Algebra End of Term Final REVIEW DO NOT WRITE IN TEST BOOKLET. 1. Graph. a. c. x x x x. Express as a single logarithm. Simplif, if possible. a. 5 c. 3 3. The volume V of a clinder varies jointl with the height h and the radius squared r, and cm 3 when cm and cm. Find V when cm and cm. Round our answer to the nearest hundredth. a. cm 3 c. cm 3 cm 3 cm 3. Given and, find. 5. Use the Binomial Theorem to expand the binomial. a.
c.. Divide b using snthetic division. 7. Find the sum S for the geometric series 9 + 7 + 1 + 3 +... a.,0 c. 5909 3 5,71. Evaluate the piecewise function for and. a. ; c. ; ; ; 9. Given and, find. a. = c. = = =. Find the sum of the infinite geometric series 17 + 17 +..., if it exists. a. 1 c. The ratio diverges. 3 31. 11. Solve. a. x = 1 c. x = 1 x = 5 x = 5 1. Solve. 13. Rewrite the polnomial 5x 3 11x + x + x + x 5 + 19 in standard form. Then, identif the leading coefficient, degree, and number of terms. Name the polnomial. a. leading coefficient: ; degree: 5; number of terms: ; name: quintic polnomial leading coefficient: 19; degree: 0; number of terms: ; name: quintic polnomial c. leading coefficient: 19; degree: 0; number of terms: ; name: quintic polnomial leading coefficient: ; degree: 5; number of terms: ; name: quintic polnomial 1. Evaluate. If necessar, round our answer to the nearest tenth. a. c..3
1. 1 15. A bag contains hair ribbons for a spirit rall. The bag contains 3 black ribbons and 1 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probabilit that Lila selects a black ribbon and Jessica selects a green ribbon? Express our answer as a fraction in simplest form. a. 35 c. 5 11 70 35 1. Solve the equation. a. 3 5 c. 3 5 3 5 17. Find the product. 1. Let be a horizontal shift of units right. Write the rule for and graph the function. a. c. x x x x
19. A grab bag contains football cards and basketball cards. An experiment consists of taking one card out of the bag, replacing it, and then selecting another car What is the probabilit of selecting a football card and then a basketball card? Express our answer as a decimal. a. 0. c. 0.1 0.0 0.1 0. Write an equation in standard form for the ellipse shown with center (0, 0). Focus (0, 1) x (0, 13) 1. Write an equation in standard form for the hperbola with center, vertex, and focus.. Find the first 3 terms of the geometric sequence with and. a., 1, c., 1,,,,, 9 3. Solve the equation. a. x = 35 or x = c. x = 7 or x = 1 x = 35 x = 7. Find the 0th term in the arithmetic sequence, 1,, 17,,... a. 11 c. 1 170 171 5. Determine if the geometric series 3 + 9 + 7 + 1 +... converges or diverges. a. diverges converges
. Evaluate 1 b using mental math. a. c. 3 7 7. Use inverse operations to write the inverse of a. c. 5 9 9 5 9 9. Write the expression in radical form, and simplif. Round to the nearest whole number if necessar. a. ; 3 c. ; ; 1 ; 9. 9. Identif the conic section the equation represents. a. ellipse c. hperbola circle parabola 30. Find the 5th term of the arithmetic sequence with and. a. 1 c. 1 3 31. Find the geometric mean of and. a. 1 c. 1 3. Write in expanded form. 33. Write the exponential equation in logarithmic form. 3. Write the function in vertex form, and identif its vertex. a. ; c. ; vertex: (, ) vertex: (1, ) ; ; vertex: (, ) vertex: (1, ) 35. Solve the equation. 3. Graph the ellipse.
a. 1 c. 1 1 1 1 1 1 1 x (5, ) 1 1 1 1 x (5, ) 1 1 1 1 1 15 1 9 ( 5, ) 3 1 15 1 9 ( 5, ) 3 1 15 1 3 9 1 15 1 x 1 15 1 1 15 1 3 9 1 15 1 x 1 15 1 37. Determine whether the sequence,,, 1, 0,... appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. a. Yes; common difference ; next three terms are 1,, Not an arithmetic sequence c. Yes; common difference 7; next three terms are 7,, 1 Yes; common difference ; next 3 terms are,, 3. Using the graph of as a guide, describe the transformation and graph. a. Compress f horizontall b a factor of c. Stretch f verticall b a factor of 5 and translate it left units. and translate it down units.
