Algebra 1 Semester 2 Final Review

Unit 6 - Solving Systems of Equations

100

At what coordinate point do they intersect?

𝑦 = − 1/4𝑥 + 6 

𝑦 = 3/4𝑥 − 2

(Hint: y = mx + b)

(8 , 4)

200

Draw BOTH linear equations and determine where they intersect with the plotted points.

𝑦 = − 4 3 𝑥 − 5 

𝑦 = 2𝑥 + 5

(-3 , -1)

Linear equations should make an X in 3rd quadrant 

300

Solve the equation by substituting

𝑥 = −2𝑦 + 2 

3𝑥 + 2𝑦 = 22

(22 , - 4)

400

Solve the equation by elimination

6𝑥 + 7𝑦 = 28

−6𝑥 − 𝑦 = -4

(Hint: eliminate by adding)

(0, 4)

500

Solve the equation by elimination

7𝑥 − 9𝑦 = 15 

14𝑥 − 8𝑦 = −10

(Hint: eliminate by multiplying)

(-3 , -4)

Unit 7 - Exponents and Polynomials

100

Simplify the expression:

(−𝑥𝑦) ⁰

(Hint: 𝑎⁰ = 1)

1

200

Simply the expression:

2𝑝𝑟^-5

(Hint/example: 2y^-3 = 2/y³)

2p / r⁵

300

Simplify the expression:

(2𝑥²)²

(Hint: we are raising the power to a power)

4x⁴

400

Simplify the expression:

(−5𝑏 + 3 + 7𝑏³) + (𝑏² − 𝑏³ + 𝑏)

(Hint: Combine like terms)

6𝑏³ + 𝑏² - 4𝑏 + 3

500

Simplify the expression:

(3𝑎 − 4)(4𝑎² + 5𝑎 − 8)

(Hint: answer should be in standard form) 

12𝑎³ - 𝑎² - 44𝑎 + 32

Unit 8 - Factoring

100

Find the greatest common factor:

51 and 119

GFC: 17

200

Find the greatest common factor:

2𝑥³ 𝑎𝑛𝑑 5𝑥

GFC: 1𝑥 or 𝑥

300

Factor the polynomial:

−18𝑥³ − 9𝑥² + 3𝑥

(Hint: factor out the GCF)

-3𝑥(6𝑥² + 3𝑥 - 1)

400

Factor each polynomial: 

−4𝑥² − 44𝑥 − 96

(Hint: write the answer as a binominal)

-4(𝑥 + 8)(𝑥 + 3)

500

Factor out the square roots: 

𝑥² - √145,924

(𝑥 + 382)(𝑥 - 382)

Unit 9 - Quadratic Functions

100

Evaluate the quadratic equation 

𝑓(𝑥) = −𝑥² − 7𝑥 − 10 when 𝑥 = 3

(3 , -40)

200

Use factored form to solve for the vertex

𝑓(𝑥) = −𝑥(𝑥 − 4)

(2 , 4)

300

What are the x intercepts AND the vertex?

𝑓(𝑥) = −𝑥² + 2𝑥 + 15

X intercepts: (5 , 0) (-3 , 0)

Vertex: (1 , 16)

400

Which way will the parabola open?

-(x + 2)² - 2

Upwards

500

Complete the square and find the vertex:

𝑓(𝑥) = 𝑥²+ 4𝑥 − 24

(Hint: put the answer in vertex form)

𝑓(𝑥) = (𝑥 + 2)² - 28

           and

Vertex: (-2 , -28)

Unit 10 - Solving Quadratic Equations

100

Solve the equation by factoring:

x² - 9801

(-99 , 0) (99 , 0)

200

Solve using square roots: 

 y = 3(x + 7)² - 24

x = -7 + 2√2

or

x = -7 - 2√ 2

300

Solve using the quadratic formula:

2x² − 3x − 5 = 0

(5/2 , -1)

400

√45p²

3p√5

500

√72

6√2