A) (-1, -1, -2) B) No solution C) Infinite solutions D) (1, 1, 2) A) (6, 5, -3) B) No solution C) Infinite solutions D) (1, -3, -7)

Similar documents
(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)

SECTION 5.1: Polynomials

( ) = 2 x + 3 B. f ( x) = x 2 25

Quadratic function and equations Quadratic function/equations, supply, demand, market equilibrium

2. If the discriminant of a quadratic equation is zero, then there (A) are 2 imaginary roots (B) is 1 rational root

1) The line has a slope of ) The line passes through (2, 11) and. 6) r(x) = x + 4. From memory match each equation with its graph.

The x-coordinate of the vertex: The equation of the axis of symmetry:

5.1 - Polynomials. Ex: Let k(x) = x 2 +2x+1. Find (and completely simplify) the following: (a) k(1) (b) k( 2) (c) k(a)

Algebra 2 CP Semester 1 PRACTICE Exam

Given the table of values, determine the equation

Homework 1. 3x 12, 61.P (x) = 3t 21 Section 1.2

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i

3.4 The Fundamental Theorem of Algebra

Systems of Equations and Inequalities. College Algebra

Describe in words how the graph of each function below would differ from the graph of f (x).

, a 1. , a 2. ,..., a n

Identify polynomial functions

( ) ( ) ( ) ( ) Given that and its derivative are continuous when, find th values of and. ( ) ( )

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

H-Pre-Calculus Targets Chapter I can write quadratic functions in standard form and use the results to sketch graphs of the function.

Review: complex numbers

Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections 3.1, 3.3, and 3.5

f(x) = 2x + 5 3x 1. f 1 (x) = x + 5 3x 2. f(x) = 102x x

Stamford Public Schools Mathematics Department. CP Algebra II Mid-Term Exam REVIEW. January 2017

Chapter Four Notes N P U2C4

PreCalculus: Semester 1 Final Exam Review

Here are the exams I wrote when teaching Math 115 in Fall 2018 at Ferris State University. Each exam is followed by its solutions.

Question 1. Find the coordinates of the y-intercept for. f) None of the above. Question 2. Find the slope of the line:

CHAPTER 2 POLYNOMIALS KEY POINTS

Section 0.2 & 0.3 Worksheet. Types of Functions

32. Use a graphing utility to find the equation of the line of best fit. Write the equation of the line rounded to two decimal places, if necessary.

Important Math 125 Definitions/Formulas/Properties

UMUC MATH-107 Final Exam Information

2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)

5-7 Solving Quadratic Inequalities. Holt Algebra 2

Note: The zero function f(x) = 0 is a polynomial function. It has no degree and no leading coefficient. Sep 15 2:51 PM

SY14-15 Algebra Exit Exam - PRACTICE Version

Math 101 Final Exam Review Solutions. Eric Schmutz

Subtract 16 from both sides. Divide both sides by 9. b. Will the swing touch the ground? Explain how you know.

Solving Equations Quick Reference

RF2 Unit Test # 2 Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function?

8 Systems of Linear Equations

Intermediate Algebra Summary - Part II

MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

d. What are the steps for finding the y intercepts algebraically?(hint: what is equal to 0?)

Chapter 4E - Combinations of Functions

PRACTICE FINAL , FALL What will NOT be on the final

Catholic Central High School

Section 4.1: Polynomial Functions and Models

Section 4.2 Polynomial Functions of Higher Degree

MTH 65-Steiner Exam #1 Review: , , 8.6. Non-Calculator sections: (Solving Systems), Chapter 5 (Operations with Polynomials)

Functions and Equations

Algebra 2 Honors: Final Exam Review

Algebra 1 End-of-Course Assessment Practice Test with Solutions

A Partial List of Topics: Math Spring 2009

2.1 Quadratic Functions

MATH150-E01 Test #2 Summer 2016 Show all work. Name 1. Find an equation in slope-intercept form for the line through (4, 2) and (1, 3).

