Algebra 2: Midterm Final Review. additive inverse: 7 11 ;

Transcription

1 lgebra : Midterm Final Review Multiple hoice ) Write the set in set-builder notation. 0 x [, ) [, ] ) Find the additive and multiplicative inverse of 7. additive inverse: ; multiplicative inverse: 0 additive inverse: 7 ; multiplicative inverse: 7 additive inverse: 7 ; multiplicative inverse: 7 additive inverse: 7 ; multiplicative inverse: 7 ) Identif the propert demonstrated b the equation + =. ommutative Propert losure Propert istributive Propert ssociative Propert ) Simplif b rationalizing the denominator. ) Simplif the expression. ) Simplif the expression. 0 7) Simplif the expression. ssume all variables are nonzero. ) Simplif the expression. Write the answer in scientific notation

2 lgebra : Midterm Final Review 9) The commercial jet that travels from Miami to New York averages about 00 mi/h. The air distance from Miami to New York is 9 miles. Write a function to represent the distance d remaining on the trip t hours after takeoff. ) etermine whether the data set could represent a linear function. x f(x) 0 The data set is constant. annot be determined No, the data set does not represent a linear function. Yes, the data set could represent a linear function. ) Graph the line with slope that passes through (, ) x 9 9 x x 9 9 x 9 9

3 lgebra : Midterm Final Review ) Find the intercepts of, and graph the line. x-intercept:, -intercept: 9 x-intercept:, -intercept: x x x-intercept:, -intercept: 9 x x-intercept:, -intercept: x )In slope-intercept form, write the equation of the line that contains the points in the table. x 9

4 lgebra : Midterm Final Review )Write the function in slope-intercept form. Then graph the function. x x x x ) etermine if is vertical or horizontal. Then graph. The line is horizontal. The line is horizontal. x x

5 lgebra : Midterm Final Review The line is vertical. The line is vertical. x x ) Solve for. Graph the solution. x x x x

6 lgebra : Midterm Final Review ) Let be the transformation, vertical translation units down, of. Write the rule for. 7) Solve the inequalit and graph the solution set ) nchorage, laska and ugusta, Georgia have ver different average temperatures. This is a table of the average monthl temperature in each cit. Make a scatter plot for the temperature data, identif the correlation, and then sketch a line of best fit and find its equation. verage Temperatures (ºF) Jan Feb Mar pr Ma Jun Jul ug Sep Oct Nov ec nchorage 9 7 ugusta Positive correlation Negative correlation ugusta ugusta Positive correlation nchor. Negative correlation nchor.

7 lgebra : Midterm Final Review ugusta ugusta nchor. nchor. 0) Translate so that the vertex is at (, ). Then graph. x x x x 7

8 lgebra : Midterm Final Review ) lassif the sstem, and determine the number of solutions. This sstem is inconsistent. It has infinitel man solutions. This sstem is consistent. It has infinitel man solutions. This sstem is inconsistent. It has no solutions. This sstem is consistent. It has one solution. ) Two snow resorts offer private lessons to their customers. ig Time Ski Mountain charges $ per hour plus $0 insurance. Powder Hills charges $ per hour plus $0 insurance. For what number of hours is the cost of lessons the same for each resort? hours hours hours hours ) shop makes tables and chairs. Each table takes hours to assemble and hours to finish. Each chair takes hours to assemble and hour to finish. The assemblers can work for at most 00 hours each week, and the finishers can work for at most 0 hours each week. The shop wants to make as man tables and chairs as possible. Write the constraints for the problem, and graph the feasible region. Let t be the number of tables and c be the number of chairs. 7 c 0 7 c t t

9 lgebra : Midterm Final Review c c t t ) Graph the linear equation in three-dimensional space. z (0, 0, ) (0,, 0) (, 0, 0) <> x (0,, 0) (, 0, 0) x (0, 0, ) < > z z (0, 0, ) (0,, 0) (, 0, 0) <> x z (0, 0, ) (0,, 0) (, 0, 0) x < > 9

10 lgebra : Midterm Final Review ) Graph the inequalit. x x x x

11 lgebra : Midterm Final Review ) Graph the sstem of inequalities. x x x x 7) Which point gives the minimum value of in the feasible region shown? 7 R U S T 7 x

