Math 111 Chapter 1 Sections 1 & 2 Reviews
Mixtures : (1st % × Amt) + (2nd % × Amt) = Final % × Amt
How many gallons of cream containing 25% butter fat
and milk Let x = # gal cream 0.25x = # gal of butter fat in cream 0.25x + 0.035(50  x) = 0.125(50) x = 20.93 (rounded) 
Your 8 quart radiator is full with a 30%
antifreeze mixture. How much pure antifreeze should be added to get a 50% antifreeze mixture. 
In the chemistry lab you have 20 oz of a 10% acid solution. How much 60% acid solution should you add to get a 35% acid solution? 
Work Problems: (part done by A ) + (part done by B) = 1 whole job
Ron, Mike, and Tim are going to paint a house
together. Ron can Let t be time needed to paint the side. (1/4)t + (1/3)t + (1/2)t = 1 
Section 1.2 Quadratic Equations and Their
Applications Solve by factoring Solve by taking the square root Solve by completing the square Solve by using the Quadratic Formula The discriminant of a Quadratic Equations Applications 
A quadratic equation is an equation that can be
written in the following standard form: ax² + bx + c = 0, where a,b,c are real numbers and a ≠ 0 The Zero Product Principle If A and B are algebraic expressions such that AB = 0, then A = 0 or B = 0 
1.2: Factoring and using Zero Product Principle Solve by factoring... x^{2} + x = 12 Solve by
factoring... 2x^{2}  5x
= 12 
1.2: Square Root Procedure If x^{2} = c, then Solve by using the square root method. 2x^{2} = 48
Solve by using the square root method. (x + 2)^{2} = 36 
Geometrically Completing the Square 
1.2: Completing the Square
Solve by completing the square

1.2: Completing the Square Solve by "completing the square" x^{2}  2x 5 = 10 2 x^{2} + 4x  4= 0 
The Quadratic Formula The solutions of the equation are : a ≠ 0 Solve by using the quadratic equation : 12x^{2}  x  6 = 0 x^{2} = 2x  2 
1.2: Discriminant and solutions to the quadratic
equation The equation ax^{2} + bx + c = 0 , with real coefficients and a≠0, has as its discriminant b^{2}  4ac If b^{2}  4ac > 0 then two distinct real solutions. If b^{2}  4ac = 0 then one real solution. If b^{2}  4ac < 0 then two distinct nonreal complex solutions. The solutions are conjugates of each other 
Determine discriminant and state the number of
solutions a) 4x^{2}  5x + 3 = 0 b) x^{2} + 2x  15 = 0 c) 4x^{2} + 12x + 9 = 0 Now graphically 
1.2: Applications The
Pythagorean Theorem a^{2} + b^{2} = c^{2} Garfield's Proof of the Pythagorean Theorem 