L What are the properties that should be used to isolate the variable in the equation? 3x + 11 = 5

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1 lgebra Name: MITERM REVIEW Part Hour: ate: L... What are the properties that should be used to isolate the variable in the equation? x + = 5 additive identit and multiplicative identit additive inverse and multiplicative identit additive identit and multiplicative inverse additive inverse and multiplicative inverse L... Which propert would best be used to solve this problem mentall? 5 distributive associative commutative closure L... Wh is the product of two even integers alwas an even number? Let the even integers be represented b a and b. a b = (a + b), which is alwas even a b = (ab), which is even when (ab) is even but odd when (ab) is odd a b = (ab) = (a)b, which is alwas even a b = (ab) = (ab), which is alwas even L... Wh is the multiplicative inverse of a negative integer also negative? The product of a number and its multiplicative inverse equals -, so the number must be negative. The multiplicative inverse of a number is alwas negative. The product of a number and its multiplicative inverse equals, so the number must be negative. The sum of a number and its multiplicative inverse equals 0, so the number and its multiplicative inverse must have the same sign. US ommon Mid-Term Exam lgebra REVEIW Page

2 .. 5. Evaluate for x = Evaluate the following expression when x =, =, and z =. x z Seven times the sum of a number and five is 75. Which equation represents the previous sentence? 7x = 75 7x + 5 = 75 x + 5 = 75 7(x + 5) = Which of the following best describes the expression below? x I earned $ more than four times what I earned last week. I earned $ minus four times what I earned last week. I earned $ less than four times what I earned last week. I earned $ more than four times the difference between what I earned this week and last week. US ommon Mid-Term Exam lgebra REVEIW Page

3 < x < 7 > x > < x < 8 8 < x < < x < 6 < x < < x < 8 > x > Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $ snail travels at a rate of. feet per minute. a. Write a rule to describe the function. b. How far will the snail travel in 9 minutes? ; 9.7 ft ; 9.7 ft ;. ft ;. ft US ommon Mid-Term Exam lgebra REVEIW Page

4 ... rstal earns $.50 per hour mowing lawns. a. Write a rule to describe how the amount of mone m earned is a function of the number of hours h spent mowing lawns. b. How much does rstal earn if she works hours and 5 minutes? e careful! ; $0. ; $.00 ; $0.50 ; $ What situation does this function model? f ( x) 7.75x 50 ill has $57.75 ill earns $57.75 per week ill starts with $7.75 and earns $50 per week ill starts with $50 and earns $7.75 per week.. 5. Miguel gets billed $9.95 per month b the cell phone compan, which includes 00 minutes of talk time. If he uses more than 00 minutes, then he is charged $0.5 per minute. Miguel has onl $5.00 to spend each month on his cell phone bill. Which of the following inequalities can be solved to show the maximum number of minutes over 00, m, he can use each month? m m m m Solve the following inequalit. x 8 x x x 8 x 8 US ommon Mid-Term Exam lgebra REVEIW Page

5 .. 7. Which graph is NOT the graph of a function? - x - x x - x Which of the following sets of ordered pairs represents a function? {(, ), (, ), (0, 5), (, 6), (0, 7)} {(5, 0), (5, ), (5, ), (5, ), (5, )} {(, ), (, ), (, ), (, ), (5, 5)} {(, ), (, ), (, ), (, ), (, )}.. 9. Which of the following sets of ordered pairs represents a function? {(, -), (-, -), (0, -), (, -)} {(-, 0), (-, ), (-, )} {(,), (-,9), (,0), (-,), (, 5)} {(, ), (, ), (, -), (6, 5), (, )} US ommon Mid-Term Exam lgebra REVEIW Page 5

6 .. 0. Which of the following sets could be the domain and range for this function? {(, ), (, ), (0, 5), (, 6), (0, 7)} omain: {0,, } Range: {,, 5, 6, 7} omain: {,, 5, 6, 7} Range: {0,, } omain: {0,,, } Range: {0,, } omain: all real numbers Range: all real numbers... Which of the following sets could be the domain and range for this function? {(-, 0), (-, ), (-, )} omain: {-} Range: {-, 0,, } omain: {-} Range: {0,, } omain: {0,, } Range: {-} omain: {-, 0,, } Range: {-}..7. dolphin dove underwater following the parabolic path f(t)= t 0t, where d represents its depth in the water in feet and t is the time since its dive in seconds. What is the value of f()? -0 feet -5 feet -6 feet -00 feet..7. n object is following the path modeled b the equation -x 5x 8. What does the -intercept of the graph represent? What does the maximum point represent? the point where the object hits the ground; the highest point the object reaches the point where the object hits the ground; the point from which the object is dropped the point from which the object is thrown; the highest point the object reaches the point from which the object is thrown; the point from which the object is dropped US ommon Mid-Term Exam lgebra REVEIW Page 6

7 ... In Februar, ou have a balance of $70 in our bank account. Each month ou deposit $5. Let Januar =, Februar =, and so on. Write an equation for this situation. Use the equation to find the balance in June. 70 = 5(x ) ; $50 = 5(x ); $80 = 5(x ); $70 70 = 5x; $ Sarah pas $0 in advance on her account at the athletic club. Each time she uses the club, $0 is deducted from the account. The situation can be modeled b the equation b = 0 0x, where x is the number of visits and b is the total account balance. a. Graph the equation. b. Find the account balance after 8 visits. b thletic lub ccount 00 b thletic lub ccount x x $0 $90 b thletic lub ccount b thletic lub ccount x x $0 $0 US ommon Mid-Term Exam lgebra REVEIW Page 7

8 .. 6. n equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and s = length of a side?. s = P. P = s. P = + s. P = (s + s + s).. 7. The length of a rectangle is centimeters more than times the width. If the perimeter of the rectangle is 6 centimeters, find the dimensions of the rectangle. length = 5 cm; width = 8 cm length = cm; width = 5 cm length = cm; width = 8 cm length = 8 cm; width = 5 cm.. 8. The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation. Time (das) ost ($) dollars per da; the cost is $5 for each da. dollars per da; the cost is $5 for each da. dollars per da; the cost is $75 for each da. dollars per da; the costs $ for 50 das US ommon Mid-Term Exam lgebra REVEIW Page 8

9 lgebra Name: MITERM REVIEW Part Hour: ate:. 9. The rate of change is constant in the table. Find the rate of change. Explain what the rate of the change means for the situation. Time (hours) 0; Your car travels for 0 hours. 60; Your car travels 60 miles. istance (miles) ; Your car travels 65 miles ever hour. ; Your car travels 65 miles ever hour Which of the following equations represents the graph below? 6 5 x + - x + x x x US ommon Mid-Term Exam lgebra REVEIW Page 9

10 ... Match the equation with its graph. 7x + 7 = x x x x Write an equation in point-slope form for the line through the given point with the given slope. (, 6); m = US ommon Mid-Term Exam lgebra REVEIW Page 0

11 .... line passes through (, 5) and (, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. 5 = (x + ); = x + 8 ; + 5 = (x ); = x... Which of the following is the equation of the graph below? x = - = - x = = x Which of the following is the equation of the graph below. x = - = - x = = x 5 US ommon Mid-Term Exam lgebra REVEIW Page

12 .. 6. Find the slope and -intercept of the line. x + = ; ; ; ; Which of the following represents a line that is parallel to the line = x? -x x - x x.. 8. Which of the following lines is perpendicular to - x and passes through the point (, 5)? x x x + 5 -x Which statement is true about these equations? = x 5 = -x + 5 The equations represent parallel lines. The equations represent perpendicular lines. The equations represent intersecting lines that are not perpendicular. The equations represent the same line. US ommon Mid-Term Exam lgebra REVEIW Page

13 .. 0. Solve the sstem of equations using substitution. x + = 7 = x + (6, ) (6, 7) (5, )... Solve the sstem using elimination. x + = 6 x + 8 = 0 (, ) (, ) (, ) (, )... How can the graph of = x be translated so that its equation becomes = x +? It can be shifted right units and up unit. It can be shifted left units and down unit. It can be shifted right unit and up units. It can be shifted left unit and down units.... How does the graph of the function ( ) compare with the graph of ( )? It is verticall stretched b a factor of and shifted down units. It is verticall stretched b a factor of and shifted right units. It is horizontall stretched b a factor of and shifted down units. It is horizontall stretched b a factor of and shifted right units. US ommon Mid-Term Exam lgebra REVEIW Page