12 lgebra : Midterm Final Review ) Use substitution to determine if (0, ) is an element of the solution set for the sstem of equations. (0, ) is not a solution of the sstem. (0, ) is a solution of the sstem. 9) Use elimination to solve the sstem. (, 0) (, ) (, ) (0, ) 0) lassif the sstem as consistent or inconsistent, and determine the number of solutions. onsistent. Infinitel man solutions. onsistent. One solution. Inconsistent. No solutions. Inconsistent. Infinitel man solutions. ) Evaluate, if possible. Not possible ) Tell whether the product of is defined. If so, give the dimensions of PQ. defined; undefined defined; defined; ) Find the product, if possible. = = Not possible

13 lgebra : Midterm Final Review ) Evaluate, if possible. Not possible ) Find the determinant of the matrix. 0 ) Find the determinant of ) Find the inverse of the matrix, if it is defined. ) Write the matrix equation for the sstem, and solve. ; ; (0, ) (0, ) ; ; ( 0, ) (, )

14 lgebra : Midterm Final Review 9) Graph. x x x x

15 lgebra : Midterm Final Review 0) Using the graph of as a guide, describe the transformations, and then graph the function. is translated 7 units left and units up. is translated units right and 7 units down. g(x) g(x) f(x) f(x) x is translated units left and 7 units up. x is translated 7 units right and units down. g(x) g(x) f(x) f(x) x x ) The parent function is reflected across the x-axis, verticall stretched b a factor of 7, and translated right units to create g. Use the description to write the quadratic function in vertex form. ) Solve the equation b completing the square. x = 7 or x = 7 x = or x = x = or x = x = or x = ) Write the function in vertex form, and identif its vertex. ; vertex: (, ) ; vertex: (, ) ; vertex: (, ) ; vertex: (, )

16 lgebra : Midterm Final Review ) Solve the equation. ) Graph the complex number. imaginar imaginar real real imaginar imaginar real real ) Write a quadratic function that fits the points (0, 7), (, ), and (, 7). 7) Find the zeros of b using the Quadratic Formula. ) Find the number and tpe of solutions for. annot determine without graphing. The equation has one real solution. The equation has two nonreal complex solutions. The equation has two real solutions.

17 lgebra : Midterm Final Review 9) The perimeter of a right triangle is 0 ft, and one of its legs measures ft. Find the length of the other leg and the hpotenuse. ft, 7 ft ft, 0 ft ft, ft ft, 9 ft 0) Solve the inequalit b using algebra. ) Graph the complex number. imaginar imaginar real real imaginar imaginar real real ) Find the absolute value. 7 ) dd. Write the result in the form. ( 9 ) + ( + 7 ) 7 + 7

18 lgebra : Midterm Final Review ) Multipl. Write the result in the form. ) Rewrite the polnomial x + 7x x + x x in standard form. Then, identif the leading coefficient, degree, and number of terms. Name the polnomial. leading coefficient: ; degree: ; number of terms: ; name: quintic polnomial leading coefficient: ; degree: 0; number of terms: ; name: quintic polnomial leading coefficient: ; degree: 0; number of terms: ; name: quintic polnomial leading coefficient: ; degree: ; number of terms: ; name: quintic polnomial ) Find the product. 7) Find the product. ) Use Pascal s Triangle to expand the expression. 9) ivide b using snthetic division. 0) Use snthetic substitution to evaluate the polnomial for. ) Graph the function.

19 lgebra : Midterm Final Review 0 0 x x x x 0 0 ) dd. Write our answer in standard form. ) For and, find. ) etermine whether the binomial ( ) is a factor of the polnomial. ( ) is not a factor of the polnomial. ( ) is a factor of the polnomial. annot determine. ) Factor. ( ) ( ) 9

20 lgebra : Midterm Final Review ) Identif all of the real roots of. 7) Write the simplest polnomial function with the zeros,, and. 0

