NC Math 3 Check-Up 1

NC Math 3 Standard A-APR.6

Rewrite simple rational expressions in different forms; write $$\frac{a\left(x\right)}{b\left(x\right)}$$ in the form $$q\left(x\right)+\frac{r\left(x\right)}{b\left(x\right)}$$ , where 𝑎(𝑥), 𝑏(𝑥), 𝑞(𝑥), and 𝑟(𝑥) are polynomials with the degree of 𝑟(𝑥) less than the degree of 𝑏(𝑥).

Tips & Tricks

Graph the problem along with the answer choices and find the one that matches!

NC Math 3 Standard A-APR.6

Rewrite simple rational expressions in different forms; write $$\frac{a\left(x\right)}{b\left(x\right)}$$ in the form $$q\left(x\right)+\frac{r\left(x\right)}{b\left(x\right)}$$ , where 𝑎(𝑥), 𝑏(𝑥), 𝑞(𝑥), and 𝑟(𝑥) are polynomials with the degree of 𝑟(𝑥) less than the degree of 𝑏(𝑥).

NC.M3.A-CED.1

Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically.

Tips & Tricks

Most equations can be solved graphically. To do so, set y = left side of the equation and y = right side of the equation and then locate the intersection.

NC.M3.A-SSE.2

Use the structure of an expression to identify ways to write equivalent expressions.

NC.M3.A-SSE.2

Use the structure of an expression to identify ways to write equivalent expressions.

Tips & Tricks

When trying to find equivalent expressions, graph your given expression and each of the answer choices to see which one is a match.

NC.M3.F-BF.1B

Build a new function, in terms of a context, by combining standard function types using arithmetic operations.

Tips & Tricks

When looking for equivalent expressions, graph the problem along with the answer choices and find the one that matches!

NC.M3.A-CED.1

Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically

NC.M3.F-BF.1a

Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (include reading these from a table).

NC.M3.F-LE.4

Use logarithms to express the solution to $$ab^{ct}=d$$ where 𝑎, 𝑏, 𝑐, and 𝑑 are numbers and evaluate the logarithm using technology.

Tips & Tricks

Most equations can be solved by finding the intersection of the left side of the equation with the right side of the equation when graphed.

NOTE: Use parentheses around complex exponents.

NC.M3.F-BF.4a

Understand the inverse relationship between exponential and logarithmic, quadratic and square root, and linear to linear functions and use this relationship to solve problems using tables, graphs, and equations.

INVERSE FUNCTIONS SWITCH X AND Y.

Therefore (7, 8) will change to (8, 7) on the inverse.