SAT alg n adv

Question 1

What is linear equation slope-intercept form, and what do the letters represent?

Answer 1

y=mx+b where m is the slope, and b is the y-intercept

Question 2

What is linear equation standard form, and how do you graph it?

Answer 2

Ax+By=C
To graph, you must convert it to slope-intercept form

Question 3

What is linear equation point slope form?

Answer 3

y-y1=m(x-x1) Where y is the x1 and y1 are the coordinates of a point, and m is the slope

Question 4

What are the rules for linear equation standard form?

Answer 4

1. A must be positive
2. All terms must be integers

Question 5

Methods for solving systems of equations

Answer 5

1. Substitution (substitute 1 variable for another)
2. Elimination (eliminate a variable)

Question 6

What must you do when solving an inequality and you divide/multiply by a negative?

Answer 6

You flip the inequality sign.

Question 7

What is quadratic function:
Standard form
Intercept form
Vertex form

Answer 7

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)

Question 8

What are the steps to graphing a quadratic equation?

Answer 8

1. Find the Axis of Symmetry with the equation (-b/2a)
2. If a is positive, the graph opens towards the positive
   If a is negative, the graph opens towards the negative
3. 3. Plug the Axis of Symmetry into the equation to find the vertex
4. Find the Y-intercept
5. 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

Question 9

What do you need to know to graph a quadratic equation?

Answer 9

Axis of symmetry (-b/2a), vertex, x intercepts, y intercept

Question 10

What is the goal of factoring?

Answer 10

To find the X-intercepts of a quadratic function

Question 11

How do you factor when A=1?

Answer 11

x^2+5x+6
A= 1 B= 5 C=6

1. 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)

Question 12

How do you factor when A isn’t 1?

Answer 12

You

Question 13

What is the quadratic formula?

Answer 13

In words:
X intercepts = -b plus or minus the square root of b squared minus 4 ac all over 2a

Answer 14

You use factor by grouping.
3x^2 -4x -15

1. Find what multiplies to (A*C) but multiplies to B.
   -9 & 5
2. Split B into those numbers and group the 2 sides.
   3x^2 -9x +5x -15
   (3x^2-9x) (5x-15)
3. Factor the 2 sides
   3x(x-3) 5(x-3)
4. Group like terms
   (3x+5)(x-3)

Question 15

Exponential growth and decay

Answer 15

yp=a(b)^x
If b>1, it’s growth
If B<1, it’s decay

Question 16

How do you simplify radicals?

Answer 16

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

Question 17

How do you rationalize the denominator?

Answer 17

You multiply the entire fraction by the radical in the denominator.

Question 18

Rules for multiplying/dividing exponents with the same base

Answer 18

multiplying: add the exponents
dividing: subtract the exponents

Question 19

How do you rationalize an expression?

Answer 19

1. Factor everything you can
2. If it’s 1 sided, you’re done
3. if it’s 2 sided, duplicate-cancel anything you can find. What you’re left with is the final solution.

Question 20

What does the PSAT advanced math/ heart of algebra section mainly focus on?

Answer 20

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.