# In-Depth Math Review:

##### Arithmetic
Content Category Skills Example Lessons
Operations with Integers Order of operations, adding, subtracting, multiplying, and dividing basic integers \$72+4÷2+5\$ Intro to PEMDAS
Operations with Fractions Adding, subtracting, multiplying, and dividing fractions \$2/3+(3/4×1/2)+(3/4-1/3)\$ Adding & Subtracting Fractions Multiplying & Dividing Fractions
Operations with Decimals Adding,subtracting,multiplying,and dividing decimals \$7.46+1.85+2.5×3\$ Decimals Decimals rounding
Operations between mixed numbers and improper fractions Adding, subtracting, multiplying,and dividing using mixed numbers and improper fractions \$7(1/2)+ 18.85+4(2/3)\$ Improper Fractions and Mixed Numbers
Exponents Raising numbers to "a power" (how many times a number is multiplied by itself) \$2^4+3^2\$ Intro to Exponents Exponent Rules, Like Bases, & Negative Exponents Scientific Notation
Square Roots A number that produces a specified quantity when multiplied by itself. \$√4+√81\$ Simplifying Roots & Radicals
Ratios and Proportions "Part over whole" or fractions that equals a similar fraction \$X/2=12/8\$ Ratios & Proportions
Percentages "A part" of a certain value which is used in operations. 20% of 100 + 30% of 60 Percents as Ratios Percent Increase & Decrease Percents As Decimals Hard Multi-Step Percent Problems
Averages Another word for the "mean" which is a sum of all numbers in a set of data divided by the amount of numbers Steve tried to compute the average of his 5 test scores. He scored 86 on one, 55 on the next one, then 99, 77, and 90. What is Steve's average test score? Calculating The Mean (Average)
Geometry Knowing both the area and the perimeter of triangles, quadrilaterals, and circles If one angle of a triangle is 95 degrees and another is 35 degrees, what is the third angle of the triangle? 180 Triangle Rule Problems Areas of Rectangles & Squares Rectangles & Squares Basic Circle Area Problems
##### QAS: Quantitative Reasoning, Algebra, and Statistics
Content Category Skills Example Lessons
Substituting values for x Being given a value for x and plugging in What is the value at \$(x^2-2)/(x-1)\$ when x=2? Intro to Variables & Expressions
Setting up an Equation Translating an equation from words into numbers and variables A car's distance is determined by the velocity multiplied by the amount of time the car is at that speed.If a car can go at a maximum velocity of 225 meters per second, what equation shows how far the car has travelled at its maximum speed? How to Translate Words Into Equations
Operations with Polynomials Adding,subtracting,multiplying,and dividing equations with multiple variables Simplify: \$2a+3b-(-6a+4b)\$ Adding Polynomials (a.k.a. Combining Like Terms) Distribution (a.k.a. "multiplying stuff out") Solving Equations With Distribution Basic FOIL on 2-by-2 parentheses
Factoring Undoing a polynomial and simplifying it into its most basic equations as well as using it to find certain input values What is one possible factor of \$x^2+4x+3\$ ? Factoring Stuff Out (a.k.a. "distrubution in reverse") Easier Factoring Problems Factoring Difference of Squares Hard Factoring Problems
Linear Equations with One Variable An input which leads to an output and using the output to solve for the input Solve for x when \$2(x-2)=-10\$ Solving Equations With Addition & Subtraction Only] Solving Equations With Multiplication & Division] Solving Two Step Equations
Exponent Properties Multiplying, dviding, or taking the power of a number or variable to a power \$(x^2)((x^5)^2)/ x^9\$ =? Basic Exponent Rules & Rational Expressions Negative Exponents Common Algebraic Canceling Mistakes
Irrational functions and multiplying by the Complex Conjugate Simplifying a polynomial over a polynomial and being able to simplify roots in a denominator. \$ √x/(3√x- √y)\$ Dividing Roots & Rationalizing Denominators Solving Rational Equations (x's in denominators)
