MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Algebraic Concepts Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the inequality. ) - - 0x - -x - ) A) x > -0 B) x < -0 C) x 0 D) x 0 ) -5x - 9-3(4x - ) ) A) x -5 B) x < -5 C) x > -5 D) x -5 Solve the inequality and give the solution in interval notation. 3) -30r + 5-5(5r + ) 3) A) (4, ) B) (-, 4) C) (-, 4] D) [4, ) 4) 7x and 9x - 4 < 9 4) A) [- 7, 5 9 ) B) [- 7, 3 9 ) C) (- 7, 5 9 ] D) (- 7, 3 9 ] Solve the inequality. -3(4 - x) 5) -4 < < 5 9 5) A) < x < 3 B) < x < 8 7 C) < x < 8 3 D) - 3 < x < 8 3 Solve the problem. 6) The water acidity in a pool is considered normal when the average ph reading of three daily measurements is greater than 7. and less than 7.8. If the first two ph reading are 7.5 and 7.85, find the range of ph values for the third reading that will result in the acidity level being normal. A) 6.5 < x < 8.3 B) 7.7 < x < 9.5 C) 7. < x < 7.8 D) 7. < x < 8.9 6) Solve the inequality and give the solution in interval notation. 7) 9x - 8 > 8 or -x ) A) [4, ) B) (4, ] C) (4, ) D) (-, ) Find the solution set for the equation. 8) 7m + = 6 8) A) {, - 4 } B) {- 4 7, 8 7 } C) {4 7, } D) 9) x = 5 9) A) {-, 6} B) {-6, 6} C) {-, } D) {-6, }

2 Find the solution set for the inequality. 0) 5m ) A) {m m 5 } B) {m m or m 5 } C) {m m - 5 or m 8 5 } D) {m - 5 m 8 5 } ) m ) A) {m m - or m 5} B) {m m - 5 or m } C) {m - 5 m } D) {m - m 5} Determine whether the given ordered pair is a solution to the given equation. ) (6, -5); 3x + 8xy - y = -37 ) A) yes B) no Determine if the relation illustrated is a function. Give the domain and range of the function or relation. 3) {(, -4), (-5, -3), (-5, 0), (4, 3), (0, 5)} 3) A) not a function B) function domain: {-4, -3, 0, 3, 5} domain: {, 4, -5, 0} range: {, 4, -5, 0} range: {-4, -3, 0, 3, 5} C) function domain: {-4, -3, 0, 3, 5} range: {, 4, -5, 0} D) not a function domain: {, 4, -5, 0} range: {-4, -3, 0, 3, 5} Determine whether the graph illustrated represents a function. Give the domain and range of the relation or function. 4) 4) A) function domain: range: {y y 3} C) not a function domain: {x x 3} range: B) function domain: {x x 3} range: D) not a function domain: range: {y y 3} Evaluate the function for the indicated value. 5) f(x) = x + ; find f(-3) 5) A) 3 B) -36 C) -3 D).73

3 6) f(x) = x + 7 ; find f(-4) 6) x3 + 7x A) - 4 B) C) D) Solve the problem. 7) The population of fruit flies, p, after n days from the first mating of ten flies is given by the function p(n) = 0.07x + 0.3x. Find the population of fruit flies after i) 0 days ii) 30 days A) i) 30 B) i) 6 C) i) 30 ii) 66 ii) 9 ii) 9 D) i) 6 ii) 66 7) Write the equation in standard form. 8) y + 5 = - (x - 9) 8) 5 A) x + 5y = 43 B) x + 5y = -7 C) x - 5y = -7 D) x - 5y = 43 Find the slope of the line through the given points. If the slope is undefined, so state. 9) (-7, -9) and (-7, 3) 9) A) 3 7 B) 6 7 C) 0 D) undefined Solve the inequality and give the solution in interval notation. 0) -5 -x - 5 < -3 0) A) (-5, -4] B) [4, 5) C) (4, 5] D) [-5, -4) Solve for k if the line through the two given points is to have the given slope. ) (, 4) and (4, k), m = 3 ) A) k = -7 B) k = 6 3 C) k = 7 D) k = Find the slope of the line. If the slope is undefined, so state. ) ) A) - B) C) D) - 3

