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Level 174

Algebra II


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read and understand
Identify what you know and what you want to find out.
make a plan
Decide a way to solve the problem.
solve the problem
Carry out and find the answer.
look back and check
See if your answer is reasonable and correct.
cubed
A number with an exponent of 3 is often said to be
Squared
A number with an exponent of 2 is often said to be
Addition Property of Equality
For all real numbers x, y, and z, if x = y, then x + z = y + z.
Division Property of Equality
For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.
distributive property
Multiplying a sum by a number is the same as multiplying each term by the number and then adding (or subtracting ) the products.
Multiplication Property of Equality
For all real numbers x, y, and z, if x = y, then xz = yz.
Subtraction Property of Equality
For all real numbers x, y, and z, if x = y, then x - z = y - z.
Formula
An equation that relates two or more quantities
Equation
A mathematical sentence that contains an equals sign
inverse operations
operations that undo each other
Identity
The product of any number and one is that number.
reciprocal
One of two numbers whose product is 1; it is also called multiplicative inverse.
Like Terms
expressions that contain the same variables to the same power
equivalent equations
Equations that have the same solution(s).
Coefficient
the decimal part
1/aⁿ
a⁻ⁿ =
x³y²x³y⁵= x⁶y⁷
Example of the product rule for exponents
x⁸/x³ = x⁵
Example of the quotient rule for exponents
(x⁵)² = x¹⁰
Example of the power rule for exponents
Linear Equation
A polynomial equation of the first degree whose graph is a line.
Arithmetic sequence
a sequence of numbers that has a common difference between every two consecutive terms
geometric sequence
a sequence of numbers that has a common ratio between every two consecutive terms
Rate of change
A value that results from dividing the change in a function (y-values) of a variable by the change in the variable (x-values). It is another name for slope.
slope
(y₂-y₁)/(x₂-x₁)
V = s³
Volume of a cube
Volume of a Cylinder
V = pi r squared h
V = Bh
Volume of ANY prism
Markup
the amount added to the cost to determine the retail price
Discount
the amount subtracted from the cost to determine a new selling price
Linear Equation - Slope-intercept form
y = mx + b
Linear Equation - Point-slope form
y - y₁ = m (x - x₁)
Linear Equation - Standard form
Ax + By = C where A, B, and C are real numbers
Excluded value
a value for which an expression is undefined
Standard form of a polynomial is
ordering the terms from those with the highest power, to the lowest power.
Lead Coefficient
The coefficient of the leading term of a polynomial in standard form.
box-and- whisker plot
a graphic way to display the median, quartiles, and extremes of a data set on a number line to show the distribution of the data
Stem and Leaf Plot
A display where the data is organized by place value, very useful if you need to find the mean, median, or mode of the data set. The data is divided in to two parts.
Inner Quartile Ratio (IQR)
The difference between Quartile 3 and Quartile 1
parallel lines
2 lines that never cross/intersect and stay the same distance apart
results from expanding (a - b)²
Perfect Square Trinomial a² - 2ab + b²
results from expanding (a + b)²
Perfect Square Trinomial a² + 2ab + b²
Graph for a Direct Variation
This graph will be a line which must go through the origin
FOIL - First Outer Inner Last
a technique used to multiply two binomials
Graph for an Inverse Variation
This graph will be a hyperbola which has vertical and horizontal asymptotes. A hyperbola has two branches. They are mirror images of one another.
Inverse Variation
A situation when one value increases and the other value decreases. y = k/x k≠0
direct variation
A situation when one value increases as the other vaule increases or as one decreases the other decreases. y = kx k≠0
Difference of two squares a² - b²
results from expanding (a - b)(a + b)
Coinciding Lines
Given two lines with the same slope and the same y-intercepts, you know the lines are?
Intersecting lines
Two or more lines that meet at a common point.
Perpendicular lines
lines in a plane that intersect to form 4 right angles
Pythagorean Theorem
in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
A = s²
Area of a square
A = lw
Area of a Rectangle
A = bh
Area of a Parallelogram
A = ½bh
Area of a triangle
Area of a trapezoid
A = ½h(b₁+ b₂)
skew lines
Non coplanar lines that aren't parallel or intersecting