Section 1
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Algebraic proportion
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Section 1
(50 cards)
Algebraic proportion
Two rates or ratios, in fraction form, set equal to each other. It is important to place the same units in the numerator and denominator. You must then cross-multiply and set those two products equal to each other.
Scientific notation
Useful in writing very large or very small numbers. **The exponent that 10 is raised to becomes the number of places the decimal will move. With a positive exponent, the decimal moves to the right, making the number bigger. With a negative exponent, the decimal moves to the left, making the number smaller. **In scientific notation, there should only be one number in front of the decimal point, and it should not be 0. It doesn't matter how many numbers are to the right of the decimal point, but it usually isn't more than two or three. Example: 1.5 x 10^4 = 15,000 1.5 x 10^-4 = 0.00015
Standard notation
The typical way numbers are written. Example: 15,000
Variable
A symbol or letter that can be used to represent an unknown value.
Unit rate
A unit rate is any rate where the value of the denominator is 1. 150 miles /3 hours = 50 miles/1 hour = 50 mph
Pythagorean theorem
a^2 + b^2 = c^2 where c is the hypotenuse
Algebraic expression
Has terms that include numbers and variables that are connected by addition, subtraction, multiplication, and division. HAS NO EQUAL SIGN
Slope of vertical line
Always undefined
Exponent rules
Any number raised to the power of 1 is itself. Any number raised to the power of 0 is 1. **Parenthesis make a difference! (-4)^2 = -4 x -4 = 16 -4^2 = -1 x 4 x 4 = -16
Area of a triangle
A = 1/2 (base x height)
Steps to solve for x (or any variable) in linear equations
1)Clear fractions by multiplying both sides of the equation by the least common denominator. 2)Distribute if necessary. 3)Combine like terms. 4)Add or subtract to get the variable term alone. 5)Multiply or divide so the coefficient on the variable is 1.
Inequality
Solution will be a range of numbers, sometimes an infinitely large range.
Area of a circle
A = Pi R Squared
Slope equation
M = Y2 - Y1 ___________ X2 - X1 *Doesn't matter which point is 1 or 2, result will be the same. Just make sure to choose which point is 1 and 2, then stick with it through entire equation.
Coefficients
Numbers used to multiply variables. When you don't see a coefficient, it is implied to be 1.
Expressions vs. equations
Expressions have no equal sign. Equations have an equal sign.
Order of operations
1. Perform operations inside grouping symbols, such as (parenthesis) or [brackets]. *with nested parenthesis or brackets, always do the innermost grouping first, then work out. 2. Simplify exponents. 3. Perform multiplication & division from left to right. 4. Perform addition & subtraction from left to right. PEMDAS Parenthesis Exponents Multiply Divide Add Subtract **still do multiplication/division from left to right **still do addition/subtraction from left to right
Right triangle
Has an angle equal to 90 degrees.
Finding x and y intercepts of a linear equation
At the x intercept, y value = 0. At the y intercept, x value = 0.
Positive slope vs. negative slope
Positive --> Uphill (left to right) Negative --> Downhill (left to right)
Circumference of a circle
C = Pi x D C = 2 x Pi x R
Associative property
Regardless of the order or grouping of three or more items, the outcome is the same. Applies to: Addition Multiplication
Contradiction
False equation with no solution.
Negatives and inequalities
Any time you multiply or divide both sides of an inequality by a negative number, flip the inequality sign.
Slope-Intercept Form
Y = MX + B Where M = slope and B = y value of y intercept.
Ratios
Ratios compare two quantities with the same unit. Can be written using colon notation 1/2 --> 1:2
Operations
Addition Subtraction Multiplication Division
Constants
Constants are terms with no variables. They can also be considered like terms.
Percent
Means "per cent" or per 100. For example 50% is simply 50 per 100.
THINGS TO REMEMBER WHEN TEST TAKING
* Remember to look carefully for negative signs and carry them all the way through the problem! *When you are converting to scientific notation, go carefully and methodically. *Read each problem mindfully. Know what each problem is asking and how you're asked to write the answer. *With any problem, go methodically. One step at a time.
Polynomial
Greek: poly=many nomials=names, terms Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. *Negative exponents not allowed *Fraction exponents not allowed *Variable exponents not allowed
Commutative property
Changing the order of the terms does not change the outcome of the operation. Applies to: Addition Multiplication
Improper fraction
A fraction where the numerator is greater than the denominator. Example 16/8.
Dividing fraction
To divide fractions, multiply the reciprocal (multiply opposites). Example 1/3 divided by 1/2 = 2/3
Like terms (common terms)
Terms that have the same variables and those variables are raised to the same power. When you have an expression with like terms, you can combine those terms. Combining like terms will simplify the expression. When combining like terms, combine the coefficients of the like terms, but leave the variables alone. 4x + 5x - 7 = 9x - 7
Compound inequality
Consists of 2 inequalities connected by either the word "OR" or the word "AND." OR: Any value of the variable that makes either inequality true is in the solution set. AND: Solution set only contains numbers that satisfy BOTH inequalities.
Slope of horizontal line
Always zero
Hypotenuse
The longest side of a right triangle.
Conversion factor
A number that relates the amount of one thing to the amount of another. Always equal to 1.
Ordered pair
Pair of values in parenthesis (x, y)
Identity equation
Equation where the solution is all real numbers.
Slope
Rise _______ Run Vertical change _________________________ Horizontal change
Point-slope equation
y-y1 = m(x-x1) Where M = slope and (x1, y1) = coordinates of the point. If you can fill in M, y1 and x1, you can then isolate y and convert the equation to slope-intercept form.
Pi
3.14 (rounded to 2 decimals) Circumference/diameter of any perfect circle
Linear equation
-Equal sign -Expression on both sides of equal sign -No variable has exponent greater than 1
Similar triangles
Angles inside each triangle have the same measure and their sides are in proportion to each other. A missing side can be determined using an algebraic proportion.
Mixed number
Contains a whole number and a fraction. Example 1 5/8.
Rules for Products & Quotients
When multiplying or dividing two numbers with the SAME sign, the product or quotient will be POSITIVE. When multiplying or dividing two numbers with DIFFERENT signs, the product or quotient will be NEGATIVE.
Rate
Rates compare two quantities with different units. "Per" = division 35 miles per hour = 35 miles/1 hour *You technically have the freedom to choose which quantity goes in the numerator and which in the denominator, but think about which rate makes the most sense or which is relevant to the question.
Evaluate
To find a value for an expression by substituting a value in for your variable.
Section 2
(17 cards)