4 Write the equation of the line. 3) 3) A) y = - 5 x + B) y = - 5 x - 7 C) y = - 5 x - 3 D) y = - 5 x Write the equation in slope-intercept form. 4) -3x + 5y = 5 4) A) y = x + 3 B) y = x - 5 C) y = 3 5 x + 3 D) y = 5 3 x - 5 Solve the problem. 5) If one point on a graph is (4, 4) and the slope of the line is - 4, write the equation of the line in 9 5) slope-intercept form. A) y = x B) y = x C) y = x - 3 D) y = 4 9 x Determine the slope and the y-intercept of the graph of the equation. 6) 8x - y = 6 6) A) m = - 4; (0, 8) B) m = ; (0, ) C) m = 4; (0, -8) D) m = 8; (0, 6) 4 Given the graph of an equation of the form y = mx + b, what can be said about m and b? 7) 7) A) m > 0, b < 0 B) m > 0, b > 0 C) m < 0, b > 0 D) m < 0, b < 0 4

5 Two points on L and two points on L are given. Determine whether L is parallel to L, L is perpendicular to L, or neither. 8) L: (, ), (3, 0); L: (3, -), (5, -) 8) A) parallel B) perpendicular C) neither Determine whether the two given lines are parallel, perpendicular, or neither. 9) 3x = 5y + 0 y = 3 5 x - 9) A) parallel B) perpendicular C) neither Find the equation of a line with the properties given. Write the equation in the form indicated. 30) Passing through (3, 5) and perpendicular to the line whose equation is -7x + y = 6; slope-intercept form A) y = - 7 x B) y = - 7x - 38 C) y = - 7 x D) y = 7 x ) Find the requested value. 3) f(x) = 4x + 3x -, g(x) = x - 7 Find f() + g(). A) 4 B) C) -5 D) 7 3) 3) f(x) = x - 4, g(x) = -x + 3x - 5 Find (f g)(). A) -6 B) -50 C) 78 D) -78 3) 5

6 Graph the inequality. 33) x + 3y 6 33) A) B) C) D) Find the solution to the system of equations by substitution. 34) x + 4y = 7-3x - y = - A) (0, 0) B) (7, 0) C) infinite number of solutions D) no solution 34) Solve the system of equations using the addition method. 35) 3x + y = 0 35) x + 5 y = 3 A) (, 5) B) (0, 5) C) (-, 6) D) no solution 36) 3x + 5y + z = 5x - y - z = 33 5x + y + 3z = A) (5, -, -4) B) (-, 5, -4) C) (-4, -, 5) D) (5, -4, -) 36) 6

7 Solve the problem. 37) Mr. Alexander earns a weekly salary plus a commission from his position as a salesman. One week his total compensation on sales of $4000 was $640. The next week his total compensation on sales of $3000 was $600. Find Mr. Alexander's weekly salary and his commission rate. A) weekly salary: $480 B) weekly salary: $400 commission rate: 4% commission rate: 4.8% C) weekly salary: $470 commission rate: 5% D) weekly salary: $490 commission rate: 3% 38) A twin-engined aircraft can fly 6 miles from city A to city B in 3 hours with the wind and make the return trip in 6 hours against the wind. What is the speed of the wind? A) 85 mph B) 34 mph C) 68 mph D) 5 mph 37) 38) Find the domain of. x ) x - 8 A) 8 B) 5 8 C) 9, -9 D) 9 39) 40) x - 5 x - 5x - 7 A) -5, -, 7, 5 B) - 7, C) -5, 5 D) -, 7 40) Solve the equation and check your solution. 4) x 3 - x 8 = 4 4) A) 4 B) C) 96 5 D) 3 4) 7 x = 7 - x 4) A) 7 7 B) 7 6 C) 4 D) 3 Write the expression in exponential form. Assume that all variables represent positive real numbers. 43) 9 x + 5y 43) A) (x + 5y)/9 B) (x + 5y)3 C) (x + 5y)/3 D) ( 3 x y)/3 Write the expression in radical form. Assume that all variables represent positive real numbers. 44) 6xy3 5/3 A) x y3 3 B) 5 6x y3 3 C) 3 6x y3 5 D) 3 x y3 5 44) 7

