SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Honors Algebra 1 Semester 2 Final Exam Review Packet Name Date Period SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the equation. 1) 27x = 81 1) 2) (x + )2 = 17 2) ) 2(x - 7 ) = 4 ) Perform the indicated operation. If possible, simplify your answer. 4) x + - 2x 5x x + 6 4) 5) 6 - x x - - 2x x 5) 6) x2-2x x2-9x + 20 x - 5 x2 + x 2x x2-7x ) 7) x2 + 5x + 6 x2 + 7x + 10 x2 + x x2 + 9x ) Solve the problem. 8) A stocker at a grocery store has created a display of stacked cans such that the top row contains 4 cans, the second row contains 7 cans, the third row contains 10 cans, and so on for six rows. Write the finite series of this sequence, and find the total number of cans in the display. 8) 9) Doctors predict that by administering a vaccine, the number of new cases of a certain childhood disease will decrease by half each year. If 800 people were afflicted with the disease in 2000, estimate the number of new cases in (Round to the nearest whole number, if necessary.) 9) 10) Find the midpoint of the line segment whose endpoints are 1, - 7 5, 1, 5. 10) 11) Police use the formula s = 0fd to estimate the speed s of a car in miles per hour, where d is the distance in feet that the car skidded and f is the coefficient of friction. If the coefficient of friction on a certain dry road is 0.82 and a car was traveling on it at a rate of 70 mph, how far will the car skid? (Round to the nearest foot.) 11) 12) Find the midpoint of the line segment whose endpoints are (4, 5), (-7, -9). 12) 1

2 1) Find the distance between the points (-7, 7) and (6, -2). 1) 14) A lecture hall has 15 rows with 1 seats in the first row, 17 seats in the second row, 21 seats in the third row, and so on. Deisgn an equation that represents the sequence whose terms correspond to the seats in each row. Find the number of seats in the seventh row. 14) 15) If R(x) = x5 + 6x4 + 2x - 8, use the remainder theorem to find R(-2). 15) Solve. 16) The profit that the vendor makes per day by selling x soft drinks is given by the function P(x) = x2 +.2x Find the number of soft drinks that must be sold to maximize profit. 16) 17) When an object is dropped to the ground from a height of h meters, the time it takes for the h object to reach the ground is given by the equation t =, where t is measured in 4.9 seconds. If an object hits the ground after falling for 7 seconds, find the height from which the object was dropped. 17) 18) One pump can drain a pool in 7 minutes. When a second pump is also used, the pool only takes 5 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use? 18) 19) 12x - 7 = x ) 20) Mark and Rachel both work for Smith Landscaping Company. Mark can finish a planting job in hours, while it takes Rachel 4 hours to finish the same job. If Mark and Rachel will work together on the job, and the cost of labor is $40 per hour, what should the labor estimate be? (Round to the nearest cent, if necessary.) 20) 21) Khang borrows $6250 at a rate of 10% compounded monthly. Find how much Khang owes at the end of 5 years. 21) Use: A = P 1 + r n nt. Round to two decimal places. 22) x = 0 22) 2) x = 18x ) 24) The cost in thousands of dollars for a company to manufacture x hundred laptop computers is given by the function C(x) = x2-0x Find the number of laptop computers that must be produced to minimize the cost. 24) 2

3 Simplify the complex fraction. 25) x2 + 8x + 15 x2 + 9x + 18 x2 + 5x x2 + 9x ) Divide. 26) (5xy6-15xyz2 + x2y2z) 5xy 26) Use radical notation to write the expression. Simplify if possible. 27) (6x)2/9 27) 28) / 28) Find the root. Use absolute value bars when necessary. 29) 8 (2xz)8 29) Find the domain of the rational function. x2-9 0) g(x) = x2-5x + 6 0) Graph the exponential function. 1) f(x) = 1 x ) Perform the indicated operations. Assume that all variables represent positive numbers. 2) 28x x 2) ) ( x - 19) 2 )

4 Find a general term an for the sequence whose first four terms are given. 4), 12, 21, 0,... 4) 5), 9, 27, 81,... 5) Use synthetic division to divide. 6) (2x + 6x2-16x + 20) (x + 5) 6) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function. Find the vertex, y-intercept, and x-intercepts (if any). 7) F(x) = x2-6x + 5 7) A) 0 B) vertex: (1, 2) x-intercept: (0, 0), y-intercept: (0, 5) 4

5 C) vertex: (1, 2) x-intercept: (5, 0), y-intercept: none D) vertex: (1, 2) x-intercept: none, y-intercept: (0, 5) E) vertex: (1, 2) x-intercept: none, y-intercept: (0, 5) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the indicated term of the sequence. 8) If the third term of a geometric progression is 5 and the fourth term is -20, find a1 and r. 8) 9) If the second term of an arithmetic progression is -4 and the eleventh term is 68, devlop a planand the fifteenth term. (*Be sure to show ALL work!*) 9) 5

6 40) Design a quadratic equation in vertex form such that the parent graph f(x)=x2 has been reflected across the x-axis and translated 5 units right and units down. 40) Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. 41) 5x-1/4(5x2 - x1/4) 41) 42) 22x1/4y7 x1/4 1/2 42) Solve the equation for x. 4 4) x - 1 x + 1 = 1 2x2 + 2x 4) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 44) 44) 49x 2 45) ) For the given functions f and g, find the composition. 46) f(x) = x - 4x; g(x) = -x Find (f g)(x). 46) Solve the equation by completing the square. 47) x2 + 12x = ) Find the vertex of the graph of the quadratic function. 48) f(x) = x2 + x ) Use the discriminant to determine the number and type of solutions of the equation. 49) 16x2-8x + 1 = 0 49) Use the quadratic formula to solve the equation. 50) 4x2 = -12x ) 6

7 51) Given the parent function f(x) = x2, describe the transformations that occur to result in the function g(x) = -x2 +14x (Hint: You can read transformations of a parent function best from vertex form.) 51) 52) Seven students ordered onion rings. The mean number of onion rings is 16. If the five number summary is 9, 11, 16, 21, 22, how many onion rings might each student have been served? 52) 5) Create a box plot from the given data set. 5) Population City (in millions) Chicago 2.90 Dallas 1.19 Detroit 0.95 Houston 1.95 Los Angeles.69 New York 8.01 Philadelphia 1.52 Phoenix 1.2 San Antonio 1.14 San Diego