SAT alg n adv Flashcards
What is linear equation slope-intercept form, and what do the letters represent?
y=mx+b where m is the slope, and b is the y-intercept
What is linear equation standard form, and how do you graph it?
Ax+By=C
To graph, you must convert it to slope-intercept form
What is linear equation point slope form?
y-y1=m(x-x1) Where y is the x1 and y1 are the coordinates of a point, and m is the slope
What are the rules for linear equation standard form?
- A must be positive
- All terms must be integers
Methods for solving systems of equations
- Substitution (substitute 1 variable for another)
- Elimination (eliminate a variable)
What must you do when solving an inequality and you divide/multiply by a negative?
You flip the inequality sign.
What is quadratic function:
Standard form
Intercept form
Vertex form
Standard form: Y= Ax^2+By+C
Intercept form: y=a(x-p)(x-q) where P and Q are the coordinates of the X intercepts
Vertex form: y=a(x-h)^2 +k where the vertex is at (h,k) (to graph, plug x-intercept coordinates into equation to find the y-coordinate of the vertex)
What are the steps to graphing a quadratic equation?
- Find the Axis of Symmetry with the equation (-b/2a)
- If a is positive, the graph opens towards the positive
If a is negative, the graph opens towards the negative - Plug the Axis of Symmetry into the equation to find the vertex
- Find the Y-intercept
- Find the X-intercept either by factoring, completing the square, or the quadratic formula
Tip: If A is bigger, the graph is narrower
If necessary, use a table to determine points on the graph
What do you need to know to graph a quadratic equation?
Axis of symmetry (-b/2a), vertex, x intercepts, y intercept
What is the goal of factoring?
To find the X-intercepts of a quadratic function
How do you factor when A=1?
x^2+5x+6
A= 1 B= 5 C=6
- Find what adds to adds to B and multiplies to C.
It would be 2 and 3
The factored equation now becomes
(x+2)(x+3)
How do you factor when A isn’t 1?
You
What is the quadratic formula?
In words:
X intercepts = -b plus or minus the square root of b squared minus 4 ac all over 2a
You use factor by grouping.
3x^2 -4x -15
- Find what multiplies to (A*C) but multiplies to B.
-9 & 5 - Split B into those numbers and group the 2 sides.
3x^2 -9x +5x -15
(3x^2-9x) (5x-15) - Factor the 2 sides
3x(x-3) 5(x-3) - Group like terms
(3x+5)(x-3)
Exponential growth and decay
yp=a(b)^x
If b>1, it’s growth
If B<1, it’s decay
How do you simplify radicals?
Use the “jailbreak method” -
1. Write down a factor tree of the number
2. Write down the radical in standard form
3. Jailbreak any pairs of numbers or variables
4. Combine like terms
How do you rationalize the denominator?
You multiply the entire fraction by the radical in the denominator.
Rules for multiplying/dividing exponents with the same base
multiplying: add the exponents
dividing: subtract the exponents
How do you rationalize an expression?
- Factor everything you can
- If it’s 1 sided, you’re done
- if it’s 2 sided, duplicate-cancel anything you can find. What you’re left with is the final solution.
What does the PSAT advanced math/ heart of algebra section mainly focus on?
It focuses on critical thinking. It’s about using concepts you know to solve crazy problems.
Here’s an example:
Simplify the equation.
A+b A-b
_____ = - _____
d-c -d+c
What you would have to do is multiply the right side by a negative to give both sides the same denominator, and then you would continue as normal from there.