MATH 1113 Exam 1 Review

Lecture 6: Sections 2.2 and 2.3 Polynomial Functions, Quadratic Models

1. Write in symbols: (a) The quotient of -6 and the sum of 2 and -8. (b) Now Simplify the expression in part a. 2. Simplify. x 4, given x=-2 and y=4

Reference Material /Formulas for Pre-Calculus CP/ H Summer Packet

5.1 Polynomial Functions

Unit 1 Vocabulary. A function that contains 1 or more or terms. The variables may be to any non-negative power.

May 16, Aim: To review for Quadratic Function Exam #2 Homework: Study Review Materials. Warm Up - Solve using factoring: 5x 2 + 7x + 2 = 0

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

Math 46 Final Exam Review Packet

Math Studio College Algebra

Polynomial Degree Leading Coefficient. Sign of Leading Coefficient

The Graph of a Quadratic Function. Quadratic Functions & Models. The Graph of a Quadratic Function. The Graph of a Quadratic Function

PRINTABLE VERSION. Practice Final. Question 1. Find the coordinates of the y-intercept for 5x 9y + 6 = 0. 2 (0, ) 3 3 (0, ) 2 2 (0, ) 3 6 (0, ) 5

MAT116 Final Review Session Chapter 3: Polynomial and Rational Functions

3. Solve the following inequalities and express your answer in interval notation.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review

QUADRATIC FUNCTIONS AND MODELS

1. Find all relations which are functions. 2. Find all one to one functions.

Lesson 9 Exploring Graphs of Quadratic Functions

3 What is the degree of the polynomial function that generates the data shown below?

Math Exam Jam Solutions. Contents. 1 Linear Inequalities and Absolute Value Equations 2

Sect Polynomial and Rational Inequalities

Chapter 8 ~ Quadratic Functions and Equations In this chapter you will study... You can use these skills...

2012 Texas Essential Knowledge and Skills for Algebra II in Pearson Texas Algebra II

Quadratics. SPTA Mathematics Higher Notes

1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

Algebra 2 CP Semester 1 PRACTICE Exam January 2015

Sample Final Exam. Math S o l u t i o n s. 1. Three points are given: A = ( 2, 2), B = (2, 4), C = ( 4, 0)

Algebra II Assessment. Eligible Texas Essential Knowledge and Skills

Algebra 2 Semester Test Review

UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS

MATH 1314 Test 2 Review

Chapter 2: Polynomial and Rational Functions

Sections 7.1, 7.2: Sums, differences, products of polynomials CHAPTER 7: POLYNOMIALS

PRINCIPLES OF MATHEMATICS 11 Chapter 2 Quadratic Functions Lesson 1 Graphs of Quadratic Functions (2.1) where a, b, and c are constants and a 0

Alg II Syllabus (First Semester)

Algebra 1 Teachers Weekly Assessment Package Units 10. Created by: Jeanette Stein & Phill Adams Algebra 1 Teachers

Integrated Math 10 Quadratic Functions Unit Test January 2013

1.5 F15 O Brien. 1.5: Linear Equations and Inequalities

3.1. QUADRATIC FUNCTIONS AND MODELS

11 /2 12 /2 13 /6 14 /14 15 /8 16 /8 17 /25 18 /2 19 /4 20 /8

Transcription:

Algebra st Semester Final Exam Review Multiple Choice. Write an equation that models the data displayed in the Interest-Free Loan graph that is provided. y = x + 80 y = -0x + 800 C) y = 0x 00 y = 0x + 800. Write an equation that models the data displayed in the Interest-Free Loan graph that is provided. y = x + 0 y = x 0 C y = x + 0 y = - x 0. Solve the following system: x y z 9 x y z x y z 0 (-, -, -) No solution C) Infinite solutions (,, ). Solve the following system: x 6y z x y z x y z (6,, -) No solution C) Infinite solutions (, -, -7). A Major League Baseball stadium sells three types of tickets. Reserved tickets are sold for $0 each, field-level tickets are sold for $0 each, and box seat tickets are sold for $00 each. A graph depicts these three types of tickets sold for their Friday night game. What does the point of intersection represent? When all three ticket prices generate the same revenue. When all three types of tickets have sold the same amount. C) When all three types of tickets cost the same amount. When all three types of tickets reach their maximum revenue

