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Name: _________________________________________ Hour: ___________ Algebra 1 Review Final Exam 1. Define the following words and given example of each. a. Rational b. Irrational c. Integer d. Whole e. Natural 2. What is the value of x? π₯ 9 = 16 4 Solution: x = 36 3. Solve. 4(π₯ + 2) β π₯ = 29 Solution: x=7 4. What is the slope of the linear function? 2 Slope: m = 3 5. Simplify. 3(2π₯ β 4π¦ + 2) β (2π₯ + 4π¦ β 5) Solution: 4x β 16y + 11 6. Given the following equation, solve for y. βπ₯ + 2π¦ = 6 Solution: 1 y =2π₯ + 3 7. Identify the equation of the graph shown. Equation: y = 2x OR y = 2x + 0 8. The cost of tuition at Meramec Community College is $195.00 per credit hour. Each student also has to pay $75.00 in fees. Model the cost, C, for x amount of credit hours taken. Equation: C = 195x + 75 9. Find the rate of change represented in the given graph. Rate of Change: 40 mph 10. What is the y β intercept of the given graph? (Remember to write your answer as a point) Solution: (0, 6) 11. Graph the following equation. 5π₯ β 3π¦ = 12 12. On a family vacation Kaylaβs family traveled 620 miles in 10 hours. How far did they go in 4 hours? Solution: x = 248 miles 13. Simplify. 4(2π₯ β 3π¦ + 5π§) + 3(6π₯ β π¦ β 4π§) Solution: 26x β 15y + 8z 14. Solve for x. 6(π₯ + 4) = 2π₯ + 36 Solution: x = 3 15. Solve for x. β5π₯ + 12 = 47 Solution: x = -7 16. Write an equation for the line that passes through points A and D. Equation: 2 8 π¦ = 7π₯ β 7 17. Jason works in a factory and makes $11.15 per hour. He does this for 12 weeks of the summer. He works about 28 hours each week. Estimate about how much money he will make this summer. Solution: $3746.40 18. Simplify the following expression. 3(π + 4) + 2(π β 7) Solution: 3m + 2n - 2 19. Estimate the value of the y intercept for the given graph. Y- Intercept: about (0, 2.7) 1 20. Write an equation of a line that has a slope of β 4 and passes through the point (8 ,3). Equation: 1 π¦ = β4π₯ + 5 21. A golf driving range charges a fee of $23.00 to practice and then $2.25 for a bucket of balls. Write an equation in slope intercept form that models the charges C in terms of the number of bucket of balls b that you use. Equation: C = 2.25b + 23 22. Christopherβs weight is 15 pounds greater than his brotherβs. Together they weigh 315 pounds. Let x represent the weight of Christopherβs brother, write an equation that can be used to determine what each one weighs. Equation: Chris = 165 lbs Brother = 150 lbs 23. Simplify. 7β3 62 β24 Solution: 1 3 24. Make a table for the following equation. π¦ = 2π₯ + 3 Table: x Y -2 -1 -1 1 0 3 1 5 25. Use the following table to determine the Range when the Domain is 4. X Y 0 1 2 3 4 5 Range: When x = 4, y = 5 26. Solve and graph the inequality. 7π₯ + 4 β₯ 6π₯ β 8 Solution: π₯ β₯ β12 Graph: Closed circle on -12, shade to the right. 27. Label the slope and the y β intercept for the given equation. 2 π¦ = β5π₯ β 7 2 Slope: β 5 Y β Intercept: -7 28. Write the following equation in function notation. π¦ = 5π₯ + 2 Solution: f(x) = 5x+2 29. Solve the proportion. 2π₯+3 4 = 3π₯ 3 Solution: x = 1.5 30. Write an algebraic equation for the following sentence. Three times a number x plus fourteen is the same as twenty nine. Equation: 3x + 14 = 29 31. The table shows the number of people who have signed up to go to the renaissance field trip each day. How many people would you expect to sign up on day 5? Days People 1 32 2 38 3 44 4 50 Solution: 56 people 32. Using the provided graph, estimate the rental cost for 8 days. Solution: 240 Miles 33. Describe in words what the graph represents. Description: As gallons increase, cost increases.