1. Which equation below represents the quadratic formula?

*a. -b±b2-4ac2a = x

b. a2+b2=c2

c. fx=a0+n=1∞ancosnπxL+bnsinnπxL

2. Which of the following represents a set of parallel lines?

a. Option one

b. Option two

*c. Option three

3. What is the definition of an obtuse angle?

*a. an angle greater than 90°
b. an angle equal to 90°
c. an angle less than 90°

4. Which formula below represents the area of a circle?

a. A=2πr
*b. A=πr2
c. A=π2r
d. A= √π
5.
What geometric term is represented by the image below?

a. a corner
*b. a cross-section
c. the circumference
d. the perimeter

11. Using the data in the table below, calculate the mean, or average, number of points scored by Player B.

| Game 1| Game 2| Game 3| Game 4| Game 5|
Player A| 13| 12| 9| 11| 13|
Player B| 12| 11| 15| 20| 12|

*a. 14
b. 11.5
c. 13
d. 13.67

6. This instrument is commonly used by surveyors. It measures horizontal and vertical angles to determine the location of a point from other known points at either end of a fixed baseline, rather than measuring distances to the point directly. What is it called?

a. triangulator
b. binocular
c. tripod
*d. theodolite

7. What is the name of the missing shape in the flowchart below?

a. Acute
b. Obtuse
*c. Isosceles
d. Right

8. What category includes all of the items on the list below?
* Square
* Rectangle
* Rhombus
* Parallelogram
* Trapezoid
* Pentagon

a. Quadrilaterals
b. Triangles
c. Ellipses
*d. Polygons

9. Determine the area of the shaded portion in the diagram below.

A B

C D

* ABCD is a square
* ABCD touches the circle at 4 points
* The length of one side of the square ABCD is 2 cm

a. π– 4
*b. 2π – 4
c. 3π 2 – 4
d. 4π 3 – 4
e. 5π – 4

...Quadratic Equation:
Quadratic equations have many applications in the arts and sciences, business, economics, medicine and engineering. Quadratic Equation is a second-order polynomial equation in a single variable x.
A general quadratic equation is:
ax2 + bx + c = 0,
Where,
x is an unknown variable
a, b, and c are constants (Not equal to zero)
Special Forms:
* x² = n if n < 0, then x has no real value
* x² = n if n > 0, then x = ± n
* ax² + bx = 0 x = 0, x = -b/a
WAYS TO SOLVE QUADRATIC EQUATION
The ways through which quadratic equation can be solved are:
* Factorizing
* Completing the square
* Derivation of the quadratic formula
* Graphing for real roots
Quadratic Formula:
Completing the square can be used to derive a general formula for solving quadratic equations, the quadratic formula. The quadratic formula is in these two forms separately:
Steps to derive the quadratic formula:
All Quadratic Equations have the general form, aX² + bX + c = 0
The steps to derive quadratic formula are as follows:
Quadratic equations and functions are very important in business mathematics. Questions related to quadratic equations and functions cover a wide range of business concepts that includes COST-REVENUE, BREAKEVEN ANALYSIS, SUPPLY/DEMAND & MARKET EQUILIBRIUM....

...Quadratic equation
In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form
where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, the quadratic coefficient, the linear coefficient and the constant or free term.
Solving the quadratic equation
A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.
Factoring by inspection
It may be possible to express a quadratic equation ax2 + bx + c = 0 as a product (px + q)(rx + s) = 0. In some cases, it is possible, by simple inspection, to determine values of p, q, r, and s that make the two forms equivalent to one another. If the quadratic equation is written in the second form, then the "Zero Factor Property" states that the quadratic equation is satisfied if px + q = 0 or rx + s = 0. Solving these two linear equations provides the roots of the quadratic.
Completing the square
The process of completing the square makes use of the algebraic identity...

