**Algebra I SOL Topics and Formulas**

**Algebra I SOL Topics and Formulas**

**Expressions**

**Expressions**

Follow order of operations PEMDAS

Combine like terms (same variables with same exponents)

**Input **

**Input**

**Output**

= y (output)
**Output**

X= input (replace every x in the equation with the number in ( )

Plug in value for x

f(7) = 3x – 5 y= 3(7) – 5

y=16

**Equations, Inequalities **

In calculator
**Equations, Inequalities**

Go to Menu Equation Solver

Type in the equation exactly how you see it ( include ( ) if needed) Hit exe TWICE!!

Inequalities:

Use the same steps as solving equations.

**(if multiplying or dividing by a negative FLIP the sign in your answer!!!)

**Function, Patterns**

**Function, Patterns**

Function: x does not repeat (domain is all different numbers) Graphs use vertical line test (can only cross at one point)

EX1: {(3, -4), (3, 5), (4, 6)} EX2: {(7,1), (8,1), (9,1)} EX3 EX4 not a function – the x’s repeat function

EX5: EX6:

Functions Not a Function

– Not a function D:{3,5}

R: {4, 10}

Not a function Dividing by a

negative….
* flip* the sign!

8 9 1 2

5 4

5 6 1

2 3 4

4 10 3

3 5 6

1 2 1

function not a function – use the vertical line test not a function – use the vertical line test D = { all real numbers}

R = { all real numbers greater than 0}

**Linear Equations, X, Y, Intercepts **

**Linear Equations, X, Y, Intercepts**

y=mx+b m=slope b=y-intercept

Ax + By = C standard form

Horizontal line (HOY) slope = 0 equation starts with y Ex. y=4

Vertical line (VUX) slope = undefined equations starts with x Ex. x=4

To fine the x and y intercept from standard form: Ax + By = C 3x-4y=12

x-intercept y-intercept

Cover up the y value Cover up the x value

Solve for x Solve for y

### 3x=12

### -4y=12

### X=4

### y=-3

### On Calculator:

### Solve for y=mx+b

### Menu

### Graph

### Type in equation

### F6 Draw

### F5 GSOLV

### F1 ROOT for the x-intercept

### F4 YICPT for the y-intercept

**Slope**

**Slope**

Slope= m=

Positive Negative Zero Undefined

x y x y x y x y

1 2 3 4 5 6 7 8 9 10
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10 *x*
1
2
3
4
5
6
7
8
9
10
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
*y*
f(x)=abs (x+2)

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
**x**
**y** x^2/9+y^2/25=1

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
**x**
**y** x=3

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9 10
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10 *x*
1
2
3
4
5
6
7
8
9
10
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
*y*

**Write Linear Equations **

**Write Linear Equations**

Y=mx+b slope intercept (where it crosses the y axis)

(m is your slope ( ) , b is the y-intercept) Ax+By=C Standard Form

-A, B, and C cannot be fractions -A cannot be negative

- GCF has to be 1

b (y-intercept) Writing an equation of a line from a graph:

### 1. Find b (y-intercept)

### 2. Find m (slope)

### 3.

Count up and over to the other point### .

*rise*

*run*

*y*=−3

5 *x*+1

### 4. Plug in m and b into the equation y=mx+b

Writing an equation of a line from a point and a slope:

(5,-2) m=−3

5

### 1. Label your point and your slope

### x=5 y= -2 m=

−_{5}3

### 2.

y= mx+b plug in the values for y, x, and m y=mx+b-2=−3

5 (5) +b

### 3.

Solve for b -2= -3+b1=b

### 4. y=mx+b plug in the values for m, and b

### y=

−35 x +1

Writing an equation from two points: (5, -2) (1,0)

In Calculator

### 1. Menu

### 2. Stats

### 3. Place x values in L1

### 4. Place y values in L2

### 5. F1 Graph

### 6. F1 Graph

### 7. F2 x

### 8. F1 ax+b

### 9. Replace the a value for a and the b value for b

**Systems of Equations: 2 equations, 2 variables, 2 answers **

If the 2 lines intersect the solution is (x,y)
**Systems of Equations: 2 equations, 2 variables, 2 answers**

*you only see two lines touch and make an X*

Slope (m) are different

Y-int. (b) are different –10–9–8–7–6–5–4–3–2–1 1 2 3 4 5 6 7 8 9 10*x*

If they do not cross then they are parallel, no solution *you only see two lines that do NOT touch*

