Alg Semester 2 Midterm Review

Alg Semester 2 Midterm Review

Your midterm will be on Wednesday and Thursday this week!

Details

• 15 questions

• No CER

• Mostly covers Unit 3, but several Unit 1 and 2 questions are included

Solving for a multi-step Equation

• Clear any complex fractions

• Apply the distributive property

• Combine like terms on the same side of the equal sign

• Use inverse operations to move all variables to one side

• Solve for the remaining 2 step equation

Multiple Choice

Solve the equation:

$$-10+2\left(2x-3\right)-5x=2$$  

• x = 2

• x = -18

• x = 16

• x = -4

Multiple Select

Choose the relations that represent a function

Multiple Choice

True or false: The graph represents a function

• True

• False

Systems of Equations

• Used to compare two options or situations

• The solution is an ordered pair

• Substitution: isolate a variable on one equation, then ​substitute into the other.

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Multiple Choice

Solve the linear system using substitution:

$$5x+2y=23$$   $$-3x+y=6$$   

• (1,9)

• (2,5)

• (1,-3)

• (2,1)

Simplifying Exponents

• Use exponent rules to simplify

• Must have the same base for rules to apply

• All answers must have positive exponents

• Anything to the power of zero is 1

• Any base without an exponent has an invisible exponent of 1

Multiple Choice

Simplify the expression: $$3^{-\frac{5}{2}}$$  

• $$3^5$$  

• $$\frac{1}{3^5}$$  

• $$\frac{1}{\left(\sqrt{3}\right)^5}$$  

• $$\sqrt{3^5}$$  

Multiple Select

Select all statements that are correct

• $$\left(x^3y\right)^3=x^9y^3$$

• $$\left(x^4y^2\right)^4=\left(xy\right)^{10}$$

• $$\left(\frac{x^2}{y^3}\right)^2=\frac{x^4}{y^6}$$

• $$x^4y^2z^0=1$$

• $$x^{-15}\cdot x^4=x^{11}$$

Simplifying Radicals

• Radicals can be simplified before you add or subtract

• Only coefficients get added or subtracted, radicands stay the same

• Multiplication or division does not need like radicands

• A simplified radical is one where no more perfect squares can be factored out

Multiple Choice

Solve the expression below: $$\sqrt{3}+\sqrt{27}$$  

• $$4\sqrt{3}$$  

• $$\sqrt{30}$$  

• $$3\sqrt{9}$$  

• 3

Multiple Select

Select all expressions that are true statements

• $$\sqrt{7}+\sqrt{175}=6\sqrt{7}$$

• $$\sqrt{80}-\sqrt{20}=2\sqrt{5}$$

• $$7\sqrt{5}-\sqrt{15}=4\sqrt{5}$$

• $$2\sqrt{80}+\sqrt{45}=9\sqrt{5}$$

Multiple Choice

Simplify the expression. Then choose the response that is in its simplest form: $$\frac{\sqrt{270}}{\sqrt{15}}$$  

• $$\frac{3\sqrt{30}}{\sqrt{15}}$$  

• $$\sqrt{18}$$  

• $$3\sqrt{2}$$  

• 9

Polynomials

• Must always be written in standard form (descending degrees)

• Multiple variables in one term: Add exponents together to determine the degree

• Variables without exponents have an invisible exponent of 1

• Constants have a degree of zero

• Subtracting polynomials is simply "adding the opposite"

Multiple Select

Select all polynomials in standard form:

• $$8x^2y+6xy^2z+9xyz$$

• $$2x-x^3-2x^2$$

• $$-4xy^3+5x^3+xy+1$$

• $$x^5+5x^2y^2+6y^2$$

• $$10x^4y^3-12x^3y^2-x^2y+4x$$

Multiple Choice

Add the polynomials. Make sure your response is in standard form: $$\left(4x^2+3xy-y^2\right)+\left(x^2-8xy-2y^2\right)\ =\$$  

• $$5x^2+11xy-y^2$$  

• $$5x^2-5xy-3y^2$$  

• $$3x^2+5xy-y^2$$  

• $$3x^2+11xy+3y^2$$  

Multiple Select

Select all expressions that are true statements

• $$\left(xy^2\right)\left(x^2y\right)=x^2y^2$$

• $$7x^3\left(5x-3\right)=\ 35x^4-21x^3$$

• $$2x^4\left(-3x^2-6x\right)=\ -5x^6-12x^5$$

• $$4x^2\left(5x^2+5xy-7y^2\right)=\ 20x^4+20x^3y-28x^2y^2$$

• $$5x^3y\left(x^2-y+3\right)=\ 5x^5-5x^3+15x^3y$$

Multiple Choice

Subtract the polynomials. Make sure your answer is in standard form:

$$\left(4x^2+7x-2\right)-\left(2x^2-6x+4\right)=$$  

• $$6x^2+13x-2$$  

• $$6x^2+x+2$$  

• $$2x^2+x-2$$  

• $$2x^2+13x-6$$  

Multiple Choice

Select the binomials that represents this expression: $$12x^2+26x+12$$  

• (2x+5)(6x +7)

• (4x+5)(3x+2)

• (-4x+5)(-3x+2)

• (6x+4)(2x+3)