x Stretch f verticall b a factor of 5 and translate it right units. x x Compress f horizontall b a factor of and translate it up units. x 39. Solve the equation. or or 0. Express as a single logarithm. Simplif, if possible. 7 3 1. Simplif. a. c. x. Classif the sstem, and determine the number of solutions. a. This sstem is consistent. It has infinitel man solutions. This sstem is inconsistent. It has infinitel man solutions. c. This sstem is inconsistent. It has no solutions. This sstem is consistent. It has one solution. 3. Find the center and radius of a circle that has a diameter with endpoints and.
a. center ; radius c. center ; radius 0 center ; radius 0 center ; radius. Write the equation of the line that is tangent to the circle at the point. a. = 3 x 5 c. = 3 x 5 5. Find the determinant of. a. 1 c. 0 1 00. Solve. Check our answer. a. c. There is no solution because the original equation is undefined at. 7. Use Cramer s rule to solve the sstem of equations. a. (1, 15) c. (, 30) ( 15, 1) (, ). Solve and graph. a. x 1 7 5 1 0 1 3 5 7 9 The inequalit has no solution. The solution set is the empt set. 7 5 c. The solution set is the set of all real numbers. 1 0 1 3 5 7 9 7 5 1 0 1 3 5 7 9 x 1 7 5 1 0 1 3 5 7 9 9. Find the inverse of the matrix, if it is define
50. Find the first 5 terms of the sequence. a. 9, 11, 15, 3, 39 c.,,, 9, 1 5,, 1, 9, 5 5,, 1, 1, 3 51. Add. 5. In slope-intercept form, write the equation of the line that is parallel to = x + 5 and passes through (, ). a. = x + 9 c. = 1 3 x 71 3 = x + = 1 3 x 3 53. There are 5 singers competing at a talent show. In how man different was can the singers appear? a. was c. was 5 was 0 was 5. Using the graph of as a guide, describe the transformation and graph. a. Translate down units. c. Translate right units. x x Translate left units. Translate up units.
9 3 x x 55. Expand the series and evaluate. a. 50 c. 0 5 5. Write the logarithmic equation in exponential form. 57. Find the 7th term of the geometric sequence with and. a. 13,1 c.,37,7 91 5. An experiment consists of rolling a number cube. What is the probabilit of rolling a number greater than? Express our answer as a fraction in simplest form. 59. Find the sum for the arithmetic series. a. 17 c. 193 19 3 0. Write the equation in standard form for the parabola with vertex and the directrix. 1. Simplif. Assume that all expressions are define
. The data {9,, 1, 1, 9} represent a random sample of the number of das absent from school for five students at Monta Vista High. Find the mean and the standard deviation of the data. a. The mean is 5., and the standard deviation is about 3.. The mean is 5., and the standard deviation is about 1.9. c. The mean is, and the standard deviation is about 13.3. The mean is 5., and the standard deviation is about 3.. 3. Write the equation of the circle with center and containing the point.. Find the minimum or maximum value of. Then state the domain and range of the function. a. The maximum value is. D: {x x 13 }; R: {all real numbers} The minimum value is 13. D: {all real numbers}; R: { 13} c. The maximum value is. D: {all real numbers}; R: { 13} The minimum value is 13. D: {x x 13 }; R: {all real numbers} 5. Write... as a fraction in simplest form. a. 93 00 c. 31 333 93 31 0 33
