MAT 116: College Algebra
MAT 116: College Algebra
MAT 116: College Algebra
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<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
Section 1.1:Equations in one variable<br />
•Linear equation in one variable<br />
• 4+2x =8,<br />
•Absolute Value<br />
• |x| +2=4 , |7u +2| + 4 = 10<br />
•Rational expressions<br />
3<br />
•<br />
x +2 = 11
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
Section 1.2: Constructing models to solve problems<br />
•Functions<br />
•f(x),G(r),h(f),P(r)<br />
•Finding sales tax<br />
•$10,987 total with a sales tax of 7.3%, how much tax?<br />
•Average speed<br />
•Drive 55 miles @ 50 mph and then return for total of<br />
55mph. What is average on return trip?<br />
•Concentrations<br />
•A chemist has 200 gallons of vinegar that is 4% acetic<br />
acid. How much acetic acid must he add to make a<br />
vinegar with 5% acetic acid
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
Section 1.3:Equations and graphs in two variables<br />
•Cartesian Coordinate system<br />
•Pythagorean Theorem a 2 + b 2 = c 2<br />
•Distance, Midpoint formulae<br />
•Construction of the equation of a circle<br />
•(x h) 2 +(y k) 2 = r 2<br />
•Completing the square<br />
• x2 + bx +<br />
✓ b<br />
2<br />
◆ 2<br />
•Standard form of line: Ax + By = C
•Line<br />
•Line<br />
•Line<br />
•Line<br />
•Line<br />
•Line<br />
•Line<br />
•Line<br />
•Line<br />
•Line<br />
•Line<br />
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
Section 1.4: Linear Equations in two variables
•Slope<br />
•<br />
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
Section 1.4: Linear Equations in two variables<br />
Rise<br />
Run<br />
= y 2 y 1<br />
x 2 x 1<br />
•Point-Slope form<br />
•y y 1 = m(x x 1 )<br />
•Slope-Intercept form<br />
•y = mx + b<br />
•Parallel Lines<br />
•m 1 = m 2<br />
•Perpendicular Lines<br />
• m 1m 2 = 1 OR m 1 = 1 m 2
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
•Quadratic equation<br />
•ax 2 + bx + c =0,<br />
Section 1.6:Quadratic equations<br />
• Factoring (x ↵)(x )=0<br />
•Square Roots, x 2 = k ) x = p k<br />
•Completing the square<br />
x 2 + bx + c =<br />
✓<br />
x 2 + b 2◆ 2<br />
b 2 4 + c =0
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
•Quadratic Formula<br />
Section 1.6: Quadratic Equations<br />
b ± p b 2<br />
• 2a<br />
4ac<br />
• Discriminant b 2<br />
4ac<br />
• 2 solutions<br />
• 1 solution<br />
• zero solutions
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
Section 1.7: Linear and Absolute Value Inequalities<br />
•Interval Notations<br />
•(a, b),<br />
•[a, b),<br />
{x|a
<strong>MAT</strong> <strong>116</strong>: <strong>College</strong> <strong>Algebra</strong><br />
Chapter 1<br />
Section 1.7: Linear and Absolute Value Inequalities<br />
•Compound Inequalities<br />
•Intersection and Union<br />
•A \ B,<br />
•A [ B,<br />
only elements in A that are also in B<br />
all elements in A, also all elements in B<br />
• example: Let A =[3, 9),B =( 6, 7]<br />
•A \ B =?<br />
•A [ B =?
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