Review for Final Exam Math 124A (Flatley) Name Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x - 14 1) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Solve the linear equation. 2) 45 = 6x + 3 2) 3) -5x + 1 + 2x + 3 = 10 3) Write the inequality in interval notation and graph on a real number line. 4) -3 < x 1 4) 1
Translate the English statement into a mathematical statement. Do not solve. 5) Five times a number, decreased by 2 is 6 less than the number. 5) Determine whether the equation is a function. 6) y2 + x = 9 6) 7) x - 3y = 8 7) Solve the inequality. Graph the solution set and write it in interval notation. 8) -2(4x - 6) < -10x + 16 8) 2
9) 8x - 6 4x - 12 9) Solve for y. 10) 6x - 7y = 1 10) Solve. 11) A rectangular carpet has a perimeter of 270 inches. The length of the carpet is 89 inches more than the width. Find the dimensions of the carpet. 11) 12) A train leaves a town traveling at a speed of 20 miles per hour. Thirty minutes later another train, traveling at 60 miles per hour, leaves the same town in the same direction on a parallel track. How long will it take this train to catch up? 12) 3
Provide an appropriate response. 13) Plot the following ordered pairs in the same xy-plane. Tell in which quadrant or on what coordinate axis each point lies. A(2, -4), B(0, 1), C(-4, 0), D(3, 2), E(-2, -3), F(-1, 3) 13) 14) Determine whether the ordered pair is a point on the graph of the equation y = 2x2-16x + 30. a. (3, 5) b. (3, -5) c. (5, 5) 14) 4
Graph the equation by plotting points. 15) y = 2x + 8 15) 16) y = 5x2 16) 5
Graph the linear equation, using any appropriate method. 17) x - y = -5 17) 18) 8x + 3y = 0 18) 6
19) 6x - 7y = 42 19) 20) 1 5 x + 1 2 y = 1 20) 7
21) x = 3 21) Provide an appropriate response. 22) Find and interpret the slope of the line containing the points (-6, 14) and (10, 4). 22) 8
23) Draw a graph of the line that contains the point (2, 4) and has a slope of - 5. Do not find 6 23) the equation of the line. 24) Determine whether the graphs of the following pair of linear equations are parallel, perpendicular, or neither. 3x - 8y = -14 32x + 12y = -6 24) Find the equation of the line with the given properties. Express your answer in slope-intercept form. 25) Through the point (-2, 5) and having a slope of 4 25) 9
26) Through the points (1, -4) and (-7, 6). 26) 27) Parallel to 4x + y = 4 and through the point (2, -3) 27) Provide an appropriate response. 28) Determine whether (6, -1) is a solution to the linear inequality x + 2y > -6. 28) 10
Graph the linear inequality. 29) y 2x - 1 29) 30) 4x - 3y 0 30) 11
Find the domain of the function. 31) f(x) = 2x - 3 x + 6 31) 32) H(q) = 10q - 4 6 32) Find the zero of the linear function. 33) G(x) = -8x - 48 33) 12
Graph the linear function. 34) F(x) = -2x + 8 34) Solve the compound inequality. Express the solution using interval notation. Graph the solution set. 35) x 5 and x -3 35) 36) 12 < 3x 15 36) 13
37) -15-3c + 3 < -9 37) 38) 0 2x + 1 2 < 3 38) 39) 9x - 6 < 3x or -2x -6 39) Solve the absolute value equation. 40) x = 5 40) 14
41) x - 9 = 4 41) Solve the inequality. Graph the solution set, and state the solution set in interval notation. 42) x < 2 42) 43) 5k + 8 < -5 43) 44) x - 1 + 5 10 44) 15
Solve the system of equations by graphing. 45) 2y + 2 = 0 x - 3y = -1 45) Solve the system of equations using substitution. 46) x - 5y = -13 4x - 6y = -10 46) Solve the system of equations using elimination. 47) x - 7y = -24 3x - 8y = -33 47) 16
48) x + 3y = 6 5x + 3y = -18 48) Graph the system of linear inequalities. 49) y 2x + 2 x + y -2 49) Simplify the expression. 50) -110 50) 17
51) 2-4 51) 52) -2-3 52) 53) 55 5-6 53) Determine the coefficient and degree of the monomial. 54) 3 7 x 4 54) 18
Simplify the polynomial by adding or subtracting, as indicated. Express your answer as a single polynomial in standard form. 55) (4x + 4) + (6x - 17) 55) 56) (7x5 + 8x2) + (6x5-4x2) 56) Find the value of the polynomial function. 57) f(x) = 9x2 + 5x; f(4) 57) Find the product. 58) (2x6y5z)(-9x7yz3) 58) 19
