Algebra
Substituting values
Evaluate algebraic expressions
If , find the value of
If , find the value of
If , , and find the value of
PEMDAS
- Parenthesis
- Exponents
- Multiplication and Division, left to right
- Addition and Subtraction, left to right
Linear Equations
Equation – statement that two expressions are equal
Solve – find variable value(s) that make stmt true
Solution set – set of the values that make it true
Equivalent – two stmts with same solution set
Contradiction – equation with no solution set
Identity – equation with infinite solution set
A linear equation in one variable is an equation that can be written in the form
(an equation that is not linear is called non-linear)
Addition property
Multiplication property
1. Familiarize yourself with the problem
Read problemAnalyze situation
List given info and question to answer
Do we need a formula?
SketchChartField a guess
2. Translate to Math - write the equation
Identify quantities
Label quantities
Model - write the equation
3. Do the math
4. State the answer
5. Check your work
Four students about to purchase concert tickets for $18.50 each, discover that they can purchase 5 tickets for $80. How much would each person save if they found a fifth person, and split the cost?
A $200 CD player is on sale for 20% off. What is the cost of the CD player?
Sarah purchases a camera for $90 on a 25% off sale. What is the normal price of the camera?
You take your family to a fancy restaurant, and receive a bill for $38. You decide to leave a 15% tip. How much is the tip?
Fractions and Rational Expressions
Write as a mixed number.
Write as an improper fraction.
+,-,*,/ Fractions (LCD), Decimals, percent
How many yards of material from a 24-yard cloth remain after 3 pieces, each yards long, and 5 pieces, each yard long, are removed?
Averages
Mean, median, mode 8, 7, 3, 2, 7, 5, 2
You have taken 3 of 4 tests in your math course, and received 84, 72, and 75. How much must you score in your 4th test to get a B in math?
An airplane flew for 8 hours at an airspeed of x mph, and for 7 more hours at 325 mph. The average airspeed was 350 mph. Solve for x.
Slope of a line;
Find the slope of the line
Find the slope of a line from the point to the point .
Find the equation of a line from the point to the point .
Setting up equations
linear modeling,
To model a quantity that is changing at a fixed rate, with a linear function f,
f(x)=(const rate of chg)x+ (initial value)
A 100 gallon tank is initially full of water and being drained at 5 gallons per minute.
A driver of a car is initially in Wichita KS, 545 miles from home, traveling toward home on
I-35 at 70 miles per hour. Write a formula for a linear function f that models the distance between the driver and home after x hours.
direct variation, ratios, similar triangles
If you can buy 3 bottles of a sports drink for $7, how much will 12 bottles cost?
The cost of tuition is directly proportional to the number of credits taken. If 11 credits cost $720.50, find the cost of taking 16 credits.
A person 6 feet tall stands 50 feet from a street lamp. If the person casts a shadow 10 feet long, how tall is the street lamp?
Linear equations/two variables
Solve 2x2 systems of equations
In one day, Glovers, Inc., sold 20 pairs of gloves. Cloth gloves sold for $24.95 per pair, while pigskin gloves sold for $37.50 per pair. The company took in $687.25. How many of each pair were sold?
Exponents, square roots, and scientific notation
Exponents as shorthand for multiplication
Square Roots
Exponents and radicals
exponent manipulation
Product Rule:
Quotient Rule:
Neg Exponent Rule:
Zero Exponent Rule:
Power Rules:
Scientific Notation
A real number r is in scientific notation when r is written as , where and n is an integer.
Dist to sun = 93,000,000
Pop of world in 2050 = 9,000,000,000
Mass of the earth – kg
The solar wind carries particles from the sun at about meters per minute. The distance from the sun to the earth is about meters. How long does it take for a particle to travel from the sun to the earth?
Basic operations/polynomials
Add, sub, mult, div algebraic expressions
Factoring polynomials
FOIL
Factor quadratics
Solve quadratic equations
Rational expressions
Solve rational equations
Solve for x: