ALLEN PARK HIGH SCHOOL Second Semester Review

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1 Algebra Semester Review Spring 0 ALLEN PARK HIGH SCHOOL Second Semester Review Algebra Spring 0

2 Algebra Semester Review Spring 0 Select the best answer for all questions. For questions through use the graphs to determine the number of solutions each system has. y. x = 4 y= x no solution B. one solution two solutions D. infinitely many solutions. x = 4 x= y no solution B. one solution two solutions D. infinitely many solutions y = x x = y y = x 4 y = x x 4 x = 4. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. y = x+ y = x no solution B. infinitely many solutions one solution; (4, D. one solution; (, 4 4. Use substitution to solve the system of equations; y= x+ 4x+ y= (, B. ( 0,9 (, D. ( 9,0. Use substitution to solve the system of equations; 4x+ y = x+ y = 9 (, B. infinitely many solutions (, 0 D. (,. Use elimination to solve the system of equations; x y= 4 (, B. ( x+ y= 4. Use elimination to solve the system of equations; x+ y= (, B. (, (,0 D. ( 0, 4x+ y= 8. Use elimination to solve the system of equations; 4x+ y = 8 (, B. (, 0, (, D. (, x+ y = 9 (, D. ( φ

3 Algebra Semester Review Spring 0 For questions 9 through 8, simplify each expression ( ab( ab ab B. ab ab D. ab. ( 4hi j ( hij 0 h i j B. h i j h i j D. h i j. ( g h g h B. g h 8g h D. g h. x x x B. ( ab. b ab b a a a mn 9 4mnp m p n 9 B. B. B. 9 x x D. a b a 9 m np a b 4 D. a D. m p n D. x 9a b 4 a 9 m n p. Find the area of the triangle to the right using the area formula: A=bh/ m B. 4m 4m D. m m. Find the area of the rectangle to the right using the area formula: A=l w ab B. 8a b 8a b D. ab 8m a b

4 Algebra Semester Review Spring 0 8. Find the volume of the cube below using the area formula: V=s ; where s = side length. x 4 B. x x D. x 4 9. Express the number 0.00 in scientific notation..0 B... D Express the number 8,0,000 in scientific notation. 8. B D. 8.. Express the number in the statement in standard notation. In 0, Netflix served.9 new deliveries in the U.S.,90,000 B.,900,000 9,000,000 D. 9,000. Express the number in the statement in standard notation. The distance from Earth to the Sun is approximately 9. miles. 9,00,000 B ,000,000,000 D. 9,000,000. Express the number in the statement in standard notation. 8 A Octometer is m. 0,000,000 B D For questions 4 through, evaluate. Express the result in scientific notation. 4. (. 4 ( B D..08. (. (. B... 4 D B.. 9. D.. 4. Find the degree of the polynomial a + a a 4a. B. 4 D Find the degree of the polynomial 4ab + ab ab. 4 B. 9 8 D.

5 Algebra Semester Review Spring Find the degree of the polynomial 9xy + 8xy xy +. 4 B. D. 0. Arrange the terms of the polynomial so that the powers of x are in descending order for xy+ xy + x+ y y + xy + x y+ x B. x + y + xy + x y x + xy + x y+ y D. x + x y+ xy + y. Arrange the terms of the polynomial so that the powers of x are in descending order for 4 xy+ 9xy + y + x 4 4 x + x y+ 9x y + y B. x + y + x y+ 9x y x + 9x y + x y+ y D. y x + x y+ 9x y + x For questions through, find the sum or difference.. Find ( a+ 4a + ( 9+ a 4a + a B. 4a + a+ 9 4a + a 9 D. 0a + a + a. Find ( x 4y x + ( y x x + x+ y 4y B. x + x+ y 4y x x y 4y D. x + x y 4y + 4. Find ( 8a+ 4a ( a 4a + a+ B. 4a + a+ 4a a+ D. 4a + a. Find ( p+ 8q q ( q 9q+ 4p 4p + p+ q+ q B. 4p + p q+ q 4p + p+ q+ q D. 4p + p+ q+ q. Find the product of r ( r 8r 4r r 4r + r B. r 4r r r 4r + r D. r 4r + r. Find the product of st ( st 4 9st t 0 s t s t 8s t B. st + st 8st 8 st + st 8st D. st st + 8st 8. Solve the equation ( x ( x 4 = +. 9 B. 9 p 8 8= 4p p Solve the equation ( ( B. D. D.

6 Algebra Semester Review Spring 0 y+ + y= y Solve the equation ( ( 9 B. 9 4 m+ m 4 = 4m+ ( m. 4. Solve the equation ( ( B. 9 D. D Solve the equation q( q = 0. { 0, } B. { 0, } {, } D. { 0 } 4. Solve the equation ( r+ 4( r = 0. { 4,} B. { 0, 8} {, } D. { 4, } 44. Solve the equation ( x+ ( x = 0. {, } B. {,} {, } D. {, } 4. Solve the equation k = 4k. { 0 } B. 4. Find the product of ( r ( r 4 0, , D., 4 r 4 B. r + r 4 r + D. r r 4 4. Find the product of ( t v( 4t v +. 0t 8v B. 0t 8tv 8v 0t + 8tv 8v D. 0t tv 8v 48. Find the product of ( x 4( x x + +. x + x B. x + x x 4 x + x + x 4 D. x + x x Find the product of ( h +. h + h+ B. h + h + h+ D. h + 0. Find the product of ( c 4( c c + B. 9c 4c 9c + 4c D. 9c 4. Find the GCF of t and t. 4 4 t B. t t D. t 8. Find the GCF of 4 xy, xy, and 8xy. 8 x y B. 8x y 4xy D. xy. Factor the polynomial g+ h. ( g+ h B. ( g+ 0h g( + h D. h( g+

