Algebra 2
Writing Assignment: Algebra of Quadrilaterals
Each problem is worth 5 Points
Total Points: 50
Solve each system of equations. Show your work.
1. Use the following image for problems (a) (f). ABCD is a parallelogram.
(a) Angle DAB measures (4 x 2
Algebra 2
Writing Assignment: Solving Rational Functions
5 points each
Total Points: 50
Solve for x. Show all work and check your answers.
1.
2 3 22
+ =
x 5 5x
5x(2/x+3/5)=(22/5x)5x 10+3x=22 10-10+3x=22-10 3x/3=12/3
x=4 Check 2/4+3/5=22/20 .5+.6=1.1
1.1=1
Algebra 2
Solving Exponential and Logarithmic Functions
5 Points Each
Total Points: 50
Please show all work that leads to your answer and round answers to the nearest hundredth. Be sure to
check your answers.
1. 7 x = 124
xlog7=log124
x=log124/log7
Check
1. y > -6x 2
y > -10 + 5x
y0
2. y < 8x 5
y -9x + 10
3. y 0
x0
x<2
4. x 4
y > -1
5. 2y + x < 6
3x y > 4
6. x + y > 7
y<0
7. 2x y < 4
x+1>3
8. y x 1
y < 2x 2
9. 3x < 2y
y0
10. x + y < 2
2x y < 3
11. y < 0
x>4
12. 2x + y > 3
xy 2
Algebra 2
Triangles Writing Assignment
Each problem is worth 5 points.
Total = 50 points
Answer each of the following problems. Show all your work.
1. Triangle ABC is congruent to triangle DFE. Find y.
45=5y-10
55=5y
y=11
2. Triangle ABC is congruent to t
Algebra 2
Writing Assignment: Geometry of Circles
Each problem is worth 5 Points
Total Points: 50
p is equal to 102 ?
1) Point C is the center of the circle. What is the measure of ACB if mAB
ACB=102
q is equal to 302 ?
2. Point C is the center of the cir
T-Unit Circle Assignment
Total Points = 64
Each missing coordinate is worth 2 points.
Please fill in the cosine and sine values for all the given angles. Make sure to show your work for
each of the calculations.
Work through the following example, and the
1. f(x)=sin(x)-5
Domain: All real numbers
Range: -6y-4
2. f(x)=2cos(x)
Domain: All real numbers
Range: -2y2
3. f(x)=cos(x-45)
Domain: All real numbers
Range: -1y1
4. f(x)=tan(x)-3
Domain: All real numbers except at x = 90 + n180
Range: All real numbers
5.
Algebra 2
Unit: Exponential and Logarithmic Functions
Section: Graphing Logarithmic Functions and Domain and Range
Graphing Exponential and Logarithmic Functions Assignment
Total Points = 30
Each problem is worth 5 points
Directions: Answer each of the fo
Algebra 2
Writing Assignment: Solving Radical Functions
5 Points Each
Total Points: 50
Solve for x. Show all your work and be sure to check your answers.
1.
2.
3.
4.
5.
2x 3 = 5
sqrt2x-3^2=5^2
2x-3=25
2x-3+3=25+3
2x=28
2x/2=28/2
x=14
Check
7 3x = 1
sqrt2(
Algebra 2
Writing Assignment: Systems of Equations
Each problem is worth 5 Points
Total Points: 50
Solve each system of equations. Show your work.
1. -2x + 3y = 8
3x y = -5
-2x+3y=8 -2x+3y=8
Final answer: (-1, 2)
3(3x-y=-5) 9x-3y=-15
7x-0y=-7
7x/7=-7/7 x=
A.1 Algebra Review
Let letters such as x, y, z, a, b, c represent numbers.
A collection of distinct objects is called a set. The objects in the set are called elements. Typically, set builder notation represents sets. cfw_ x | 0 < x < 5, x is an integer
T
A.2 Geometry Review
Pythagorean Theorem
leg
b
c hypothenuse
a Leg
b=4
hypothenuse c
a=15
Rectangle
w
l
Triangle
h
b
Circle
r
Sphere
r
Rectangular Box
h w l
Volume = lwh
Right Circular Cylinder
r
h
A.3 Polynomials
A monomial in one variable is the product of a constant and a variable raised to a nonnegative integer power. Thus, a monomial is of the form
ax
k
where a is a constant, x is a variable, and k > 0 is an integer.
Monomial
Coefficient
Degree
A.4 Rational Expressions
If we form a quotient ofpolynomials is The quotient of two two polynomials, the result isational expression. called a r called a rational expression.
The polynomial in the denominator of a rational expression cannot be equal to 0
A.6 Equations
An equation in one variable is a statement in which two expressions, at least one containing the variable, are equal. To solve an equation means to find all those values of the variable that result in a true statement.
Procedures that Result
A.7 Complex Numbers; Quadratic Equations with a Negative Discriminant
Complex numbers are numbers of the form a + bi, where a and b are real numbers. The real number a is called the real part of the number a + bi; the real number b is called the imaginary
A.8 Setting Up Equations; Applications
Verbal Description
Language of Math
Mathematical Problem
Real Problem
Solution
Steps for Setting Up Applied Problem
Read the problem. Assign variable(s). Make a list of known facts, translate them into mathematical
Algebra 2
Writing Assignment: Quadrilaterals Challenge Problems
Each problem is worth 5 Points
Total Points: 10
1. The following is a parallelogram. Find x and y using the given information.
AB & DC
AB = 5x - 2y
DC = 4
AD = y
BC = 5 - x
A
B
D
AB=DC
5x-2y=
A.6 Polynomial Division; Synthetic Division
Find the quotient and remainder when 2 x 8 x + x 4 is divided by 2 x 1
Divisor
3 2 2
2 x 1 2 x 8x + x 4
Dividend
2
3
2
x 2 3 2 2 x 1 2 x 8x + x 4
x 2 3 2 2 x 1 2 x 8x + x 4 2x
3
x
x 2 3 2 2 x 1 2 x 8x + x 4 2x
3