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1 1. Find the product, if possible. AB, if A = 0 1, B = Find the equation of the parabola with vertex at the origin that passes through the point 4, b g and opens to the left. = x = x x = x = 3. he number of bacteria present in a culture is B = 0e t where t is the time in minutes. Find the time required, to the nearest half minute, to have 1600 bacteria present min 14.0 min 14.5 min 13.0 min 4. A group of 95 people attend a ball game. here were four times as man children as adults in the group. Set up a sstem of equations that represents the numbers of adults and children that attended the game and solve the sstem to find the number of children that were in the group. R S a + c = 95 c = 4a 76 children R S a + c = 95 c + 4a = children 5. Use snthetic division to find f 5 R S a + c = 95 c + 4a = children b g if f x x x x x x R S a + c = 95 c = 4a 19 children bg = , none of these 6. Find an equation that represents a circle. 11 6x + 4x 3 = 0 4x 11x = 0 3x 11x 6 6 = x 6 = 1 of 1

2 7. Solve for x. 1 = 4 6 x Find the partial fraction decomposition for the rational expression. x x x x x + 6 x x + 6 x 4 x x 4 x 6 b g that represents as a function of x. mb 9 gb 9gb 5 5gr l 9,, 3, 5q mb 9 gb 3gb 9 5gr mb 9, gb, 3, 5gb, 3, 9gb, 5, 3gr 9. Find a set of ordered pairs x,,,,,,,. Perform the sequence of row operations on the matrix. (a) Swap R and R. 1 (b) Replace R b R plus 3 times R. 1 (c) Replace R b R plus 5 times R of 1

3 11. he table shows the time spent researching the stock market each week and the percent gain for an investor. Research (h) Gain (%) a. Create a scatter plot of gain versus research and find the line of best fit. b. Estimate the percent gain from researching the stock market for 0 h. a. Gain (%) Stock Market Gains a. Gain (%) Stock Market Gains Research (h) Research (h) (b) 56% a. Gain (%) b. 61% Stock Market Gains Research (h) b. 61% none of these 1. Find the determinant of the matrix Evaluate the expression of 1

4 14. Find the slope-intercept form of the equation of the line through the point 4, 3, b g perpendicular to the graph of = 1. = 4 = 3 x = 4 x = Find x such that the points are collinear., 13,, x, 0, 17 b gb gb g Given the graph of a function fbg, x find the graph of fbg. x x x x x x 4 of 1

5 17. Find the equation that represents the graph. x x + = x + = 1 8 x = x = Evaluate the expression without using a calculator. ln 5 e 1 5e e 19. Find the domain and range of the function. fbg x = x 4 x b g g b g b g b g b 4 Domain: b, g; Range: b 4, g Domain:, ; Range: 4, Domain:, ; Range:, Domain:, ; Range:, 5 of 1

6 0. For the graph of the quadratic function, find the direction of the opening and the coordinates of the vertex. fbg x = bx + g + 5 Downward;, 5 Upward;, 5 b g Downward; b, 5g b g Upward; b, 5g 1. Evaluate the function at the specified value(s) of the independent variable and simplif. fbg x = 4x 6x ; f 4 b g Find the conic section represented b the equation 9x = Hperbola Ellipse Circle Parabola 3. Use the Horizontal and Vertical ine ests to determine which of the following is a function that has an inverse. (i) (ii) x x (iii) (iv) x x ii and iv onl i, ii, and iv onl iv onl i and iv onl 6 of 1

7 4. Find the function that represents the graph. x f x bg R = S bg R = S f x 3, x 1 x 3, x < 1 3, x 1 x 3, x > 1 bg R = S bg R = S f x f x 3, x 1 x 3, x > 1 3, x 1 x 3, x < 1 bg = 5. et f x 4x 4. Find the graph of f and f 1. x x x x 7 of 1

8 6. Find a polnomial function that has zeros at 1,, and 1 and matches the graph below. 0 x 3 fbg x = x + x + x + fbg x = x x 1 3 fbg x = x x x + fbg x = x x 7. Use a graphing utilit to find an relative minimum or maximum values of the function. 3 fbg x = x 6x + 9x b g b, g b g b, g Relative minimum: 3, 1 Relative maximum: 1 7 Relative minimum: 1, Relative maximum: 3 8. Find all the zeros of the function. fbg x = 4x + 7x + 8 b g b, g b g b, g Relative minimum: 3, 3 Relative maximum: 1 5 Relative minimum: 3, Relative maximum: 1 7 ± 79i 8 7 ± 177 i 8 7 ± 177i 8 7 ± 79 i 8 9. Determine the domain of the function. f bg b x 1 g x = x 6 x + 4 b gb g All real numbers x 6, x 4 All real numbers x 4, x 6 All real numbers x 4, x 1, x 6 All real numbers 8 of 1

9 30. Evaluate the logarithm using the change-of-base formula. log Find the four real zeros of the polnomial. 4 3 fbg x = x + x + 36x + 56x + 3,, 4,,, 4,,, 4,,, 4, 3. Find the value of x. log 6 4x + 5 = 3 b g he table below shows the number of hours, H, spent per person plaing video games from 1995 to 000. et t represent the ear with t = 4 corresponding to Year Hours, H a. Find a linear model and determine its correlation coefficient. b. Find a quadratic model and determine its correlation coefficient. c. Use the correlation coefficient to determine which model best fits the data. a x ; b x x ; c. Quadratic model a x ; b x x ; c. inear model a x ; b x x ; c. inear model a x ; b x x ; c. Quadratic model 9 of 1

10 34. Find the graph of the sstem. Use the graph to determine if the sstem is consistent or inconsistent. If the sstem is consistent, determine the number of solutions. 3x = 3 R S 6x = 1 x x Consistent, infinitel man solutions Inconsistent x x Consistent, one solution Inconsistent 35. Find the vertical asmptote(s), if an, for f x bg = x 4x 4 5x 14. x =, x = 7 x =, x = 7, x = 6 x = 6, x = No vertical asmptotes 36. Solve the exponential equation algebraicall. 600 = e x of 1

11 37. Find the graph of the equation. x = x x x x 38. Evaluate the determinant Use the properties of logarithms to expand the expression. (Assume all variables are positive.) log b 3 x 4 z log x + z b b g log x + 15 log 1 log z b b b 3 4 logb x + logb logb z blog b xgblogb g 4 log z b 11 of 1

12 40. Divide and write the result in standard form. 9 i 7 + 4i i i Determine whether or not matrix B is the inverse of matrix A. A = 1 4 7, B = i i B is the inverse of A. B is not the inverse of A. AB = and BA = AB = 0 1 and BA = AB is not defined because the dimensions of A and B do not allow multiplication. B is not the inverse of A. BA is not defined because the dimensions of A and B do not allow multiplication. B is not the inverse of A. 4. ist the possible rational zeros of f, then use a graphing utilit to determine which of those are actual zeros of f. 3 fbg x = x + 8x + 11x 0 Possible zeros: ± 1, ±, ± 4, ± 5, ±, ± 0 Actual zeros: 4, 1, 5 Possible zeros: ± 1, ±, ± 4, ± 5, ±, ± 0 Actual zeros: 1, 4, 5 Possible zeros: ± 1, ±, ± 3, ± 4, ± 5, ±, ± 0 Actual zeros: 4, 1, 5 Possible zeros: ± 1, ±, ± 3, ± 4, ± 5, ±, ± 0 Actual zeros: 1, 4, 5 1 of 1

Algebra 2 End of Term Final REVIEW

Algebra 2 End of Term Final REVIEW 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