Slope (m) are the same Y-int. (b) are different

If they are the same line, infinitely many solutions. *you only see one line*

Slope (m) are the same Y-int (b) are the same

On Calculator:

Set each formula in standard form . Set Each formula in slope intercept form y=mx+b

Menu Menu

EQUA Graph

F1: Simultaneous Type in both equations

F1: 2 unknowns (x and y) F6: Draw

Type in A, B, and C for each equation F5: ISCT (they intercept, 1 solution (x,y))

F1: Solve You see 2 lines DO NOT touch, no solution

You only see ONE line, infinitely many

**If you get MA ERROR you must graph your lines, your answer will be Infinitely many or No Solution.

**Monomials, Exponents, Scientific Notation**

**Monomials, Exponents, Scientific Notation**

Product of Powers-same base Power of a Power

Power of a Product Quotient of a Power

Power of a Quotient Negative Exponents

or

### is always equal to 1

Scientific Notation 2.53 x = 253,000 3.06 x = 0.0000306**Polynomials **

**Polynomials**

Add/Subtract like terms

(The same variables with the same exact exponents)

1 2 3 4 5 6 7 8 9 10
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10 *x*
1
2
3
4
5
6
7
8
9
10
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
*y*

Multiply/Distribute, FOIL (First Outer Inner Last)

### (x+2)(2x-3)

### 2x

2_{+x-6}

**Rules for Factoring:**

**Rules for Factoring:**

### 1. Look for a GCF

### a. If you find one take it out.

### In Calculator:

### i. Menu

### ii. Run

### iii. Optn

### iv. F6

### v. F4 num

### vi. F6

### vii. F2 GCD

### Type in your #’s with a comma in between.

### Ex.1 (5, -10, -20)

### Ans:

### 5

Ex 2)

Ex 3)

### ** When taking out a variable as the GCF, take out the one with the lowest exponent.

### Ex:

### 2. If there are 4 terms:

### b. Break your four terms into two groups

### c.

Take out the GCF of the 1st_{ ( ) }

### d.

Take out the GCF of the 2nd_{ ( ) *** you MUST make the ( ) match the first one!!!}

** Notice that our ( ) match!!

e. Bring the GCF from step C and D into one set of ( ) and bring one of the matching ones down

f. If you have a GCF in step a bring that out in front.

3. When you have 3 terms. In Calculator:

a. Take out the GCF

b. Set the equation equal to zero c. Menu

d. EQUA

e. F2 Polynomial

f. F1: 2nd_{ degree (highest exponent after the GCF)}

g. Type in the values for A, B, and C (if there is no A, B, or C in your equation type in 0) h. F1: Solve

These are your roots, solutions, zeros to get the factors: place in (x___) with the opposite value.

The factors will be (x+1)(x-4)

The factors will be (4x+3)(x-2)

### ***Remember you can check all your work by distributing or doing the box method.

**Radicals**

**Radicals**

To turn a root into a factor: Take the opposite sign and put in (x __) after x

Simplifying Radicals

### To simplify, use

### or break out into prime factors looking for the same repeated factors (2 or

### 3 or 4 of a kind—depending on the index).

Comes out of the radical Simplifying Radicals with variables:

**Solve Quadratic Equation**

**Solve Quadratic Equation**

Factor Polynomial like normal (using the calculator) Set each factor (set of parenthesis) equal to zero Solve for the variable

You should have two answers!

Vertex: (3,-36)

Domain: R or (-*∞ , ∞*¿ Vertex

Range: *y ≥*−36 (minimum value opens up)

Vertex

max opens down

Vertex: (-0.5,12.25)
Domain: R or (-*∞ , ∞*¿

Range: *y ≤*12.25

Using the calculator: Set equation equal to zero

**Roots:** **Y-Intercept:**

Menu Menu

Graph Graph

Type in equation Type in equation

F6: Draw F6: Draw

F5: GSOLV F5: GSOLV

F1: Root F4: Y-ICPT

1 2 3 4 5 6 7 8 9 10 –1

–2 –3 –4 –5 –6 –7 –8 –9

–10 *x*

6 12 18 24 30

–6 –12

–18 –24 –30

*y*

1 2 3 4 5 6 7 8 9 10 –1

–2 –3 –4 –5 –6 –7 –8 –9

–10 *x*

6 12 18 24 30

–6 –12 –18 –24 –30

*y*

*n*

_{ab}

_{ab}

_{}

*n*

_{a}

_{a}

_{}

*n*

_{b}

_{b}

2

### 27

### 3 3 3 3 3

*of a kind*

###

_{}

_{ }

###

_{3}

### 54

###

2

### 3

### 25

### 5

### 5

*a pair*

*x*

###

_{}

*x x*

_{}

###

*x x*

Factors

Roots, Zeros, Solutions (Where the graph crosses the x-axis)

