Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through the points ( 5, 3) and (, 6)..3 3. Write a point-slope equation of the line passing through ( 1, 8) and (, 6). In questions though 8, simplif completel using the properties of eponents. Where applicable, rewrite our answer(s) using onl positive eponents. 3.. ( 7) 5. ( ) 3 9 6. 5 5 3 1 7. 3 3 3 7 8. ( ) 3 3 100 7
3.3 9. Graph. Then identif the domain and range: (a) = 3 (b) 1 = 3. 10. Graph: 5 = + 3. Identif the domain and range. In questions 11 and 1, evaluate.. 11. log515 1. ln e 5. 13. Write the equation 3 = 81 in logarithmic form. 1. Write the equation log15 5 = in eponential form. 3 5. 15. For the equation: = ( + 3) 1 a) Find the verte. b) Write an equation for the line of smmetr. c) Which wa does the graph open? d) Identif whether the graph has a maimum or minimum value. e) What is the maimum or minimum value? f) Sketch the graph. g) Identif the domain and range.
5.3 16. Use the function = (3 + 1)( 1) What are the -intercepts of the function s graph? What are the coordinates of the graph s verte? 5.5 17. Solve using the quadratic formula: 3 7 0 + =0 18. Given: = 9 1+ a) Find the value of the discriminant. b) Determine the number of solutions. 7. 19. Graph: < 7.5 0. Graph: + 3 > 1 7 7.5 1. Write the sstem of inequalities defining the shaded region. 3
Calculator Round an decimal answers to the nearest hundredth..1. Identif the graph in which varies directl as. A B C D.1 3. For the equation = 5, does var directl with? Answer es or no..1. Find the domain and range of the function f () = 8 + 5 for 3.. 5. The table below gives the number of hours a local baseball team spent on batting practice during each week and the number of hits the had in games that weekend. Number of hours Number of hits 0 3 5 5 7 8 10 10 a) Show that the data have a linear relationship b making a scatter plot and drawing a line of best fit. Find an equation of the line. b) Use our equation to predict the number of hits following a week when 0 hours were spent on batting practice..5 c) What is the coefficient of correlation?
.5 6. What tpe of relationship---positive, negative, or none---is shown b the scatter plot? 3.3 7. A medication is eliminated from a person s bloodstream at a rate of 10% per hour. Suppose a tablet contains 30 mg of medication. Write an equation for the amount of the medication in the bloodstream after hours. How man hours will it take for half the tablet to be eliminated? 8. A computer programmer earned a earl salar of $0,000 in 1990 and averaged a % raise each ear after that time. a) Find the doubling time for the programmer s salar. b) Calculate the programmer s salar in 1998. 3. 9. If $3900 is deposited in an account at the bank and earns 6% annual interest, compounded continuousl, what is the amount in the account after ears? 3.5 30. In one state, the Real Estate Board estimates that the median cost of housing will increase eponentiall according to the data in this table. Years since 1990 Median cost (in dollars) 0 77,000 1 79,000 83,000 3 90,000 99,000 a) Enter the data into a graphing calculator and perform an eponential regression. What equation do ou get? b) Estimate the median cost of housing in the ear 005 using our equation for part a. 5
.1 31. Graph = + 5 and its inverse in the same coordinate plane, then find an equation for the inverse..3 3. Epress in terms of logarithms of,, and z: log a 5 z 33. Epress in terms of logarithms of m, n, and h: 6 3 log a mnh In questions 3 and 35, write as a single logarithm..3 3. 7log + 5log b 1 35. log log 6 p 3 b p. 36. Evaluate log 5 130 In questions 37 through 0, solve.. 37. log ( + 6) log = 38. 3e = 5. 7 5.1 39. 3 = 36 0. 5= 93 5. 1. Write an equation in verte form for a parabola that has verte (3, ) and passes through the point (1, ). 6
5.3. Write an equation for the parabola shown. (3, 6) (1, 0) (5, 0) In questions 3 and, write in verte form. 5. 3. = + + 1.. = 3 6+ 1. 5. 5. The equation h= 16t + 0t+ 5 gives the height h, in feet, of a baseball as a function of time, t, in seconds, after it is hit. What is the maimum height the baseball reaches? 5. 6. Find the maimum value or minimum value for the function: f ( ) = + 6+ 5. 5.6 7. Given: = 10 17 0. Write the quadratic function as a product of factors. 5.6 8. Solve using factoring: + 5= 0. 5.5 9. Find the intercepts of the graph of = 13+ 36. 7
In questions 50 and 51, use a graphing calculator to solve each sstem. (The graphs of the equations ma intersect more than once.) 7.1 50. = 3 ( ) = 9 5 51. = = 3 1 In questions 5-5, solve each sstem algebraicall. 7.1 5. = = + 7.-3 53. = 1 + = 7.-3 5. = 8= Formulas Note: Onl a list of formulas will be given to ou on the final. You must appl the correct formula to the correct problem. 1 1 = 1 + a( 1 ) = ab = a + b b ac = a( p)( q) = a( h) + k = a + b + c ± a b b ac b a A = Pe rt r A= P 1+ n nt 8