...Summer 2010-3 CLASS NOTES CHAPTER 1
Section 1.1: Linear Equations
Learning Objectives:
1. Solve a linear equation
2. Solve equations that lead to linear equations
3. Solve applied problems involving linear equations
Examples:
1. [pic]
[pic]
3. A total of $51,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment?
4. Shannon, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $608 for 56 hours worked. What is her regular hourly wage?
Answers: 1. [pic]
2. [pic]
3. $24,000 in CDs, $27,000 in bonds 4. $9.50/hour
Section 1.2: Quadratic Equations
Learning Objectives:
1. Solve a quadratic equation by (a) factoring, (b) completing the square, (c) the
quadratic formula
2. Solve applied problems involving quadratic equations
Examples:
1. Find the real solutions by factoring: [pic]
2. Find the real solutions by using the square root method: [pic]
3. Find the real solutions by completing the square: [pic]
4. Find the real solutions by using the quadratic formula: [pic]
5. A ball is thrown vertically upward from the top of a...

...There are now two separate equations: 60 = 6b - 6c and 60 = 3b + 3c
Solve both equations for b: b = 10 + c b = 10 - c
Now make both equations equal each other and solve for c: 10 + c = 10 - c 2c = 0 c = 0
The speed of the current was 0 mph Now, plug the numbers into one of either the original equations to find the speed of the boat in still water.
I chose the first equation: b = 10 + c or b = 10 + 0 b = 10
The speed of the boat in still water must remain a consistent 10 mph or more in order for Wayne and his daughter to make it home in time or dinner.
My Solution: c = current of river b = rate of boat d = s(t) will represent (distance = speed X time) Upstream: 60 = 6(b-c)
Downstream: 60 = 3(b+c)
There are now two separate equations: 60 = 6b - 6c and 60 = 3b + 3c
Solve both equations for b: b = 10 + c b = 10 - c
Now make both equations equal each other and solve for c: 10 + c = 10 - c 2c = 0 c = 0
The speed of the current was 0 mph Now, plug the numbers into one of either the original equations to find the speed of the boat in still water.
I chose the first equation: b = 10 + c or b = 10 + 0 b = 10
The speed of the boat in still water must remain a consistent 10 mph or more in order for Wayne and his daughter to make it home in time or dinner.
My Solution: c = current of river b = rate of boat d = s(t) will...

...Balancing Equations
Balancing equations is a fundamental skill in Chemistry. Solving a system of linear equations is a fundamental skill in Algebra. Remarkably, these two field specialties are intrinsically and inherently linked.
2 + O2 ----> H2OA. This is not a difficult task and can easily be accomplished using some basic problem solving skills. In fact, what follows is a chemistry text's explanation of the situation:
Taken from: Chemistry
Wilberham, Staley, Simpson, Matta
Addison Wesley
1. Determine the correct formulas for all the reactants and products in the reaction.
2. Write the formulas for the reactants on the left and the formulas for the products on the right with an arrow in between. If two or more reactants or products are involved, separate their formulas with plus signs.
3. Count the number of atoms of each element in the reactants a products. A polyatomic ion appearing unchanged on both sides of the equation is counted as a single unit.
4. Balance the elements one at a time by using coefficients. A is a small whole number that appears in front of a formula a an equation. When no coefficient is written, it is assumed to be 1. It is best to begin with an element other than hydrogen or oxygen. These two elements often occur more than twice in an equation.
5. Check each atom or polyatomic ion to be sure that the equation is balanced....

