Download AH Quarterly 3 Review Packet

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Algebra 1 Honors Quarterly #3 Review Packet
Lessons 7.1 and 7.2 Multiplication & Division Properties of Exponents
Simplify each expression. Your answer should only contain positive exponents.
a.) (-3x2y)3(11x3y5)2
b.)
12 x8 y 7
 4x
2
y 6 
2
Lesson 7.3 Rational Exponents
Write each expression in radical form
a.) (5 x)
1
2
b.)
4m
1
2
c.) z
2
3
Lesson 7.4 Scientific Notation
Evaluate. Express each answer in scientific notation & standard form.
a.)
 3.4 10  5 10 
3
4
 4.9 10 
 2.5 10 
3
b.)
4
Lessons 7.5 & 7.6 Exponential Functions (Growth & Decay)
a.) The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in
1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. Write a
function that models the value of the car over time. The auction took place in 2004. What was the
approximate value of the car at that time?
b.) The number of acres of Ponderosa pine forests decreased in the western United States from 1963 to
2002 by 0.5% annually. In 1963, there were about 41 million acres of Ponderosa pine forests. Write a
function that models the number of acres of Ponderosa pine forests in the western United States over
time. To the nearest tenth, about how many millions of acres of Ponderosa pine forests were there in
2002?
Lesson 7.7 Geometric Sequences as Exponential Functions.
Write a rule for the nth term of each geometric sequence. Then find a7 .
a.) 1, -5, 25, -125, ...
b.) 13, 26, 52, 104, …
Lesson 7.8 Recursive Formulas
Write the first five terms of each sequence.
a.) a1  5, an  an1  5; n  2
b.) a1  1, an  2an1; n  2
Lesson 8.1 Adding & Subtracting Polynomials
Find each sum or difference.
a.)  4m 2  m  2   (3m 2  10m  7)
b.)
Lessons 8.2 & 8.3 Multiplying Polynomials
Simplify each expression.
a.) x 2 (7 x  5)  (2 x  6)( x  1)
b.)  6 z 2  z  1  9 z  5 
Lesson 8.4 Special Products
Find each product.
2
a.)  3 x  4 
b.)  5 x  2 y 
2
 4d  6d
3
 3d 2    9d 3  7d  2 
c.)  2 x  1 2 x  1
Lesson 8.5 Using the Distributive Property
Factor or solve.
a.) 45r 3  15r 2
b.) 12a 2  3a  8a  2
c.) 9 x 2  x  0
Lesson 8.6 Solving x2 + bx + c = 0
Factor or solve.
a.) x 2  9 x  14
b.) a 2  6a  16
c.) x 2  3x  18
Lesson 8.7 Solving ax2 + bx + c = 0
Factor or solve.
a.) 2 x 2  7 x  3
b.) 3a 2  14a  5
c.) p (20 p  3)  2
d.) A baseball player hits a baseball into the air with an initial vertical velocity of 72 feet per second. The
player hits the ball from a height of 3 feet. Write an equation that gives the baseball’s height as a function of the
time (in seconds) after it is hit. After how many seconds is the baseball 84 feet above the ground?
e.) A person throws a ball upward from a 506 foot tall building. The ball’s height h in feet after t seconds is
given by the equation h = -16t2 + 48t + 506. The ball lands on a balcony that is 218 feet above the ground. How
many seconds was it in the air?
Lesson 8.8 Differences of Squares & 8.9 Perfect Squares
Factor each polynomial completely.
a.) 4 y 6  16 y 4
b.) h3  4h 2  25h  100
c.) 9 x 2  12 x  4
Lessons 9.1 Graphing Quadratic Functions & 9.2 Solving Quadratic Equations by Graphing
Use the f(x) = x2 + 4x + 3 to answer the following questions.
a.) Write an equation for the axis of symmetry.
b.) Find the vertex & state whether it is a
maximum or a minimum.
c.) State the domain & range of the function.
d.) Graph the function.
x
y
e.) What are the roots/zeros/solutions of this equation?
Lesson 9.3 Transformations of Quadratic Functions
Describe how the graph of each function is related to the graph of f(x) = x2.
a.) g(x) = (x – 5)2 + 4
b.) h(x) = -2x2 – 3
Lesson 9.4 Solving Quadratic Equations by Completing the Square
Find the value of c that makes the expression a perfect square trinomial.
a.) x2 + 6x + c
b.) x2 + 12x + c
Solve by completing the square. Round to the nearest hundredth if necessary.
c.) x2 – 16x = -15
d.) 2x2 + 20x – 8 = 0