Chapter 6 General Concepts Review PDF

Chapter 6 General Concepts Review 6.1 Directions: Multiply to obtain equivalent expressions. Simplify if possible. 𝑥−1 𝑥+2 2𝑥+1 𝑥+1 1) ⋅ ` 2) ⋅ 𝑥+1 𝑥+2 𝑥...

Chapter 6 General Concepts Review 6.1 Directions: Multiply to obtain equivalent expressions. Simplify if possible. 𝑥−1 𝑥+2 2𝑥+1 𝑥+1 1) ⋅ ` 2) ⋅ 𝑥+1 𝑥+2 𝑥 𝑥+1 𝑥 2 +6𝑥+8 𝑥+3 𝑢𝑣+7𝑣 2 3𝑢2 +6𝑢𝑣+3𝑣 2 3) ⋅ 4) ⋅ 𝑥 2 +4𝑥+3 𝑥+2 6𝑢+6𝑣 7𝑢2 +𝑢𝑣 Directions: Find the reciprocal. 𝑥+𝑦 1 5) 6) 3𝑎 + 𝑏 7) 𝑧 3+𝑦 2 Directions: Divide and simplify. 𝑥+6 𝑥+3 𝑦 2 +4𝑦+4 𝑦+2 8) ÷ 9) ÷ 𝑥+1 𝑥+2 𝑦 2 +6𝑦+9 𝑦+3 6.2 Directions: Add or subtract. Simplify if necessary. 5 3 3 8 10) + 11) + 𝑥 𝑥 𝑥+1 𝑥+1 4𝑥+3 2𝑥+1 3 5 12) − 13) + 𝑥+1 𝑥+1 2𝑥 𝑥 −3𝑧 2𝑧+1 6 3 14) − 15) + 1−𝑧 𝑧−1 5 𝑥 3𝑥 2 4 1 16) + 17) − 𝑥+2 𝑥+3 𝑥 𝑥+1 6.3 Directions: Simplify. 3 2− 1+2𝑥 −1 𝑎 18) 1 19) 5+ 3+𝑥 −1 𝑎 6.4 20) Divide 8𝑥 2 + 4𝑥 + 12 by 4𝑥 21) Divide 6𝑥 3 +2𝑥 2 + 8𝑥 by 2𝑥 22) Divide 2𝑥 2 + 3𝑥 + 5 by 𝑥 + 1 23) Divide 𝑥 4 + 𝑥 3 + 𝑥 2 + 2𝑥 + 1 by 𝑥 + 1 24) Divide 𝑥 3 + 𝑥 + 1 by 𝑥 + 1 6.5 Directions: Use synthetic division to find the quotient and remainder. 2𝑥 3 −7𝑥 2 −11𝑥−20 2𝑥 3 +5𝑥 2 +5𝑥+6 25) 26) 𝑥−5 𝑥+2 2𝑥 4 −30𝑥 2 −2𝑥−1 𝑥 5 +𝑥 4 +𝑥 3 +𝑥 2 +𝑥+1 27) 28) 𝑥−4 𝑥+1 6.6 Directions: Solve. 1 2 2 3 29) = 30) = 𝑥 3 𝑥 𝑥−4 𝑥 5 3 31) = 32) 𝑥+ =4 𝑥−3 𝑥−3 𝑥 1 1 1 2 2𝑥−1 1 33) + = (𝑥−1)(𝑥−2) 34) + = 𝑥−1 𝑥−2 𝑥+4 𝑥 2 +2𝑥−8 𝑥−2 6.7 35) Sally can type one page in ten minutes. Tim can type one page in fifteen minutes. How long will it take them, working together, to type 100 pages? 36) A swimming pool has 2 input pipes, A and B. Pipe A can fill the pool in 2 days. Pipe B can fill the pool in 3 days. How long will it take to fill the pool using both pipes? 37) Gerome’s new tractor plows four times as fast as Luke’s old one. Working together they can plow Luke’s field in 4 hours. How long would it take Luke to plow his field working alone? 38) It takes two hours to drive between the towns of Potter and Germantown. It takes 8 hours to make the trip by bicycle. How long will it take for a car and bicycle to meet, starting at opposite towns at the same time? 39) Two canoeists paddle 10 km upstream in 5 hours. They make the return trip in only 1 hour. Assuming that the canoeists paddle at a constant rate, what is the speed of the current? 6.8 40) The volume V of a pyramid with a square base of length L and altitude H is given by: 1 2 𝑉= 𝐿𝐻 3 Solve for H. 41) If an initial amount P is invested at annual interest rate R, then the amount F after one year is given by the formula: 𝐹 = 𝑃(1 + 𝑟) If an amount of $120 is invested and grows to $138 after one year, what is the interest rate? 6.9 42) The length of a spring varies directly as the force applied to it. When the spring is stretched 4 inches, the force is 8 pounds. Find the constant of variation and the equation of variation. 43) The voltage V, in volts, in an electrical circuit varies inversely as the resistance R, in ohms. The voltage in the circuit is 12 volts when the resistance is 240 ohms. Find the equation of variation. 44) The cost C, in cents, of lighting a 100-watt light bulb varies directly as the time t, in hours, that the light is on. The cost of using the light for 1000 hours is 15 cents. Write the equation of variation. Determine the cost of using the light for 2400 hours. 45) The time t required to harvest the potato crop varies inversely as the number n of people on the job. It takes 8 hours for 10 people to do the job. How long will it take for 36 people to do the job?