14 ... Examine the graph below. What do ou know about the standard form of the equation of this parabola? ( ) is positive and is negative. is negative and is positive. oth and must be positive. oth and must be negative x.. 5. The graph shown below is x. How would the graph -x 5 differ from the given graph? x It is verticall stretched b a factor of, opens down, and moves up 5 units. It is verticall stretched b a factor of, opens up, and moves down 5 units. It is horizontall stretched b a factor of, opens down, and moves up 5 units. It is horizontall stretched b a factor of, opens up, and moves down 5 units. US ommon Mid-Term Exam lgebra REVEIW Page

15 .. 6. What are the zeros of the function: = x x? x = or x = - x = - or x = x = - or x = x = or x = The graph of a quadratic equation intersects the x-axis in exactl one point. Which of the following statements is/are true? The equation has one zero. The equation is of the form = a(x b). The discriminant is zero.,, and are true If the vertex of the graph of a quadratic function is located on the x-axis, how man distinct real solutions does the equation have? The graph of the equation = x + opens up with a vertex at (0, ). How man real solutions does the equation have? no real solutions real solution real solutions number of real solutions cannot be determined What is the factored form of 6x 9 (x ) (x )(x + ) (x ) (x )(x + ) US ommon Mid-Term Exam lgebra REVEIW Page 5

16 .. 5. Factor the following expression. x 60x + 75 (x 5)(x ) (x 5)(x + 5) (x 5)(x 5) (x 5) Find the zeros of the function. = (x ) (x + 7) x =, x = -7 x = ½, x = 7 x = x =, x = -7, x = What is the maximum value of the function f(x) = x + x What is the line of smmetr in the graphed quadratic function? x = - x = - = - = x US ommon Mid-Term Exam lgebra REVEIW Page 6

17 Find the equation of the axis of smmetr and the coordinates of the vertex of the graph of the function. ; vertex: ; vertex: ; vertex: ; vertex: Factor the following expression. x 60x + 75 (x 5)(x ) (x 5)(x + 5) (x 5)(x 5) (x 5) Factor the following expression 6x 6 = (8x 6) (8x 6)(8x + 6) (x ) (x )(x + ) Which of the following represents the vertex form of the equation: =x x 6? = (x + ) + = (x ) + = (x + ) 0 = (x ) Which of the following represents the vertex form of the equation: = x + x + 8? = (x + ) = (x + ) + = (x + ) + 6 = (x + ) + 7 US ommon Mid-Term Exam lgebra REVEIW Page 7

18 Solve the following equation using the quadratic formula. x 5x 0 x -5 x -5 7 x 5 x Use the quadratic formula to solve the equation. If necessar, round to the nearest hundredth. 8, 8 9, 9, 8, 8 L.. 6. Simplif the following: i i I L.. 6. Simplif the expression. i i i The formula for the perimeter of a rectangle is shown below. Solve the formula for the variable l. P = l + w l = P w l = P w l = P w l = P w 00 0 US LGER HIGH SHOOL SEMESTER EXM REVIEW Page 8

19 The formula for a circle centered at the origin is shown below. Solve the equation for. = r x = x r x + = r = r x = x r What are the zeros of the function? ( 9,0) and (,0 ) ( 9,0) and (,0 ) ( 9,0) and (,0 ) ( 9,0) and (,0 ) What are the zeros of the function? 5( x )( x 5) (,0) and (5,0) ( 5,0) and (,0) and (5,0) ( 5,0) and (,0) and ( 5,0) (,0) and (5,0) What are the zeros of the function? x 8x ( 6,0) and (,0) ( 6,0) and (,0) ( 6,0) and (,0) ( 6,0) and (,0) What are the zeros of the function? x 8x 0 (,0) and ( 0,0) (,0) and (0,0) (,0) and ( 0,0) (,0) and (0,0) 00 0 US LGER HIGH SHOOL SEMESTER EXM REVIEW Page 9

