Digital SAT Math: Algebra Study Guide

One type of Math that is tested on the Digital SAT is Algebra. In this article, I'm not going to go too deep in terms of content, but I will give you a very general overview of what you should know for Algebra.

If you want a more detailed review, check out my Youtube channel @satmathwiz or other sources on Youtube, other website, etc. 

Expressions:

Definition: made up of Variables and constants. Variables are things such as x, y, z, etc and constants are just numbers. For example, 2x+y is an expression. 

Distributive property: -3(a+b)=-3a-3b, and that kind of stuff. 

Simplification: a+3b+c+4d-(3a+2c-3d+10b)=-2a-7b-c7d, and that kind of stuff

Linear Equations

Definition: statement in which 2 expressions are equal.

Ex: 3x-1=5. What is x?

Ex: (1/2)x+4=8x. What is x?

Inequalities

Ex: x-2>3x. What is x?

Slope

(y2-y1)/(x2-x1)

Parallel lines have equal slopes

Perpendicular lines have slopes that are negative reciprocals of each other (ex: 1/2 and -2/1). 

Vertical lines have an undefined slope

Horizontal line have a slope of 0 

Functions

Literally y but written in f(x). 

Ex: f(x)=x+2

Note: You might also expect function tables and plugging into functions on the real DSAT. 

Graphing Linear Functions

There are 2 equations to know:

Standard form: Ax+By=C

slope-intercept form: y=mx+b

Point-slope form: y-y1=m(x-x1), where (x1,y1) is a particular point on the line

Systems of Linear Equations

Lines can intersect at either 0,1, or infinitely many points. 

0: When the slope of the line are the same and the y intercept is different. 

1: When the slope of the line are different. y intercept can be similar or different. 

infinitely many: When two lines are the exact same line

0 Solutions

1 Solution

Infinitely many solutions

Ways to solve Systems of Linear Equations:

1. Elimination

2. Substitution

Note: Expect some word problems that involves systems of linear equations.

Ex:  John pays $9 when buying 2 cheese and 3 apples. Anna pays $20 when buying 5 cheese and 6 apples. What is the price of one cheese and one apple?

Creating Linear Models

Ex: On a weekly fishing trip, Art caught m fish each hour for 4 hours and Brian caught n fish each hour for 4 hours. Find the expression that represents the total number of fish both Art and Brian caught. 

Interpreting Linear Models

Ex: Xin is a sculptor who brings her sculptures to an art exhibit to sell. The number of sculptures that she has not yet sold can be modeled with the equation S=20-3h, where S is the number of unsold sculptures and h is the number of hours since the exhibit opened. According to the model, what is the number of unsold sculptures that Xin has at the opening of the exhibit?

System of Linear Inequalities

How to graph:

1. Graph the function as if it was not an inequality

2. if it's just greater or less than, draw dotted line. If it's greater/less or equal to, then draw straight line. 

3. If y is greater, then shade "above" the line. If y is smaller, then shade "below" the line. 

If you get a system of linear Inequalities, the trick is the area that's the most shaded is your answer. 

So in this case, the purple area is your answer, not blue or red. 

And we have reached the end. I hope that this review guide helped! 

(For some information in this article, I used the Summit Education Group's  Digital SAT & PSAT Course Book. Check out their website at mytutor.com)