ALGEBRA 2 Semester 1 FINAL EXAM NOTECARD IDEAS ..., Slides of Algebra

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ALGEBRA 2

Semester 1 FINAL EXAM

NOTECARD IDEAS

UNIT 1 Linear Functions

Possible Notecard Ideas:

Solving a system of equations:

*Substitution steps

*Elimination steps

*Graphing steps

UNIT 2 Quadratics

Imaginary Numbers Calculator button for “𝑖” … 2

nd

“decimal point”

2

Operations with complex numbers – USE CALCULATOR (in a+bi mode)

Addition: combine like terms

Subtraction: distribute negative, combine like terms

Multiplication: “box method” or distribute

Complex conjugate : 𝑎 + 𝑏𝑖 → 𝑎 − 𝑏𝑖

Multiplication with Functions

Composition of Functions

𝑔 𝑓

𝑓 𝑔

Quadratic Standard Form

0 = a x

2

+ b x + c

Quadratic Formula

a

b b ac

x

2

( ) 4

2

−  −

=

Multiply

“ac”

Add “b”

Multiply

“ac”

Add “b”

Go right to factored form

Split the Middle

+ 𝑥 +𝑥 + 𝑐

Then Factor by Grouping

UNIT 3 Polynomials

Factoring

GCF What # can divide into all the #’s?

ax + a

a(x+ 1)

2 Terms

a

2

• b

2

Difference of 2 Squares

x

2

2

2 Terms

𝟑

𝟑

𝟑

𝟑

Perfect Cube

(a - b)(a

2

• ab + b

2

(a + b)(a

2

• ab + b

2

S O M P S

3 Terms

a x

2

• b x + c

Grouping

𝟑

𝟐

1. Step 1: Group the first two terms and then the

last two terms.

2. Step 2 : Factor out a GCF from each separate

binomial.

3. Step 3: Factor out the common binomial.

Solve by Factoring

1. Factor

2. Set ( ) = 0

3. Solve for x

5

3

Lead Coefficient: 𝑎 = 1

Lead Coefficient: 𝑎 > 1

Odd function = all exponents are odd

Even function = all exponents are even

Neither function = mix of each

A CONSTANT (just a #) IS EVEN!!

Signs