Math 1010 Final Review Exponent rules o What

Math 1010 Final Review

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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