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ALGEBRA II FINAL EXAM REVIEW Name:____________________________________________ Date:___________________ Show all work! Possible 100 pts 1) (3pts) Given the sequence 6, 11, 18, 27, 38, 51 Determine the model (type and actual function) (2pts) Use 2) ( 2pts) Evaluate f(3). f(x) = 3x+1 x2 -3x+ 1, 3) ( 2pts) the model to determine the 20th term Simplify (3x-3)4 x<3 x≥3 f(3) = 4) (3pts) Simplify: 2a3b-4 -2ab -4 × (4b)4 20a 6 5) (3pts) Solve for x. 5-2⋅5x+5⋅53 = 52x 15 6) (3pts) Find the balance in an account if you deposit $10,000 paying 5.25% annual interest, compounded monthly after 5 years. 7) (3pts) Evaluate (64)2/3 (Show all steps) 8) Given f(x) = 2 x 1 4 State the Domain and Range (1 pt each) Domain: Range: 9) (3pts Solve the equation -2 + 2x - 3 = 5 11) (3pts) Solve for x. logx 27 = 3 10) (3pts Solve the equation 1 23 x - 5 = 27 2 12) (2pts) Is f(x) = 4-2t an example of exponential growth or decay? 19 1 13) Solve for x: log8 - log x = log1- log2 2 14) Evaluate log383 to three decimal places. (2 pts) (4 pts) 15) You deposit $8500 into an account that pays (4 pts 6.5% compounded quarterly. How long will it take for the balance to be $10,000? . 16) Graph the function, f(x) = (x + 3)2 - 2. List at least five ordered pairs, including the vertex. (4 pts) X Y 14 17) Given the following polynomial function, determine the left and right hand behaviors, possible number of turning points and possible number of zeros/solutions (1 pt each) P ( x ) x 4 4 x 3 x 2 12x 2 Right Hand Behavior Left Hand Behavior Possible number of turning points Possible number of solutions/zeros 18) Factor completely with respect to the integers. x3 - 2x2 - 9x + 18 19) 20) Factor completely the following polynomial 4 x 2 20x 24 (2 pts) 21) (3 pts) (3 pts) (2 pts) Find all real-number solutions. x3 + 2x2 - x - 2 = 0 Use synthetic division to evaluate the function. F(x) = x3 + 2x2 + 4x - 12 at x = -3 14 22) (3 pts) Write a polynomial whose graph has the given x-intercepts and has a leading coefficient of 1. (4, 0), (-3, 0), (2, 0) 24) (3 pts) Simplify x 2 - 2x - 35 x 2 - 49 26) (4 pts) Solve the equation. 2x - 9 x 5 + = x-7 2 x-7 23) (2 pts) One root of the equation is x = -3. Find the other roots 2x3 + 11x2 + 18x + 9 = 0 25) (3 pts) Perform the indicated operation and simplify. x 2 - x - 2 x 2 - 6x + 8 ¸ 3x 2 3x -12 27) (3 pts) Add and simplify. 2 3 + 2 3x 6x 18 28) Evaluate the six trig functions of the angle (lower right angle is 29) Given a right triangle ABC with m ) A= and b = 8, find the missing angle ( nearest whole (round to 4 decimal places) number) and the other two sides. 2 (nearest hundredth) 5 (1/2 pt each) Sin (1 pt each) = Csc Cos = Sec Tan = Cot = m A= a= = m B= 90 b= 8 = m C= c= 6 30) (2 pts) Convert the following degree 31) (2 pts) measure to radian measure : 32) Find the arc length and area of a sector if Convert the following radian measure to degrees. 33) Given the position ordered pair ( 4 , -3 ) find all six trig ratios: the radius = 4 inches and the central angle is (1 pt each) (2 pts each) Sin = Csc = Cos = Sec = Tan = Cot = Are Length: Area of Sector: 14