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Algebra 2 (Regular and Honors) and College Readiness Summer 2015 Assignment

Directions: Complete the exercises below WITHOUT the use of a calculator . Make sure to show all of work , neatly!

I . State the domain and range of each relation . Then determine whether each

relation is a function; explain your reasoning . a)

4, 5( ), 5,−1( ), 0,12( ), 0,−2( ), 7, 9( ){ } b)

II . Name the quadrant in which each point is located . a) (-3, 7) b) (10, -11) c) (0, 5)

d) 425,6

!

"#

$

%&

III . Find the product . a) 2x + 9( ) x +1( ) b) 5x −1( ) 6x −10( ) c) 3x2 − 4( ) 3x2 + 4( ) IV . The height of a rectangle is 3 units less than twice the width . a) If the width of the rectangle is represented by the variable w, write an expression for the height in terms of w.

b) Write an expression for the area of the rectangle in terms of w.

V . Factor each polynomial completely . a)

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4x 2 +12x 7 b) 81x2 −36 c)

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x 2 −16x + 63 d)

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x 2 − 7x −18 e) 25x2 − 20x + 4 f)

€

2p3 + 5p2 + 6p +15 g)

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12x 8y12 − 75x 6y16 h)

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4x 2 − 7x −15 i)

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x 2 + 40x + 400 j)

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3n3 − 4n2 + 9n −12 k)

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12a 4b −18a 3b2 + 24ab5 l)!

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x 2 + x + 0.25 m)

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4x 3 + 43x 2 + 30x n)

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4x 2 − x − 5 o) 4x2 + 4xy+ y2 p)

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x 4 −1 q)

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5 x − 3( )3 + 2 x − 3( )2 r) 25− x2

s)

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81a 2 +198ab +121b2 t)

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7x 2 − 32x − 60 u)

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12xy − 28x −15y+ 35

VI . Find the measure of x .

VII . The lengths of three sides of a triangle are given . Determine whether each

triangle is a right triangle . Show the work that leads to your conclusion . a) 6, 8, 12 b) 9, 12, 15 VIII . Complete each statement for the given property . a) Commutative Property of Addition: a + b = __________________ b) Commutative Property of Multiplication: a ∙ b = ______________ c) Associative Property of Addition: (a + b) + c = ________________ d) Associative Property of Multiplication: (a ∙ b) ∙ c = _____________ e) Additive Inverse of Addition: a _______ = ______ f) Multiplicative Inverse: a _______ = ______

IX . Solve . a) |9x + 4| - 11 = - 4 b) |7x + 2| - 8 = -15 c) - |3x + 4| = 5x + 4

d) xx 285143

−>+ e) - 8 <

21 (6x – 10) ≤ 13

f) 113#$#4x$# ≥ g) 5"#"7x"6" >

X . Evaluate each expression if a! = ! 34, b! = !−8 , c ! = !"1

2, d ! = !3 , f ! = !"1

3

a) ab2 −d b) abc+d2

XI . Solve . a)

−2 14 x−

23

"

#$

%

&'+

12 x+

34

"

#$

%

&'=5 3x−6( )

b) 23 4x−5( )= 14 7−3x( )

c)

3−15 x−8( )=3x− x4 +6"

#$

%

&'

XII . Fill in the blanks . a) Two lines are parallel if:_________________________________________________________________. b) Two lines are perpendicular if: ___________________________________________________________. c) To find an x-intercept: _________________________________________________________________. d) To find an y-intercept: _________________________________________________________________. Link to how to graph a linear function: https://weteachscience.org/mentoring/resources/lesson-plans/algebra-1-%E2%80%93-how-to-graph-a-linear-equation-using-slope-and-y Link to how to graph a linear equation: http://www.regentsprep.org/regents/math/algebra/AC1/EqLines2.htm Link to how to graph an absolute value function: http://www.algebra.com/algebra/homework/absolute-value/absolute-value.faq.question.363181.html Link to how to graph linear inequalities: http://www.mathwarehouse.com/algebra/linear_equation/linear-inequality.php XIII . Sketch the graph . a) y = 3x + 5

b) y = x2−3

c) 4x −3y =12 d) y−1= −4 x + 5( ) e) y = 7 f)! x = 7 !g)! y = x + 2 −3 h)! y = x − 4 +1 i)!3x + 7y < −21 j)! y ≥ x +1 + 6 Link to how to write an equation in standard form: http://www.algebralab.org/studyaids/studyaid.aspx?file=algebra1_5-5.xml XIV . Write the equation of a line in standard form with the given characteristics . a) Passes through (6, 1) and is perpendicular to the line

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3x − 4y = 2. b) Has an x-intercept of (9, 0) and a y-intercept of (0, -3). c) Passes through the point (4, 7) and is parallel to the line that passes through the points (-1, 8) and (5, -6).

Link to solving systems of equations: http://www .mathwarehouse .com/algebra/ l inear_equation/systems-of-equation/ index .php XV . Solve each system . a)

3x − 6y = 25x + 4y =1

b) 2x + y =14x + 2y = 3

c) x + 2y = 42x + 4y = 8

d) x

3−y

4=1

x

2−y

3= −2

Link to solving systems of inequalities by graphing: http://www .mathwarehouse .com/algebra/ l inear_equation/systems-of-equation/system- l inear- inequality .php XVI . Solve the system of inequalities by graphing . a)

y < 2x −3y ≥ 4

b) y > 2y ≤ −2x > 3

c) y ≤ − x +1 + 4y > 2

Link to simplifying expressions with exponents: !http://www .purplemath .com/modules/simpexpo .htm XVII . Simplify . Your answer should contain only positive exponents . a)

2x4( )−3⋅2x4

b) 2x2y4 ⋅ 4x2y4 ⋅3x

3x−3y2

c) 2pm−1q0( ) ⋅2m−1p3

2pq2

XVIII . State the standard form for a quadratic equation and the quadratic formula .

Link to solving quadratic equations: http://www.sosmath.com/algebra/solve/solve4/s43/s43.html XIX . Solve the quadratic equation . a) 9x2 +10 = 91 b) 3x2 −16x =12 c) 3x2 −12x −3= −x2