7 Algebra Semester Review Spring Factor the polynomial j j + 4 j. j ( 4j j+ 8 B. j ( j j+ 4 j( 4j 4 j + 8j D. j ( j j + 4j. Factor the polynomial 4n + 8n+ n+, if possible. If the polynomial cannot be factored, write prime. 4n n 4n 8 n 4n+ n+ ( ( B. ( + ( + prime D. ( (. Find the GCF of 4 x yzand 4 x yz B. x y. x y x y D.. Find the GCF of x, 4y, and xy. 0 B. xy D. 4 x yz 0x y 8. Factor x x. ( x x B. 9. Factor nn ( + 4 ( n+ 4. ( n+ 4(n B. ( x x x( x D. none of these n+ (n ( n 4 (n ( 4 + D. none of these 0. If x x + x 0 is factored completely, one of the factors is x + B. x + x D. x +. Factor m + 8m+. ( m+ ( m+ B. ( m+ ( m+ 4 ( m+ ( m+ D. prime. If x 4x is factored completely, one of the factors is x + B. x x 4 D. x +. If n n is factored completely, one of the factors is n B. n n D. n 4. Factor x y. (x+ 4 y(x+ 4 y B. (x+ 4 y(x 4 y (x 4 y(x 4 y D. none of these. If n n is factored completely, one of the factors is n n B. n + n D. n + 4. Factor x + x+. (x (x 4 B. (x + (x + 4 (x + (x + D. prime. Factor x + x - 4. (x + (x 4 B. (x + 4(x - (x + (x - D. (x - (x +

8 Algebra Semester Review Spring 0 8. Factor x x 0. (x + 4(x B. (x + (x - 4 (x + (x + D. prime 9. Factor x + x+. (x (x + B. ( x + (x + (x - D. ( x - 0. Factor x x+ (x - 4(x 9 B. (x + 9(x + 4 (x + (x + 8 D. prime. Solve x +x 8 = 0 by factoring., -9 B. -, 9 -, -9 D. ±. Solve ( x - =., B. -, -, - D. -,. What is the equation for the axis of symmetry of y = x + 4x+ 9 x = B. x = - x = D. x = - 4. Find the coordinates of the vertex of y = x + x+. (-, - B. (, (-, - D. (,. What are the roots of the quadratic equation at the right? -., -. B. -, -.9, 0 D. -,. Find the roots of y = x +x+., B. -4., -.4 -, - D. 4.,.4. Solve the equation x x+ = 0 by using the Quadratic Formula. -, -8 B., 8, D. -, - 8. Solve the equation x x = 0 by using the Quadratic Formula. -, B., -, - D. -, 9. Solve the equation x 8x = by using the Quadratic Formula.., -0. B. -., 0.., -.4 D. -., Solve the equation x x = by using the Quadratic Formula. - B., 0 D.

9 Algebra Semester Review Spring 0 8. Solve the equation x x 0 + = by using the Quadratic Formula.., - B. -.,., -0. D. -, - 8. Simplify xy 0xy x 4y 8 B. 4x y 8 x 4y D. 4x y 8. Determine how many solutions 9x + x + 4 = 0 has using the discriminant One solution B. Two solutions No solutions 84. Determine how many solutions x + 4x = - has using the discriminant One solution B. Two solutions No solutions 8. Describe how the graph of f(x = x + is related to the graph of the parent function f(x = x Translated up units B. Translated down units Vertical shrink D. Vertical stretch 8. Describe how the graph of f(x = x is related to the graph of the parent function f(x = x Translated up units B. Translated down units Vertical shrink D. Vertical stretch 8. Describe how the graph of f(x = (x+ is related to the graph of the parent function f(x = x Translated up units B. Translated down units Translated left units D. Translated right units 88. Given the following graph, identify the corresponding quadratic equation: f(x = x + B. f(x = x - f(x = -x + D. f(x = x

10 Algebra Semester Review Spring Given the following graph, identify the corresponding quadratic equation: f(x = (x + B. f(x = (x - - f(x = (x - + D. f(x = (x Given f(x = x x, calculate the vertex and determine whether it is a maximum or minimum (, - maximum B. (, - minimum (, maximum D. (-, - minimum 9. Given f(x = -x +x +, calculate the vertex and determine whether it is a maximum or minimum (, 4 maximum B. (, 4 minimum (4, maximum D. (4, minimum 9. Find the midpoint of the line segment with the given endpoints: (, and (8, (, B. (, (, D. (-, 9. Find the midpoint of the line segment with the given endpoints: (-, 0 and (, 0 (0, 0 B. (, 0 (4, 0 D. (-4, Find the midpoint of the line segment with the given endpoints: (9, -4 and (-, -4 (, 4 B. (-4, - (-4, 8 D. (, Find the distance between (-, 4 and (, 4. Simplify your answer completely B. 8 D. 4 MAJOR TOPICS YOU NEED TO KNOW!. Exponential properties. Solving systems of equations. Scientific notation 4. Degree of polynomials. Adding/subtracting/multiplying polynomials. Solving multistep equations. Factoring/solving quadratics by factoring 9. Axis of symmetry, vertex, and max/min of quadratic functions. Translations of quadratic functions. Determining the number of roots of a quadratic using the determinate. Calculating midpoint of two points. Calculating distance between two points 4. Simplifying radicals 8. Quadratic formula

11 Algebra Semester Review Spring 0