PSAT Math

Step 1: Read the question, identifying and organizing important information as you go Step 2: Chosen the best strategy to answer the question Step 3: Check that you answered the right question

slope = rise/run

m = Undefined, as the lines exist but can't be numerically calculated

m = 0

The value where the model begins

solving for a single variable in terms of another that is clearly defined

Set of multiple equations with multiple variables that are interdependent Useful for modeling and simulaion

Dependent, meaning the system has an infinite amount of solutions

Two parallel lines

Two lines that intersect at a single point

Two lines that overlap, making one

Substitution Combination

Solve the simpler of the two equations for one variable and then substitute the result into the other variable r = 2x + 6 3r + 2x = 18 6x + 18 + 2x = 18

Adding the two equations together to eliminate a variable -5x + 7y = 39 5x + 9y = 1 16y = 40

Distance/work/result = rate * time` Be sure to remember what units you're working in when doing this!

Not the same! Square feet * 1/3 * 1/3 = Square Yards

Comparison of one quantity to another Can compare a part to a part or a part to a whole

To combine a:b and b:c, make b a common value to create a:c 2:3 and 5:6, 10:15 and 15:18, 10:18

Two ratios set equal to each other Check the units of each ratios and double-check your work by cross-multiplying If a/b = c/d, then ad=bc, therefore b/a = d/a but not a/d=b/c

Percent = part/whole * 100%

Percent increase or decrease = (amount of increase or decrease/original amount) * 100%

Don't just add two percentages together, provided you're not doing P(AuB) problems.

Made up of a base (the larger number) and an exponent/power

Add the exponents

Subtract the exponents

Multiply the exponents

Apply the power to all factors in a product

One

Can be rewritten as a fraction, with 1 as the numerator and the base with a positive exponent as the denominator

You can rewrite it using two radicals: one containing the numerator and the other containing the denominator

Can be rewritten as separate radicals multiplied together

fractional exponent

positive!

It's improper to leave a radical in the denominator of a fraction, so multiply the numerator and the denominator by the offending radical

An expression comprised of variables, exponents, and coefficients, the only operations involved being addition, subtraction, multiplication, division, and integer exponents

degree, or the highest power in the variable (for one-variable terms)/the highest sum of exponents on one term (for multi-variable terms)

The x-intercepts of a polynomial Can be found by setting each factor of the polynomials equal to 0

The number of times a factor in an equation, related to zeros (x-6)(x+6) makes the solution for (x-6), 6, a simple zero (x-6)(x-6) makes the solution for (x-6), 6, a double zero

When a polynomial has a zero with an odd multiplicity, its graph will cross the x-axis When a polynomial has a zero with an even multiplicity, its graph will just touch the x-axis

Distribute each term in the first set of parentheses to each term in the second set

Use polynomial long division, which is just regular division but with polynomials

A fraction of polynomials For an expression to be rational, both the numerator and the denominator must both be polynomials Are often undefined for certain factors if a solution makes the denominator equal 0

Proper rational expression has a lower-degree numerator than denominator Improper rational expression has a higher-degree numerator than denominator

Solutions that don't satisfy the original equation and causes 0 in the denominator of any parts of the equation

Typical rational equation that models a real-world scenario Uses rate equation (distance or work = rate x time)

Rules that transform inputs into outputs Differ from equations in the sense that each input only has one output Inputs, or domain, is represented by x Output, or range, is the result of an equation and is represented by f(x)

f(x)/any other letter(x) is the output, similar to y in slope equations K is the rate of change, like m in a slope equation f(0) is the y-intercept, like b in a slope equation f(x) = kx + f(0) y = mx + b

f(x) = f(0) * (1 + r)² r is the growth/decay rate

f(x) + g(x)

f(x) - g(x)

f(x) * g(x)

f(x)/g(x)

Use result of g(x) as the x in f(x)

Multiple pieces of equations duct-taped together If the x-input falls into one of the rules listed beside the function, it will equal a certain numerical value or equation

Functions that have y-values that increase as the corresponding x-values increase

Functions that have y-values that decrease as the corresponding x-values increase

Functions that have y-values that stay the same as the x-values increase

f(x) moves left g units

f(x) moves right g units

Graphs moves up, down, left, or right

Flips the graph around an axis or line

Stretching or squashing a graph horizontally or vertically

f(x) moves up g units

f(x) moves down g units

f(x) reflected over x-axis (up-facing functions become down-facing)

f(x) reflected over y-axis (left-facing functions become right-facing)

f(x) undergoes vertical compression

f(x) undergoes horizontal expansion

f(x) undergoes vertical expansion

f(x) undergoes horizontal compression

An equation that contains a squared variable as the highest-order term

(a + b)(c + d) = ac+ ad + bc + bd

Factoring Completing the Square Quadratic Equation

-If there is a GCF for all of the factors, take it and divide the equation by it. For example, in 5x² + 10x + 15, the GCF is 5. Divide to make 5(x² + 2x + 3) -Find a * c -Find the factors of a and c that add to b -Re-write as binomials

(a needs to equal 1 to use this process) -Move the constant to the other side of the equals sign -Divide b by 2 and square the quotient -Add the result to both sides -Take the square root from both sides -Solve both the positive and negative results from the equations

b² - 4ac Its values determines the number of solutions Positive result = Two real solutions Result of 0 = One real solution Negative result = No real solutions

y = a(x - h)² + k Vertex is (h, k) k is the maximum/minimum of the graphed equation h = x is the axis of symmetry