8 Simplify the radical expression. Write the answer in radical form when appropriate. 45) 4 x 3yz ) A) x30yz50 B) x3y0z5 C) x30y0z5 D) x30y0z50 Simplify. 46) ) A) B) C) D) ) ) A) -3 3 B) -5 3 C) -5 4 D) ) x 3 64x4y - x3 3 xy + 9x 3 x7y 48) A) x3 3 xy B) -6x3 3 xy C) 3x3 3 xy D) x3 3 y 49) 5( ) 49) A) B) C) D) 30 50) ) A) 30 B) 50 C) 30 D) 60 5) ( 0 + )( 0 - ) 5) A) 8 B) 0-0 C) D) 0-5) 3 xy 3 4x0y 5) A) x4y5 3 xy B) 4x3y4 3 xy C) x3y4 3 xy D) x3y4 3 xy Simplify by rationalizing the denominator. 6 53) ) A) B) C) D) ) x - 0 x ) A) x - 6 x x - 6 B) x - 6x - 0 x x - 6 C) D) 6x + 0 x

9 Solve and check your solution(s). If the equation has no real solution, so state. 55) x x = 0 55) A) - 9 B) 9 C) - 9 D) 9 Solve. You will have to square both sides of the equation twice to eliminate all radicals. 56) x + 5 = 3 + x - 56) A) -, 38 B) -38, - C), 38 D) no real solution 57) x x = 4 57) A) 0 B), - C) - D) no real solution Add or subtract. 58) (3-3i) + ( - 7i) + (4 + 5i) 58) A) - 5i B) 5-0i C) 9-5i D) 5 + 9i Multiply. Write the result in the form a + bi. 59) (3 + 8i)(8 + 7i) 59) A) 56i + 85i + 4 B) i C) i D) -3-85i Divide. 60) 7-30i 5 - i A) 5-4i B) i C) 5 + 4i D) -4-5i 60) Evaluate. 6) i38 6) A) i B) - C) D) -i Use the square root property to solve the equation. 6) 7x + = 77 6) A) ± 6 B) ±5 C) 88.5 D) 5 63) (4x + 3) = 0 63) A) 3 ± 0 4 B) - 3 4, 7 4 C) 0 ± 3 4 D) -3 ± ) x - = ) A), - B), - C), -4 D) 4, - Solve the equation by completing the square. 65) x + 4x - 9 = 0 65) A) + 3 B) - ± 3 C) - ± 3 D) - ± 3 9

10 66) 5x - x - 5 = 0 66) A) ± 6 5 B) - ± 6 5 C) -5, 7 5 D) 5 ± 6 5 Solve the equation by the quadratic formula. 67) x 6 + x + 8 = 0 67) A) -8 ± B) C) 8 ± 4 D) 8 + Write an equation that has the given solutions. 68) -4, -3 68) A) x - 7x + = 0 B) x + 7x + = 0 C) x + x - 7 = 0 D) x - x - 7 = 0 Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real solution. 69) 7x = x ) A) two real solutions B) no real solution C) one real solution 70) x + 7x + 6 = 0 70) A) no real solution B) two real solutions C) one real solution Solve the equation. 7) (4x - 6) - 4(4x - 6) - 5 = 0 7) A) - 7 4, B) , - C) - 4 6, 7 D) 4 4, 5 4 7) x4-3x - 54 = 0 7) A) -9, 6 B) ±3 C) ±3, ± i 6 D) 3, i 6 73) x - 3 x - 70 = 0 73) A) 49 4, 00 B) 0 C) 7, 0 D) 00 74) x/3 - x/3-3 = 0 74) A) -3, B) -, 7 C) -, 3 D) -7, 75) 30x- + x- - = 0 75) A) 6, - 5 B) -6, 5 C) - 6, 5 D) 6, -5 Find the vertex and axis of symmetry of the graph of the function. 76) f(x) = x + 8x + 76) A) vertex: (-4, 5); x = -4 B) vertex: (5, -4); x = 5 C) vertex: (5, -6); x = 5 D) vertex: (-5, 4); x = -5 0

11 Determine whether the parabola opens upward or downward. 77) y = -x + x ) A) upward B) downward For the given functions f and g, find the indicated composition. 78) f(x) = 3x + 3, g(x) = 5x - (f g)(x) A) 5x + B) 5x + 64 C) 5x + 0 D) 5x ) For the given functions f and g, find the indicated value. 79) f(x) = x + 6x, g(x) = x + (g f)(4) A) 44 B) 4 C) 7 D) 40 79) Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. 80) f(x) = x ) A) one-to-one function; f-(x) = 3 x - 6 B) one-to-one function; f-(x) = 3 x - 6 C) one-to-one function; f-(x) = 3 x + 6 D) not a one-to-one function Graph the function. 8) f(x) = 3-x 8) A) B) C) D)

