR , 2, 3, 4, 5, 8, 9, 11 6, 7, 10, 12, 13, 14, 15 Do simple applications. 23, 24, 25, 26 JIT Section 3.3: Solving Other Types of Equations Solve equations with various methods including: Isolating the variable Quadratic formula Zero-factor property Factoring like a quadratic Common denominator Cross multiplication Eliminating extraneous solutions AR 4.75, AR 4.76, AR 4.79, AR 4.80, AR 4.82, AR 4.83, AR 4.84, AR 4.85, AR 4.87, AR 4.88, AR 5.46, AR 5.48, AR 5.49, AR 5.50, AR 5.53, AR , 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 Section 2.1: The Idea of Limits Problems Answer conceptual questions involving average velocity or secant and 1, 9 tangent lines. Calculate average and instantaneous velocities. 13, 17, 24 Calculate slopes of secant and tangent lines. 26, 28 Solve applications involving average and instantaneous velocities

9 Section 2.2: Definitions of Limits Problems Answer conceptual questions involving definitions of limits. 2, 33 Find limits from a graph. 3, 6, 15, 17, 23, 28, 29, (35), Estimate limits from a table. 7 Solve applications involving the evaluation of limits by graphing. 35 Estimate limits using a graphing utility. 43 Sketch graphs of functions given information about limits and function 46 values. (Skill recurs in future sections.) (43), 51 19, 20 Section 2.3: Techniques for Computing Limit Problems Answer conceptual questions involving techniques to compute limits. 3, 14, 17, 81, 85, 95 Compute limits, stating the limit laws used. 7, 11, 12 Evaluate two-sided limits using limit laws and theorems. 19, 23, 25, 29, 33, 37, 39, 41, 47, 53, 56, 90, 93 Evaluate one-sided limits using limit laws and theorems. 73, Section 2.4: Infinite Limits Problems Answer conceptual questions involving infinite limits and vertical 3, asymptotes. Find infinite limits numerically or graphically. 5, 6, 9 11 Sketch graphs or functions involving infinite limits. 17, 54 Evaluate limits analytically. 21, 27, 33, 35, 51 37, 42 Find vertical asymptotes. 45, 50, 61, 65

10 Section 2.5: Limits at Infinity Problems Evaluate limits at infinity. 7, 9, 12, 13, 17, 22, 29 Answer conceptual questions involving end behavior and horizontal 11, 63 asymptotes. Find horizontal and vertical asymptotes of functions. 37, 40, 41, 43, 81 47, 71, 75 Find slant asymptotes and sketch graphs of rational functions. 51, 55 Determine end behavior of transcendental functions and sketch their graphs. 59, 61 Solve applications involving limits used to find steady states. 65, 69 Sketch graphs of functions given information about their end behavior. 86 Find limits of sequences. 88, 91 JIT Section 6.1: The Family of Exponential Functions Graph functions of the form a^x, for a>1 AR 8.1, AR 8.3, (1), Graph functions of the form a^x, for 0<a<1 AR 8.4 1, 2, 3, 4 JIT Section 6.2: The Function e^x Graph the function y=e^x basic and translated. AR 8.5, AR 8.6, 1, 2, AR 8.7 Answer conceptual questions involving exponential and , 6 logarithm functions. Evaluate limits involving exponentials. Solve equations with exponentials. AR 8.57, AR 8.58, AR 8.60, AR 8.61

11 JIT Section 7.1: Composition Evaluate functions involving composition. AR 7.25, , State the domain and range of functions involving composition. AR 7.32, AR 7.33, AR 7.36, Combine two functions through composition , , , , , , , , , , , JIT Section 7.2: The Idea of Inverses Know and use what it means for 2 functions to be inverses of each other. AR 7.43, AR 7.44, AR JIT Section 7.3: Finding the Inverse of f by a Graph Graph the inverse of a given function that is 1-1 AR 7.47, AR 7.53, , , Determine graphically when a function is 1-1 (AR 7.47), 1.3.2, 1.3.3, 1.3.5, 1.3.6, , , , , 9, 10, 11, 12 ( 8, 9, 10, 11, 12) , , , JIT Section 7.4: Finding the Inverse of f by an Expression Algebraically determine the inverse of a 1-1 function , , (1.3.27, , ), , Know and use relationship of domain and range of inverse functions. Evaluate function and inverse values given a table of values. 1, 2, 3, 4, 5, 6, , , , ,