...
The short story Cold Equations by Tom Godwin takes place on a ship called EDS. The space cruiser is piloted by a man named Barton. He has an order of killing the stowaway who snuck onto the ship because the weight on the EDS is too much for the ship to handle. In the process of hunting down the stowaway, he realizes it was a young innocent girl named Marilyn. Once Barton understands what kind of person Marilyn is, he doesn’t kill her immediately because he knows her reasons were pure. Marilyn only wanted to see her brother, Gerry, again after ten years of being apart and was ignorant to the fact that her life can end with the decision of sneaking onto the ship. Barton begins to feel compassion after being with her and tries to comfort her, but knows what her fate is. He lets Marilyn live long enough to let her speak with Gerry once more before he follows through with the command. After Gerry and Marilyn speak he ejects her out into space. The ending was logical and no other endings would be possible because one the equation that was calibrated delicately, and two Barton could not throw the out the fever serums because that is the main reason for going on the trip to Woden.
A theoretical ending of Cold Equations could have been that Barton sacrifices himself for Marilyn, but since she is lighter than him, the fragile calibrated equation would be disrupted due to the change in weight. On EDS everything on ship is...

...addition method. 8) 3x + 7y = 40 3x + 2y = 50 A) {(-2, 18)} Solve and check the linear equation. 9) 2x - 4 + 5(x + 1) = -2x - 3 A) {- 2} B) {4 } 3 C) {4 } 9 D) {- 6} B) {(-18, 3)} C) {(-18, 7)} D) {(18, -2)} B) (28y - 28)x2 + 4(-7y + 7) D) (28x2 - 28)y + 7(4 - 4x2 )
1
Solve the equation. x x 10) 27 - = 2 7 A) { 243 } 14 B) {42} C) {3} D) { 243 } 2
First, write the value(s) that make the denominator(s) zero. Then solve the equation. x-1 x+9 11) +3 = 4x x A) x ≠ 0; {34 } 3 5 B) No restrictions; { } 6 C) x ≠ 0, 4; { 37 } 9 D) x ≠ 0; { 37 } 9
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 12) 3(2x - 36) = 6x - 108 A) Identity Solve the problem. 13) You inherit $70,000 from a very wealthy grandparent, with the stipulation that for the first year, the money must be invested in two stocks paying 4% and 10% annual interest, respectively. How much should be invested at each rate if the total interest earned for the year is to be $4000? A) $30,000 invested at 4%; $40,000 invested at 10% C) $50,000 invested at 4%; $20,000 invested at 10% B) $20,000 invested at 4%; $50,000 invested at 10% D) $40,000 invested at 4%; $30,000 invested at 10% B) Inconsistent C) Conditional
Compute the discriminant of the equation. What does the discriminant indicate about the kinds of solutions? 14) x2 - 8x + 7 = 0 A) 0; 1 real solution...

...Year & Section: _________________ Teacher: _______________
Reviewer: Quadratic Equations
I. Multiple Choice: Choose the letter of the correct answer. Show your solution.
1. What are the values of x that satisfy the equation 3 – 27x2 = 0?
A. x = [pic]3 B. x = [pic] C. x = [pic] D. x = [pic]
2. What are the solutions of the equation 6x2 + 9x – 15 = 0?
A. 1, - 15 B. 1, [pic] C. – 1, - 5 D. 3, [pic]
3. For which equation is – 3 NOT a solution?
A. x2 – 2x – 15 = 0 C. 2x2 + 12x = - 18
B. x2 – 21 = 4x D. 9 + x2 = 0
4. What are the solutions of the equation (2x – 7)2 = 25?
A. 6, - 6 B. 6, 1 C. 6, -1 D. – 6, - 1
5. Find the sum of the solutions to the equation x2 + 2x – 15 = 0.
A. 8 B. – 8 C. 2 D. – 2
6. Find the product of the solutions to the equation x2 – 8x = 9.
A. 6 B. – 6 C. 9 D. – 9
7. Which equation has [pic]as a solution?
A. (2x – 5)(x + 1) = 0 C. (5x + 2)(x + 1) = 0
B. 5x – 2)(x + 1) D. (2x + 5)(x + 1)
8. The equation x2 – 3x + a = 0 has two roots. One root of the equation is 2. What is the other root?
A. – 2 B. – 1 C. 1 D. 3
9. What is the quadratic equation determine by the roots 3 and – 4 ?
A. x2 + x – 12 = 0 C. x2 + x + 12 = 0
B....