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Math 116 Practice Midterm Exam IIb READ THE QUESTIONS CAREFULLY. SHOW ALL YOUR WORK: A WRONG ANSWER WITH GOOD WORK IS WORTH POINTS. A RIGHT ANSWER WITH NO WORK IS WORTH ZERO. PUT A BOX AROUND YOUR FINAL ANSWER. 1. Multiply the following expressions, as indicated: (2x•5x2 )•4y ; ((x2 •3y 2 )2 )•(2x3y4z) ; (3x3 •4y 2 •5z)(x−3 y −2 z −1 ) 2. Add or subtract the following polynomial expressions, as indicated: (5x2 + 8x) − (2x2 − 8) ; (3x3 + 4x2 − 8x − 3) + (2x3 − 2x2 + 6x + 4) 3. Multiply the binomials: (a) (x + 3)(2x − 5); (b) (3x + 4)(3x − 4) 1 4. Divide the polynomials as indicated: (12x3 − 28x2 − 30x − 4)÷(6x + 4) 5. Write an algebraic formula for the price of a cab ride, by deﬁning terms and changing the following description into algebraic symbols: ”The price of a cab ride is calculated by a base rate of ﬁfteen dollars, and adding thirty-ﬁve cents for each mile traveled.” Use your formula to calculate the cost of a sixty-three mile cab ride. 6. Solve for x: 3(x − 3) = −7(x + 4) + 41 ; 16 120 2 = 48 x 4(x − 3) − 5x ≥ −2 7. Solve using algebra: Two trucks leave a cafe driving in opposite directions on a freeway across Kansas. One truck goes two mph faster than the other one. After four hours, they are 424 miles apart. What was the average speed of each truck? 8. If y varies directly with x, and y = 8 when x = 5, ﬁnd y when x = 15. 9. Write the following description as an algebraic formula: ”In a circuit with current K, external resistance U, internal resistance u, and voltage B, current is equal to voltage divided by the sum of resistance and internal resistance.” Now, rearrange the formula so it gives the value of external resistance instead of current. 3 10. If y varies inversely as x, and y = 13 when x = 3, ﬁnd y when x = 6. 11. Write a formula that represents the statement: ”c varies directly with the product of n and x and inversely with g.” 12. The design of a circuit speciﬁes that the voltage cannot exceed 44 volts. If the resistance of the circuit is 8 ohms, ﬁnd the range of values that the current, in amps, can have. Use the formula voltage = current times × resistance. 13. Write the ratio as a fraction in lowest terms: 28 minutes to 4 hours 4 14. In a recent year a baseball team paid nine times as much to their ace pitcher as they paid to their shortstop. If they paid $ 20 million for the two salaries, what did they pay each player? 15. Solve and show your answer in algebraic notation: 2y − 12 ≤ 8y − 4 Solutions: 1. 40x3 y; 216x5 y 5 z; 2. 3x2 + 8x + 8; 60; 5x3 + 2x2 − 2x + 1 3. (a) 2x2 + x − 15; (b)9x2 − 16 4. 2x2 − 6x − 1 5. Let C =The price of a cab ride in dollars, and M = the number of miles travelled in the cab. Then C = 15 + 0.35M A sixty-three mile ride would cost $37.05. 5 6. x = 11 5 = 2.2; x = 360 x ≤ −10 7. Let r =the average speed of the slower truck. Then, (4r) + 4(r + 2) = 424 The slower truck averages 52 mph, and the faster truck averages 54 mph. 8. k = 58 ; y = 24 when x = 15 B−Kµ B 9. K = U +µ ; U = K 10. y = 13 2 11. c = knx g 12. maximum current = 13. 44 8 = 5.5 amps 7 60 14. The ace pitcher was paid $18 million, and the shortstop was paid $2 million. 15. y ≤ 4 3 6