Algebra End of Term Final REVIEW Answer Section MULTIPLE CHOICE 1. ANS: B REF: Page 531 OBJ: 7-.1 Graphing Exponential Functions. ANS: A REF: Page 51 OBJ: 7-.1 Adding Logarithms 3. ANS: A REF: Page 570 OBJ: -1.3 Solving Joint Variation Problems. ANS: C REF: Page OBJ: 9-.3 Evaluating Composite Functions 5. ANS: D REF: Page 37 OBJ: 11-.1 Expanding Binomials. ANS: B REF: Page 3 OBJ: -3. Using Snthetic Division to Divide b a Linear Binomial 7. ANS: D REF: Page 93 OBJ: 1-.5 Finding the Sum of a Geometric Series. ANS: D REF: Page 3 OBJ: 9-. Evaluating a Piecewise Function 9. ANS: C REF: Page OBJ: 9-.1 Adding and Subtracting Functions. ANS: B REF: Page 901 OBJ: 1-5. Finding the Sums of Infinite Geometric Series 11. ANS: B REF: Page 5 OBJ: 7-5.1 Solving Exponential Equations 1. ANS: B REF: Page 53 OBJ: 7-5.3 Solving Logarithmic Equations 13. ANS: A REF: Page 07 OBJ: -1. Classifing Polnomials 1. ANS: C REF: Page 51 OBJ: 7-.5 Changing the Base of a Logarithm 15. ANS: D REF: Page 1 OBJ: 11-3. Finding the Probabilit of Dependent Events 1. ANS: D REF: Page 31 OBJ: 5-.1 Solving Equations b Using the Square Root Propert 17. ANS: C REF: Page 1 OBJ: -. Expanding a Power of a Binomial 1. ANS: D REF: Page 15 OBJ: -9.1 Translating Absolute-Value Functions 19. ANS: D REF: Page 11 OBJ: 11-3.1 Finding the Probabilit of Independent Events 0. ANS: A REF: Page 737 OBJ: -3. Using Standard Form to Write an Equation for an Ellipse 1. ANS: C REF: Page 75 OBJ: -. Writing Equations of Hperbolas. ANS: A 3. ANS: C REF: Page 15 OBJ: -. Solving Absolute-Value Equations. ANS: A REF: Page 0 OBJ: 1-3. Finding the nth Term Given an Arithmetic Sequence 5. ANS: A REF: Page 900 OBJ: 1-5.1 Finding Convergent or Divergent Series. ANS: A REF: Page 50 OBJ: 7-3.3 Evaluating Logarithms b Using Mental Math 7. ANS: B REF: Page 99 OBJ: 7-. Writing Inverse Functions b Using Inverse Operations. ANS: D REF: Page 1 OBJ: -.3 Writing Expressions in Radical Form 9. ANS: A REF: Page 70 OBJ: -.1 Identifing Conic Sections in Standard Form 30. ANS: D REF: Page 1 OBJ: 1-3. Finding the nth Term Given Two Terms 31. ANS: A REF: Page 9 OBJ: 1-. Finding Geometric Means 3. ANS: D REF: Page 3 OBJ: 1-5.1 Writing Exponential Expressions in Expanded Form 33. ANS: A REF: Page 505 OBJ: 7-3.1 Converting from Exponential to Logarithmic Form 3. ANS: B REF: Page 3 OBJ: 5-. Writing a Quadratic Function in Vertex Form 35. ANS: B REF: Page 351 OBJ: 5-5. Solving a Quadratic Equation with Imaginar Solutions 3. ANS: C REF: Page 73 OBJ: -3.3 Graphing Ellipses
37. ANS: D REF: Page 79 OBJ: 1-3.1 Identifing Arithmetic Sequences 3. ANS: B REF: Page 1 OBJ: -7.3 Appling Multiple Transformations 39. ANS: C REF: Page 00 OBJ: -5.1 Solving Rational Equations 0. ANS: B REF: Page 513 OBJ: 7-. Subtracting Logarithms 1. ANS: C REF: Page 53 OBJ: 7-. Simplifing Expressions with e or ln. ANS: A REF: Page 1 OBJ: 3-1.3 Classifing Linear Sstems 3. ANS: D REF: Page 75 OBJ: -1.3 Finding the Center and Radius of a Circle. ANS: B REF: Page 731 OBJ: -. Writing the Equation of a Tangent 5. ANS: A REF: Page 7 OBJ: -.3 Finding the Determinant of a 3 x 3 Matrix. ANS: C REF: Page 579 OBJ: -.5 Solving Simple Rational Equations 7. ANS: A REF: Page 71 OBJ: -. Using Cramer's Rule for Two Equations. ANS: B 9. ANS: A REF: Page 79 OBJ: -5. Finding the Inverse of a x Matrix 50. ANS: B REF: Page 3 OBJ: 1-1. Finding Terms of a Sequence b Using an Explicit Formula 51. ANS: C REF: Page 5 OBJ: -3.3 Adding Rational Expressions 5. ANS: B REF: Page 119 OBJ: -.5 Writing Equations of Parallel and Perpendicular Lines 53. ANS: C REF: Page 79 OBJ: 11-1. Finding Permutations 5. ANS: D REF: Page 59 OBJ: -.1 Transforming Rational Functions 55. ANS: D REF: Page 71 OBJ: 1-. Evaluating a Series 5. ANS: A REF: Page 50 OBJ: 7-3. Converting from Logarithmic to Exponential Form 57. ANS: C REF: Page 9 OBJ: 1-.3 Finding the nth Term Given Two Terms 5. ANS: D REF: Page 0 OBJ: 11-.1 Finding Theoretical Probabilit 59. ANS: C REF: Page OBJ: 1-3.5 Finding the Sum of an Arithmetic Series 0. ANS: B REF: Page 75 OBJ: -5. Writing Equations of Parabolas 1. ANS: A REF: Page 5 OBJ: -3.5 Simplifing Complex Fractions. ANS: A REF: Page 31 OBJ: 11-5. Finding the Mean and Standard Deviation 3. ANS: A REF: Page 730 OBJ: -. Writing the Equation of a Circle. ANS: B REF: Page 3 OBJ: 5-.3 Finding Minimum or Maximum Values 5. ANS: D REF: Page 90 OBJ: 1-5.3 Writing Repeating Decimals as Fractions