Find the product of the two binomials. 59) (5x - 1)(x - 6) 59) 60) (x + 9y)(x - 3y) 60) 61) (-5x + 7y)(-3x - 8y) 61) Find the product of the polynomials. 62) (x + 10)(x2 + 5x - 6) 62) 20
Find the special product. 63) (y5-8)(y5 + 8) 63) 64) (4y + x)(4y - x) 64) 65) (x + 9)2 65) 66) (5x + 1)2 66) 21
Divide using long division. 67) p 2 + 4p - 12 p + 7 67) Divide using synthetic division. 68) 5m 3 + 22m2-45m + 18 m + 6 68) Use the Remainder Theorem to find the remainder. 69) f(x) = 3x3-6x2-4x + 17 is divided by x + 2 69) Factor out the greatest common factor. Be sure that the coefficient of the term of highest degree is positive. 70) 12x - 6 70) 22
71) 24x4 + 21x2 71) Factor by grouping. 72) 12(a + 6)2 + 10(a + 6) + 2 72) 73) 7y10-17y5-12 73) 74) 2y3 + 8y2-12y2-48y 74) 23
Factor the polynomial completely. If the polynomial cannot be factored, say it is prime. 75) x2 + 6x - 16 75) 76) x2 + 10x + 16 76) 77) x2 + 19x + 20 77) 78) x2 + 39x + 40 78) 24
79) a2-2a - 63 79) 80) 2x2 + x - 28 80) 81) 8x2 + 18x + 9 81) 82) 18z2-63z - 36 82) 25
83) 12x3y + 34x2y + 24xy 83) Factor completely, or state that the trinomial is prime. 84) x2 + 40x + 400 84) 85) 25x2-10x + 1 85) Factor the difference of two squares completely. 86) 16 - x2 86) 26
87) 36-49x2 87) 88) x4-100 88) 89) x2y2-4 89) 90) (x - 10)2 - y2 90) 27
Factor the polynomial completely. 91) x2 + 14x + 49 - y2 91) Factor the sum or difference of two cubes completely. 92) x3 + 64 92) Solve the problem. 93) Find the formula for the area of the shaded region and express it in factored form. 93) 9 y 9 y 28
Factor completely, or state that the polynomial is prime. 94) x8-1 94) 95) x2(a - b) + 49(b - a) 95) 96) x2(a - 4) + y2(4 - a) 96) State the domain of the rational expression. x + 4 97) x2 + 1 97) 29
98) 11x - 6 (x + 2)2 98) Simplify the rational expression. 99) y 2 + 3y - 10 y2-3y - 40 99) Multiply the rational expression. Express the product as a rational expression in lowest terms. x2 + 2x - 3 100) (x - 5) 100) x2-6x + 5 30
Divide the rational expression. Express the quotient as a rational expression in lowest terms. 101) (y - 9)2 11 11y - 99 121 101) 102) y2 + 5y - 6 y2 + 9y + 18 y2-1 y2 + 7y + 12 102) Perform the indicated operation and simplify the result. x 103) x2 + 6x + 5 + 5 x2 + 6x + 5 103) 31
104) 4x x - 9 + 9 9 - x 104) Find the least common denominator. 8 105) 9x4 and 4 27x2 105) 106) 8x + 1 x2 + 6x + 8 and x - 7 x2-4x - 12 106) Add or subtract, as indicated, and simplify the result. 107) y - 2 y - 1 - y - 2 y + 3 107) 32
108) x x2-16 - 8 x2 + 5x + 4 108) Simplify the complex rational expression using Method 2. 109) x - 1 x2 109) x - 1 x3 110) x + 7 x - 7 + x - 7 x + 7 x + 7 x - 7 - x - 7 x + 7 110) 33
111) x 36-1 x 111) 1 + 6 x Solve the equation. 112) 1 + 1 y = 30 y2 112) 113) x - 5 x = 24 x + 5 113) 114) x + 5 x - 2 = x + 7 x + 6 114) 34
Solve the formula for the indicated variable. 115) PV T = pv for P 115) t 116) 1 a + 1 = c for b 116) b Solve the rational inequality. (x + 12)(x - 7) 117) 0 117) x - 1 35
Solve the proportion problem. 118) 118) 3 12 x + 5 Suppose that the two triangles shown in the figure are similar. Find x. Find the constant of proportionality k, and write the linear function relating the two variables. 119) Suppose that y varies directly with x. When x = 9, then y = 72. 119) Find the quantity indicated. 120) Suppose that y is directly proportional to x. When x = 18, then y = 12. Find y when x = 60. 120) 36
Solve. 121) The velocity v of a falling object (ignoring air resistance) is directly proportional to the time t of the fall. If, after 4 seconds, the velocity is 128 feet per second, what will its velocity be after 9 seconds? 121) Find the constant of proportionality k, and write the linear function relating the two variables. 122) Suppose that y varies inversely with x. When x = 7, then y = 4. 122) 123) Suppose that y is inversely proportional to x. When x = 42, then y = 1 7. 123) 37