6. Which is the graph of y = (x + ) +? C) 7. Select the graph of: f(x) = x C) 8. The graph of y = x is shown in the standard (x, y) coordinate plane below. For which of the following equations is the graph of the parabola shifted units to the right and units down? y = (x + ) y = (x ) - C) y = (x + ) + y = (x ) + 9. The height of a bridge is given by the equation y = -x + x, where y is the height of the bridge (in miles) and x is the number of miles from the base of the bridge. I. How far from the base of the bridge does the maximum height occur? II. What is the maximum height of the bridge? I. miles I. - miles C) I. miles I. miles II. miles II. miles II. 9 miles II. 6 miles

0. The height of a bridge is given by the equation y = -x + x, where y is the height of the bridge (in miles) and x is the number of miles from the base of the bridge. I. How far from the base of the bridge does the maximum height occur? II. What is the maximum height of the bridge? I. miles I. miles C) I. miles I. miles II. 6 miles II. 08 miles II. miles II. 60 miles. Graph y = x + x + (*hint use x = b ) a C) ) Write an equation of the parabola in vertex form y = a(x h) + k that passes through (0, -) and has vertex (-6, -). y = (x + 6) y = (x 6) C) y = -(x + 6) y = -(x 6). Write an equation of the parabola in vertex form y = a(x h) + k that passes through (-7, -) and has vertex (-, 9). y = (x + ) + 9 y = 6 (x ) + 9 6 C) y = -6(x + ) + 9 y = -6(x ) + 9

. Write an equation of the parabola in intercept form y = a(x p)(x q) that has x intercepts of 9 and and passes through (0, -8). y = (x 9)(x ) y = (x + 9)(x + ) C) y = -(x 9)(x ) y = -(x + 9)(x + ). Write an equation of the parabola in intercept form y = a(x p)(x q) that has x intercepts of and -6 and passes through (, ). y = 0 (x )(x + 6) y = 0 (x + )(x 6) C) y = 0(x )(x + 6) y = 0(x + )(x 6) 6. Find the focus and directrix of the parabola with the equation y = x 0 F : 0, F :,0 F : 0, F : 0, C) D : x D : x D : y D : y 7. Find the inverse of the function: f(x) = x + g(x) = x g(x) = x C) g(x) = x g(x) = x + 8. Find the inverse of the function: f(x) = x g(x) = x g(x) = x 8x + 6 C) g(x) = (x ) g(x) = x + 9. Multiply: ( + 7i)( i) 6 + i 8 i C) + i 8 i 0. Multiply: (- + i) ( + 7i) - + i - C) - i - + i

. Factor: x x 8 (x )(x ) (x + )(x ) C) (x )(x + ) (x + )(x + ). Factor completely: x x 8x x(x 6)(x +) x(x )(x + ) C) (x + 6)(x 6) x (x +)(x ). Factor completely: x 6 x 0x (x )(x + ) (x + )(x ) C) x (x )(x + ) x (x + )(x ). Factor completely: x 6 (x 6)(x + 6) (x 6)(x + 6) C) (x 6)(x + 6) (x )(x + ) ) Factor: 9x 6 (9x-)(9x + ) (x ) C) 9(x )(x + ) (x )(x + ) 6. Solve: x + 6x = 0 0, -6 0, - C) 0, 0, 6 7. Solve: x + 6x = 0 0, 0, - C), 6 -, -6 8. Solve: x + x =, -, C), -, 9. Solve: x x = 6, - -6, C) ⅓, - -⅓,