12 Write the equation in logarithmic form. 8) 343/3 = 7 8) A) log 7 3 = 343 B) log = 7 C) log = 7 D) log = 3 Write the equation in exponential form. 83) log = - 83) 4 6 A) 4 = 6 B) 4 6 = C) 4 - = 6 D) 6 = 4 Find the unknown value. 84) log 9 8 = y 84) A) B) -9 C) 9 D) - 85) log 3 x = 85) A) 5 B) 9 C) 8 D) 6 86) log a 64 = 86) A) 8 B) - 8 C) -8 D) 8 Evaluate. 87) log A) 000 B) 30 C) 3 D) -3 87) 88) log 0 00 A) B) 0 C) - D) 00 88)

13 Graph the function. 89) y = log 5 x 89) A) B) C) D) 3

14 90) y = log /5 x 90) A) B) C) D) Use properties of logarithms to expand the logarithmic expression as much as possible. 9) loga x 4 3 x + 5 (x -) 9) A) 4 loga x - 3 loga (x + 5) - loga ( x - ) B) loga x4 + loga (x + 5)-3 - loga (x - ) C) 4 loga x + 3 log a (x + 5) - loga (x - ) D) loga x4 + loga (x + 5)/3 - loga (x - ) Write as a logarithm of a single expression. 9) 3 log log 5 (r - 7) - log 5 r 9) A) log5 3r - 4r B) log5 3 4 r - 7 r C) log5 7r - 7 4r D) log5 7 7 r - 7 r 4

15 Evaluate. 93) 7 log log ) A) 5 log 5 9 B) 56 log 56 0 C) 67 D) 9 Find the common logarithm of the number. Round answer to four decimal places. 94) log ) A) B) C) -.8 D) Find the number N. Round N to six decimal places. 95) log N = ) A) B) C) D) Solve the equation without using a calculator. 96) 4 (3x - 7 ) = 6 96) A) -3 B) 4 C) 4 D) 3 97) 3 -x = 9 97) A) 3 B) - C) D) Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. 98) log x = -3 98) A) 6 B) 8 C) 8 D) -8 99) log 5 x = 3 99) A) 5 B) 5 C) 5 D) 5 00) log (-8-3x) = 00) A) 4 B) - 4 C) -4 D) 4 0) log 9 (5x - 3) = log 9 (3x + 7) 0) A) 5 B) 4 C) D) no solution 0) log ( + x) - log (x - 3) = log 0) A) 8 B) -8 C) 3 D) no solution 5

16 Find the value of N. Round to three decimal places. 03) ln N = ) A) 8.77 B) 0.4 C) D) 0.73 Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. Write the answer rounded to the nearest ten-thousandth. 04) log ) A) B) C).806 D).5 Solve the equation. 05) ln x + ln (x - ) = ln 05) A) 3 B) C), - D) - 6

17 Algebraic Concepts Final Review Answers. ) D ) A 3) D 4) B 5) B 6) A 7) D 8) C 9) A 0) B ) C ) B 3) D 4) A 5) A 6) A 7) A 8) B 9) D 0) C ) C ) C 3) C 4) C 5) B 6) C 7) D 8) B 9) A 30) C 3) D 3) A 33) C 34) C 35) C 36) A 37) A 38) D 39) C 40) D 4) C 4) C 43) A 44) C 45) D 46) A 47) B 48) A 49) B 50) D 5) A 5) D 53) C 54) B 55) B 56) C 57) C 58) C 59) C 60) A 6) B 6) B 63) D 64) A 65) C 66) A 67) A 68) B 69) B 70) B 7) D 7) C 73) D 74) B 75) D 76) A 77) B 78) C 79) B 80) B 8) A 8) D 83) C 84) D 85) B 86) A 87) D 88) C 89) D 90) A 9) C 9) D 93) D 94) A 95) A 96) D 97) C 98) C 99) B 00) C 0) A 0) A 03) D 04) C 05) B