20 In Februar, ou have a balance of $70 in our bank account. Each month ou deposit $5. Which tpe of function would best model this situation? Linear Exponential Quadratic bsolute Value.. 7. rocket is launched from atop a 0-foot cliff with an initial velocit of 6 ft/s. Which function would best model this flight pattern of the rocket? Linear Quadratic Exponential bsolute Value.. 7. Which of the following represents the graph of a quadratic equation whose maximum is found at ( )? ( ) ( ) ( ) ( ).. 7. Which of the following represents the graph of a quadratic equation whose minimum is found at ( )? ( ) ( ) ( ) ( ) 00 0 US LGER HIGH SHOOL SEMESTER EXM REVIEW Page 0

21 lgebra Name: MITERM REVIEW Part Hour: ate: 7. Which of the following is the equation of a parabola with a vertex of (, 0) and a -intercept of (0, 8)? = (x ) = (x + ) = (x ) = (x + ) 75. Which is alwas the correct conclusion about the quantities in the function = x? The variable x is alwas more than. When the value of x is positive, the value of is also positive. The variable of is alwas less than x. The value of x decreases, the value of increases. L What is the solution to x x 5 x x x L The length of a bolt used in a car door is supposed to be cm. The actual length can var b at most 0. cm. Write an absolute value inequalit for the range of acceptable lengths. 78. Solve the equation. ( 5) = US LGER HIGH SHOOL SEMESTER EXM REVIEW Page

22 79. Solve the equation Solve the equation. x 8 = x Solve the equation. 9d + d + d + = d Solve the inequalit. 5x 7 < 8 x > 7 x < 7 8. Solve the inequalit Solve the sstem of equations using substitution. x + 5 = 5 x + 0 = 65 (, ) (, 5) (5, ) (5, ) 00 0 US LGER HIGH SHOOL SEMESTER EXM REVIEW Page

23 Solve the sstem using elimination. x + = 8 x + 6 = 8 (, ) (, ) (, ) (, ) Solve the sstem using elimination. x + 5 = 5 x + 0 = 65 (, ) (, 5) (5, ) (5, ) 87. Factor the expression. d + 0d + 9 (d + 9)(d ) (d 9)(d ) (d 9)(d + ) (d + 9)(d + ) 88. Factor the expression. 89. Factor the expression. x + 7x 6 (x )(x ) (x + )(x + ) (x )(x + ) (x + )(x ) 90. Factor the expression. m 9m 0 (7m )(m 5) (7m + )(m 5) (7m + )(m + 5) (7m )(m + 5) 00 0 US LGER HIGH SHOOL SEMESTER EXM REVIEW Page

24 9. Simplif the product. 7a (5a 6 b ) a 9 9a b 6 5a 9 a b 5a 9 ab 6 a 8 9a b 6 9. Find the slope of the line that passes through the pair of points: (5, ), (8, 0) 9. Find the slope of the line x 5 9. Write an equation of a line with the given slope and - intercept. m =, b = 0 = x + 0 = x 0 = x 0 = 0x 95. Write an equation of a line with the given slope and -intercept. m =, b = = x = x + = x = x US LGER HIGH SHOOL SEMESTER EXM REVIEW Page

25 96. Find the x- and -intercept of the line. x + = x-intercept is -; -intercept is -. x-intercept is -; -intercept is -. x-intercept is ; -intercept is. x-intercept is 0; -intercept is. 97. Graph x x x x Write an equation in slope-intercept form for the line through the given point with the given slope. ( 0, ); m = x 0 x 8 x 8 x US LGER HIGH SHOOL SEMESTER EXM REVIEW Page 5

26 99. Write the equation for the line. State whether the slope is 0 or undefined. 5 x slope is undefined x slope is 0 slope is undefined slope is x Write the equation for the line. State whether the slope is 0 or undefined. x slope is undefined x slope is 0 5 slope is undefined slope is x US LGER HIGH SHOOL SEMESTER EXM REVIEW Page 6

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