0. Solve using quadratic formula: x x + 0 = 0 i 8 i 8 C) 8 8 i 8 8. Solve: x + x 6 = 0 7 7 C) i i. Solve: x 9 = - i 9 C) i 6 9. Describe the degree and leading coefficient of the graph of function f(x) below. Odd degree, positive leading coefficient Odd degree, negative leading coefficient C) Even degree, positive leading coefficient Even degree, negative leading coefficient. Simplify: ( x 8x) ( x + x ) -x x + -x + x C) x x x x +. Simplify: (6 x x ) ( x x ) 8x x + 8x 6 x + C) x + x + x 6 + x +

6. Simplify: (x )(x x + ) x 9x - 0 x 7x + x 0 C) x + x + x + 0 x + 7. Divide: (x x 6x 8x ) (x ) x + x + x + x x x C) x 9x + x 7 + 0 x x + x + + x 8. Divide: (x + x 8x + ) (x + ) C) x 7x x x 7x x x 6 x x 7 x 6 x x 7x x 9. Solve (where do the graphs intersect) y = x + and y = x x + (, -) (, 7) (-, ) C) (-, ) (, 6) (-, ) 0. Given one factor of f(x) = x + x x is (x + ), find the other factors. (x )(x 7) (x + )(x + 7) C) (x + )(x 7) (x )(x + 7). Given one factor of x + x x is x + find the other factors. (x + )(x ) (x )(x + ) C) (x + )(x ) (x + 6)(x ). Find the zeros of the function: y = (x + 7)(x + )(x ), -7, -,, 7,,, - C) -7, -, -7, -,. Find the zeros of this function: y = x(x + )(x )(x ) -,, 0 -,, C) -,, 0, -,,

. If x is a factor of x 0x k, what is the value of k? -8 8 C) 7-7 E). If (x ) is a factor of x x + k, what is the value of k? 6 C) -9 - E) 6. Write the third degree polynomial function that would have the given zeros: -, -i x ix x + 8i x + x + 6x + C) x + ix + x + 8i x x + 6x 7. Write the third degree polynomial function that would have the given zeros:, i x + x - x + x + x - x + C) x x + x - x +x - 7 8. Simplify: + 8 + 7 77 C) 7 7 + 9. Simplify: 8 7 7 0 9 9 C) 8 0. Simplify: 0 i 0 0 C) 0i 0. Simplify: 7-7i i 7 C) 6i 6i. Simplify: (7a b 7 c) 7a 8 b c 9a 6 b 9 c C) a 8 b c 9a 8 b c. Simplify: (-r s t) 6r 7 s 6 t 6r s 8 t C) -r 7 s 6 t r s 8 t

. Simplify: 6x y 9x y y x x y y C) x x7 y 8 6 9x y. Simplify: x y 8y x x 8y x C) 8y x 8 y 6. Write x using exponents. x x C) x x 7. Write 7 c using exponents 7 c 7c C) 7 c c 8. Simplify: 7 8 6 C) 9 6 9. Simplify: 7.8 9 C) 8 6 60. Simplify using the properties of exponents: x x x x C) x 7 6 x 6. Simplify using properties of exponents: x x 0 0 9 0 x x C) x x 7 6. Solve: x 9 + = 0 7 C) 07 6. Solve: x 6 78 C) 0 6

6. f(x) = x x + g(x) = -6x + x find (f g)(x) 9x + x + 9x + 6x + C) x + x + 9 9x 6x + 9 6. If f(x) = -x + 7 and g(x) = x find (f*g)(-) - -7 C) - g(8) 66. If f(x) = x x and g(x) = x what is the value of? f ( ) C) 6 9 9 g(9) 67. If f(x) = x x + 7 and g(x) = - x what is the value of? f ( ) - C) 7 68. Graph: g(x) = x E) C)