Math 1010 Final Review

Exponent rules  What are the important exponent rules and properties?  Solve: 2 x-5 =4  What does a fraction in the exponent spot mean?  What do we do with a negative exponent?

Functions  How do you know if a function is a function?  How do you find the domain and range of a function?  How does a linear function look different than a quadratic function, log function and exponential functions?

Linear Functions  What is the general form? y = mx +b  What does the m and the b stand for?  Can you graph y=(1/2)x -4  What do you know about the slopes of parallel lines and the slopes of perpendicular lines?  What is the point-slope formula? Find equation of the line that goes through point (-2,2) and is parallel to y=3x-5

Quadratic Functions  What is the general form of the equation of a quadratic function?  What is the quadratic formula? When is it useful?  How do you find the min or max value on a quadratic graph?  How do you find intercepts… x and y?  Do you know how to graph quadratic equations?

Factoring  How do you factor into 2 sets of parentheses?  Do you know how to complete the square? x 2 + 6x -2 =0  How do you factor by grouping? y 3 +3y 2 +4y +12  What are the formulas for the sum or difference of two cubes?  What are the rules for factoring the difference of two squares?

Systems of equations  Substitution  Elimination  Do you know how to solve motion problems? D= r t A Boeing 747 jet flies 4 hrs west with a 60mph tailwind. Returning against the wind takes 5 hrs. Find the speed of the jet with no wind.  Can you solve a system of 3 equations?

Absolute Value equations and inequalities  How do you solve an absolute value equation?  How do you solve an absolute value inequality?

Rational Equations  How do you divide two fractions? (also long division)  How do you add two fractions?  What about complex rational equations?

Inequalities in TWO variables  How do you graph an inequality in 2 variables? 8x + 3y >24  When do you use a dotted line vs a solid line?

Radical Expressions and Functions  How do you “cancel” a root?  How do you multiply and simplify radicals?  How do you rationalize the denominator?  Adding radicals

Formulas  Distance formula Pythagorean's theorem  Midpoint formula?  Slope Formula  Point-Slope Formula  i and i²  Change of Base  Sum or Difference of Cubes

Complex numbers  What are complex numbers?  What does i and i 2 equal?  When do complex numbers come up in equations?

Exponential Functions and graphs  How do you graph an exponential function? y=2 x+1 -3(HI VO) You can try also making an “x,y chart” to plot more points

Logarithmic Functions  How do logs relate to exponentials? log a x=b means a b =x  What is a natural log?  What is the Change of Base formula?  What is the base of a Common Log?  Use logs to solve: 7 x-2 =60

Parabolas and Circles  What is the general equation of a circle?  What are the general equations for parabolas? (opening left/right and up/down)