12 JIT Section 8.1: Definition of Logarithms Find the logarithm of a number for a given base. AR 8.9, AR 8.10, AR , 9, 10, 11 Simplify expressions involving logarithms. AR 8.11, AR , 13, 14, 15, 16, 17, 18, 19, 20, 21 Answer conceptual questions involving exponential and logarithm functions , , , JIT Section 8.2: Logs as Inverses of Exponential Functions Understand the inverse relationships between logarithms AR 8.26, , and exponential functions Solve exponential equations , , 4, 1, , , 8.3: Solve logarithmic equations. AR 8.71, AR , 6, 7, 8, 9, , JIT Section 8.3: Law of Logarithms Apply the laws of logarithms to simplify expressions or solve equations. (watch out for extraneous solutions) Use the Change of Base Rule to evaluate logarithms and rewrite exponential expressions. AR 8.32, AR 8.37, AR 8.39, AR 8.43, AR 8.48, AR 8.75, AR 8.78, AR 8.79, , , , , , , 2, 3, 4, 5, 6, 9, , JIT Section 8.4: The Natural Logarithm Graph exponential and logarithmic functions. Write the equations for the translations. Use the inverse relationships to simplify expressions or to solve equations involving natural logs or expressions of e (watch out for extraneous solutions) AR 8.54, AR 8.56, AR 8.46, AR 8.47, AR 8.73, AR , 2, 3, , 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

13 Section 2.6: Continuity Problems Answer conceptual questions involving continuity. 2, 9 Find points of discontinuity or intervals of continuity. 7, 13, 15, 30, 39, 43, 47 Determine if functions are continuous at given values. 19, 21, 23, 87 Evaluate limits using continuity principles. 32, 49, 51, 65 53, 88 Use the Intermediate Value Theorem to show equations have solutions on 67a, 71a given intervals. Sketch graphs of continuous functions given information about their points of 85 discontinuity. Solve applications involving continuity principles. 93 Classify discontinuities. 95, 99 (*Review: Evaluate two-sided limits using limit laws and theorems.) (2.3.27) Section 2.7: Precise Definitions of Limits (Delta-Epsilon) Problems Answer conceptual questions involving precise definitions of limits. 2, 5, 49 Determine delta values associated with the precise definition of a limit. 10, 12 Use precise definitions of limits to prove statements. 19, 21 20, 22 (Skill is limited to linear functions and linear functions with a hole.) (*Review: Evaluate limits analytically.) (2.4.23) JIT Section 11.1: Working with Difference Equations Simplify the difference quotient ((*+,).((*), Simplify the difference quotient ((*).((/) *./ AR 6.43, , , , , , , 2, 3, 4, 9, 10, 12 Investigate basic application problems , , 17, 18, , , , , , , , , ,

14 Section 3.1: Introducing the Derivative Problems Answer conceptual questions involving tangent lines and derivatives. 5 Solve applications involving the use of limits to calculate derivatives. 13, 51 Use limit definitions to find equations of tangent lines. 15, 21, 25, 27, 29, 31, 35, 37, 41, (44) Use limit definitions to evaluate derivatives at given points. 44 Compute average and instantaneous rates of change from graphs and tables. 52 (Review of skill from Section 2.1) Determine functions given limits of difference quotients. 57, 60 (*Review: Evaluate limits at infinity.) (2.5.20) (*Review: Find horizontal and vertical asymptotes of functions.) (2.5.77) Section 3.2: The Derivative as a Function Problems Answer conceptual questions involving the derivative as a function. 1, 7, 8 Obtain the graphs of derivative functions from graphs of functions. 15, 17, 51 Find points where functions are continuous and differentiable. 19, 54, Find derivatives of functions using limits. 29, 35, 37, Solve applications involving derivatives as functions Use graphs of functions to analyze slopes of tangent lines. 45, (73) 47, 48, 49 Obtain graphs of functions from graphs of their derivative function Find equations of normal lines. 63, 66 Find vertical tangent lines from graphs. 73 (*Review: Find points of discontinuity or intervals of continuity.) (2.6.28) (*Review: Evaluate limits using continuity principles.) (2.6.57) Section 3.3: Rules of Differentiation Problems Answer conceptual questions involving rules of differentiation. 4, 5 Use graphs and tables to find derivatives. 11, 14 Find derivatives using rules of differentiation. 21, 28, 29, 33, 35 Solve applications involving rules of differentiation. 44 Simplify products and quotients to find their derivatives. 47, 49, 51, 57 Use derivatives to find slope locations and equations of tangent lines. 61, Find higher order derivatives of functions. 68, 72 78, 79, 80, 81 Use derivatives to evaluate limits. 82, 85 Use a calculator to approximate limits. (Review of skill from Section 2.1.) 91 (*Review: Evaluate two-sided limits using limit laws and theorems.) (2.3.33)

15 Section 3.4: The Product and Quotient Rules Problems Answer conceptual questions involving the product and quotient rules. 1, 2 Find derivatives using two different methods. 10, 11, 16 Find derivatives of products and quotients of functions involving 20, 24, 25, 37, exponentials. 48 Find derivatives of products and quotients of algebraic expressions. 21, 22, 29, 43, 53 Find derivatives using the extended power rule. 39, 41 Find slopes and equations of tangent lines of functions involving products 63, 74, 92 and quotients. Solve applications involving the product rule and quotient rule. 65 Find higher order derivatives of products and quotients. 71, 73 Find derivatives of products and quotients using given values or graphs. 78, 81 (*Review: Evaluate limits analytically.) (2.4.27) 56 Section 3.5: Derivatives of Trigonometric Functions Problems Answer conceptual questions involving derivatives of trigonometric 1, 8, 54, 72, 31, functions. 78 Find limits involving trigonometric functions. 12, 13, 14, 16, 21, 66, 70 Find derivatives of basic trigonometric functions. 23, 43 Find derivatives of products, quotients, and powers of functions with 25, 29, 31, 37, trigonometric expressions. 40, 44, 48 Solve applications involving derivatives of trigonometric functions. 55 Find higher order derivatives of functions involving trigonometric functions. 59 (*Review: Find derivatives of functions using limits.) (3.2.25) (*Review: Evaluate limits at infinity.) (2.5.17) (*Review: Find horizontal and vertical asymptotes of functions.) (2.5.75) Section 3.6: Derivatives as Rates of Change Problems Answer conceptual questions involving derivatives as rates of change. 6, 35 Find functions for velocity and acceleration given position functions. 18, 19 Solve applications involving position, velocity, and acceleration functions. 25, 36 39, 57 Find average and marginal cost profit functions Solve biological and physical applications involving derivatives as rates of 55 change. (*Review: Evaluate limits using continuity principles.) (2.6.51)

16 JIT Section 12: Decomposition of Functions Decompose a function into an inside function and an outside function. AR 7.38, AR 7.40, AR 7.41, , , , , , 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, , Section 3.7: The Chain Rule Problems Answer conceptual questions involving the chain rule. 2, 10, 77 Identify inner and outer functions for composite functions, then apply the 17, 20, 23 chain rule. Find derivatives of functions involving the chain rule by using tables and 25 graphs. Find derivatives of basic functions using the chain rule. 27, 29, 32, 33, 35, 37, 42, 44, 48, 75 Use the chain rule multiple times and use the chain rule with the product and 40, 41, 49, 59, quotient rules. 63, 66, 70, 73 Find higher order derivatives using the chain rule. 86, 89 Find slopes of curves and equations of tangent lines by using the chain rule. 93, 95 Solve applications involving the chain rule. 98 (*Review: Find derivatives of products and quotients of algebraic (3.4.19) expressions.) (*Review: Find derivatives of products and quotients of functions involving (3.4.27) exponentials.)

MATH 1040 Objectives List

MATH 1040 Objectives List Textbook: Calculus, Early Transcendentals, 7th edition, James Stewart Students should expect test questions that require synthesis of these objectives. Unit 1 WebAssign problems