Factors

Use the side arrows to go from one root to the other

**Vertex:** **Domain: **Always all real numbers or (-*∞ , ∞*¿

Menu

Graph **Range:**

Type in equations Take the y-value from the vertex insert it into equation

F6 Draw Graph opens up use *y ≥*

F5 GSOLV Graph opens down use *y ≤*

F2 for MAX (opens down) F3 for MIN (opens up)

** Line of Best Fit**

On calculator: Menu
**Line of Best Fit**

STAT

Type all values of X in list 1 Type all values of Y in list 2 F1: GPH1

F1:GPH1 F1:CALC F2: X F1: ax+b

Replace *a* and bwith the data given if it is linear

###

### Look at the scatterplot graph, decide which model is most reasonable (linear)

###

### Calculate the formula using y=ax+b plugging in a, and b

** Curve Best Fit**

**Curve Best Fit**

On calculator: Menu STAT

Type all values of X in list 1 Type all values of Y in list 2 F1: GPH1

F1:GPH1 F1:CALC F2:

### F6:draw

Look at the scatterplot graph, decide which model is most reasonable (quadratic)

Write Equation using

Plug a, b, and c back into the equation. Round to the second decimal place.

**Direct Variation**

**Direct Variation**

###

### Equation: y = kx (k is the constant of variation);

###

### graph

### is a line thru the origin

###

### Solve first equation for

*k*

###

### substitute k into another equation and solve for the unknown variable

x### Example 1: If y varies directly as x and y is 6 when x is 18, find y when x is 24.

### Set up to solve for k:

### Then plug k into the formula and find the missing variable

### X

### Y

### Direct Variation multiple DIAGONLY across.

**II **

**Inverse Variation **

**Inverse Variation**

###

### Example – the speed of a car and the time it takes to

### reach the destination

###

### Equation:

### or

### ( is the constant variation)

###

### graph

### is a hyperbola in opposite quadrants (Quad I & III or Quad II and IV)

###

### To solve find

*k*

### and substitute it and remaining numbers into eqn. again.

### Example 2:

### If y varies inversely as x and y = 10 when x = 2, find y when x = 6.

### If

### Find y now

### X Y

### Inverse you multiply INLINE (across)

### 2

### 10

### 6

### y

x y

### 6 18

### 1

### 3

*y kx*

*k*

*k*

###

###

###

### 1

### (24)

### 3

### 8

*y kx*

*y*

*y*

###

###

###

*xy k*

###

*y*

###

*k*

_{x}

_{x}

_{k}### (2)(10)

### 20

*xy k*

*k*

*k*

###

###

###

### 6

### 20

### 20

### 6

### 10

### 3

*xy k*

*y*

*y*

*y*

###

###

###

###

### 18

### 6

**Statistics**

**Statistics**

Mean- averages (add up all the data and then divide by # of objects) Mode- Most

Median- middle # put in order smallest to biggest Range- subtract the lowest value from the highest value

*Standard Deviation, Variance, and Z-score*

**o** **Calculator Instructions:**

Menu Stat

F4 Del A (you may need to hit F6 to see Del A on calc) Type in all data into L1

F6 if you don’t see CALC F2 CALC

F1 1 VAR

σx standard deviation x̅ is the mean (μ)

n is the total number of terms

Variance= (Standard Deviation)2

(std.dev × std.dev)

Z-Score

o A positive z-score: above the mean o A negative z-score: below the mean o A z-score of zero: at the mean

### o

### Formula:

Plug in the vaules you have and solve for the unknow

*Empirical*

*Rule*

In a normal distribution with mean and standard deviation : 68% of the data fall within 1 of the mean

95% of the data fall within 2 of the mean 99.7% of the data fall within 3 of the mean

*Creating a Box and Whisker *

**Calculator Instructions:**

Menu Stat

F4 Del A (you may need to hit F6 to see Del A on calc) Type in all data into L1

F6 if you don’t see CALC F2 CALC