System of Equations Solving for an intersection point of two equation at a designated x or y value. Solve for x and y: \$2x+3y=6\$ \$8x-4y=-12\$ Solving Systems of Simultaneous Equations with Elimination Solving Systems of Simultaneous Equations with Substitution Solving 3 Simultaneous Equations with 3 Unknowns
Inequalities Solving for the range of a functions x or y value using manipulation of a number line What is the range of x for the function \$2x+5<6\$ ? Solving "Linear" Inequalities
Content Category Skills Example Lessons
Complex Functions Plugging in inputs for outputs and understanding their meaning including inequalities, a system of equations (more than one variable), exponential, and absolute value A manufacturer for raw ore has one of two options for refining material: Process A or Process B. Procss A is \$A(t)=2t^2+t\$ and Process B is \$20t\$ with t being time in days. If the manufacturer has 7 days to refine ore, what is the maximum output possible? Solving Messy Equations: Combining Like Terms Solving Systems of Simultaneous Equations with Elimination Absolute Value Equations Solving Inequalities with just X Graphing Exponentials Solving Exponential Equations Using Logs
Complex Exponents Raising a number to a rational or irrational number or variable Simplify the following: \$(x^(1/2)) (y^(2/3))(z^(5/6))\$ Simplifying Roots & Radicals Rational Exponents (a.k.a. fractions upstairs) Basic Exponent Rules & Rational Expressions Common Algebraic Canceling Mistakes
Complex Numbers Numbers which equal the square root of a negative number (\$i\$) What is \$i^24\$ equal to? Imaginary Numbers & Square Roots of Negatives Complex Numbers
Arithmatic and Geometric Sequences A function which produces a series of numbers multiplied,divided, added, or subtracted by the previous terms What is the next term in the geometric sequence 64,32,16,8...? Geometric Sequences & Series Arithmetic Sequences & Series
Matrices A set of numbers which can be added, subtracted, multiplied, and divided [2 -6] - [-2 4]=? Basic Matrix Operations Multiplying Matrices The Determinant
Angles Using the degrees of an angle to solve for other angle values within a set of parallel lines, adjacent to the original angle, or "vertical" angles Solve for x: Parallel Lines & Transversals Theorems Parallel Lines & Transversals Problems
Triangles An isosceles (two sides equal), equalateral (all sides equal), or scalene (no sides equal) 3-sided shape whose angles add up to 180 degrees Solve for x: Obtuse, Acute, and Right Triangles Scalene, Isosceles, and Equilateral Triangles 180Triangle Rule Problems Triangle Exterior Angle Theorem
Congruent Triangles and Pythagorean Theorem Using congruent triangles to solve for the its angles and using the Pythagorean Theorem (\$a^2+b^2=c^2\$) Solve for x: The Pythagorean Theorem Everything You Need To Know About Congruent Triangles Tips & Tricks For Congruent Triangle Proofs SSS, SAS, ASA, AAS, SSA, H-L/h3>
Circles Using the radius and diameter to find the perimeter (circumference), area, and arc Calculate the arc of the given sector of the circle: Circle Vocab Basic Circle Proofs Circumference & Diameter Basic Circle Area Problems Areas of Circle Sectors
Rectangles A four-sided quadrilateral with two sets of equal sides Solve for x: Areas of Rectangles & Squares Rectangles & Squares
Three-dimensional concepts Taking the volume and surface area of shapes knowing information about the 2-D shape's area Surface Area of 3-D Shapes Volume of Solids
Right-triangle Trigonometry and the Unit Circle Using the degrees of an angle to solve for other angle values within a set of parallel lines, adjacent to the original angle, or "vertical" angles Calculate the missing sides: Intro to SohCahToa Solving Triangles The Unit Circle Introducing Secant, Co-Secant & Co-Tangent Inverse Trig Functions
Special Angles and Trig Identities Special cases and equations involving SohCahToa Simplify the following term: \$sin(2x)\$ The Pythagorean Identity: sin2X + cos2X = 1 Proofs Using The "Other Two" Pythagorean Identities: tan2X+1 = sec2X & 1+cot2X = csc2X Double-Angle, Half-Angle, and Sum/Difference Formulas