21 lgebra : Midterm Final Review lgebra Midterm Review nswer Section MULTIPLE HOIE ) NS: REF: Page 9 OJ: -. Translating etween Methods of Set Notation ) NS: REF: Page OJ: -. Finding Inverses ) NS: REF: Page OJ: -. Identifing Properties of Real Numbers ) NS: REF: Page OJ: -. Rationalizing the enominator ) NS: REF: Page OJ: -. Simplifing Expressions ) NS: REF: Page OJ: -. Simplifing Expressions with Negative Exponents 7) NS: REF: Page OJ: -. Using Properties of Exponents to Simplif Expressions ) NS: REF: Page OJ: -. Simplifing Expressions Involving Scientific Notation 9) NS: REF: Page OJ: -7. pplication ) NS: REF: Page OJ: -. Recognizing Linear Functions ) NS: REF: Page OJ: -. Graphing Lines Using Slope and a Point ) NS: REF: Page OJ: -. Graphing Lines Using the Intercepts ) NS: REF: Page 7 OJ: -. Writing Equations of Lines ) NS: REF: Page 7 OJ: -. Graphing Functions in Slope-Intercept Form ) NS: REF: Page OJ: -. Graphing Vertical and Horizontal Lines ) NS: REF: Page 7 OJ: -. Solving and Graphing Linear Inequalities ) NS: REF: Page OJ: -. Translating and Reflecting Linear Functions 7) NS: REF: Page OJ: -. Solving bsolute-value Inequalities with isjunctions 9) NS: REF: Page OJ: -7. pplication 0) NS: REF: Page 9 OJ: -9. Translations of an bsolute-value Function ) NS: REF: Page OJ: -. lassifing Linear Sstems ) NS: REF: Page OJ: -. pplication ) NS: REF: Page 0 OJ: -. Graphing a Feasible Region ) NS: REF: Page OJ: -. Graphing Linear Equations in Three imensions ) NS: ) NS: REF: Page 99 OJ: -. Graphing Sstems of Inequalities 7) NS: ) NS: REF: Page OJ: -. Verifing Solutions of Linear Sstems 9) NS: REF: Page 9 OJ: -. Solving Linear Sstems b Elimination 0) NS: REF: Page OJ: -. lassifing Sstems with Infinitel Man Solutions or No Solution ) NS: REF: Page OJ: -. Simplifing Matrix Expressions ) NS: REF: Page OJ: -. Identifing Matrix Products ) NS: REF: Page OJ: -. Finding the Matrix Product ) NS: REF: Page OJ: -. Finding Powers of Square Matrices ) NS: REF: Page 70 OJ: -. Finding the eterminant of a x Matrix ) NS: REF: Page 7 OJ: -. Finding the eterminant of a x Matrix

22 lgebra : Midterm Final Review 7) NS: REF: Page 79 OJ: -. Finding the Inverse of a x Matrix ) NS: REF: Page 0 OJ: -. Solving Sstems Using Inverse Matrices 9) NS: REF: Page OJ: -. Graphing Quadratic Functions Using a Table 0) NS: REF: Page OJ: -. Translating Quadratic Functions ) NS: REF: Page OJ: -. Writing Transformed Quadratic Functions ) NS: REF: Page OJ: -. Solving a Quadratic Equation b ompleting the Square ) NS: REF: Page OJ: -. Writing a Quadratic Function in Vertex Form ) NS: REF: Page OJ: -. Solving a Quadratic Equation with Imaginar Solutions ) NS: REF: Page OJ: -9. Graphing omplex Numbers ) NS: REF: Page 7 OJ: -. Writing a Quadratic Function from ata 7) NS: REF: Page 7 OJ: -. Quadratic Functions with omplex Zeros ) NS: REF: Page OJ: -. nalzing Quadratic Equations b Using the iscriminant 9) NS: 0) NS: REF: Page OJ: -7. Solving Quadratic Inequalities Using lgebra ) NS: REF: Page OJ: -9. Graphing omplex Numbers ) NS: REF: Page OJ: -9. etermining the bsolute Value of omplex Numbers ) NS: REF: Page OJ: -9. dding and Subtracting omplex Numbers ) NS: REF: Page OJ: -9. Multipling omplex Numbers ) NS: REF: Page 07 OJ: -. lassifing Polnomials ) NS: REF: Page OJ: -. Multipling a Monomial and a Polnomial 7) NS: REF: Page OJ: -. Expanding a Power of a inomial ) NS: REF: Page 7 OJ: -. Using Pascal s Triangle to Expand inomial Expressions 9) NS: REF: Page OJ: -. Using Snthetic ivision to ivide b a Linear inomial 0) NS: REF: Page OJ: -. Using Snthetic Substitution ) NS: REF: Page OJ: -7. Graphing Polnomial Functions ) NS: REF: Page 07 OJ: -. dding and Subtracting Polnomials ) NS: ) NS: REF: Page 0 OJ: -. etermining Whether a Linear inomial is a Factor ) NS: REF: Page OJ: -. Factoring b Grouping ) NS: REF: Page OJ: -. Identifing ll of the Real Roots of a Polnomial Equation 7) NS: REF: Page 7 OJ: -. Writing a Polnomial Function with omplex Zeros