Math 4: Advanced Algebra Ms. Sheppard-Brick A Quiz Review LT ,
|
|
- Lesley Mitchell Lindsey
- 5 years ago
- Views:
Transcription
1 4A Quiz Review LT , Key Facts Know how to use the formulas for projectile motion. The formulas will be given to you on the quiz, but you ll need to know what the variables stand for Horizontal: x f = x i + v xi t Vertical: y f = y i + v yi t gt 2 v yf = v yi + gt Variable Meaning Variable Meaning x i Initial horizontal position = 0 m v xi Initial horizontal velocity x f Final horizontal position v yi Initial vertical velocity y i Initial vertical position g Gravitational Constant = 10 m s! y f Final vertical position t Time When a projectile is shot at an angle, use vector components to find the initial horizontal and vertical velocity. To factor a polynomial, first factor out any common factors, then use the box method to factor the quadratic. o When you have a nonmonic quadratic ax 2 + bx + c velocity ( ), the numbers to fill in your box must multiply to a c and add to b To solve a quadratic equation, make sure one side of the equation is equal to 0. Then factor the quadratic and set all factors equal to 0. Solve all of the new equations for x. θ v xi v yi Make sure your homework is up-to-date: #1-30 in your yellow workbook should be done. Learning Targets 3.4 I can add and subtract vectors and multiply them by a constant by drawing on a grid. 3.5 I can find components of vectors. 3.6 I can add and subtract vectors and multiply them by a constant using their components 3.7 I can find the area of any triangle using trigonometry. 3.8 I can use the Law of Sines to solve triangles 3.9 I can use the Law of Cosines to solve triangles I can choose the appropriate tool(s) to solve triangles. 4.1 I can solve projectile motion problems and interpret the results. 4.2 I can factor monic quadratic expressions, and solve their equations using the Zero Product Property. 4.3 I can factor non-monic quadratic expressions, solve their equations using the Zero Product Property, and use the results to solve projectile motion problems. 1
2 Practice 1. A ball is kicked with a velocity of 8.0 m/s at an angle of 20 from a cliff 80 meters high. Variable Known? Variable Known? x i v xi x f v yi y i g y f t a. How high is the ball after 1.5 seconds? b. Assume the ball is in the air for 4 seconds. How far from the base of the cliff (horizontally) will the ball hit the ground? c. How long does it take for the ball to hit the ground? Solve an equation by graphing on your calculator to answer this question. 2
3 2. A baseball is thrown from a height of 8 meters at an angle of with an initial velocity of 5 m/s. Variable Known? Variable Known? x i v xi x f y i y f v yi g t a. How high is the ball after 1 second? b. What is the vertical velocity of the ball after 1 second? c. How long does it take for the ball to hit the ground? Factor and solve an equation to answer this question. 3
4 3. Factor the following expressions as completely as possible. Be sure to look for common factors first. a. x! + 9x + 8 b. 2x! 16x + 30 c. x! + 20x d. 2x! 5x + 2 e. 6x! 13x + 6 f. 3x! 14x! 5x 4
5 4. Solve the following equations by factoring and using the ZPP. Again, look for common factors first. a. x! 7x + 6 = 0 b. 4x! + 12x 7 = 0 c. x! 7x 18 = 0 d. 2x! + 18x! + 28x = 0 e. x! + 16 = 8x f. 6a! 4a = 10 5
6 Practice 5. Find the area of the triangle below. Show your work Use the Law of Sines to find side AB. Show your work. B 13.5 A C 7. Use the Law of Cosines to find m B. Show your work. B A 8.2 C 6
7 8. Solve the triangle (find all the missing sides and angles). Show your work. C 5.8 A B 7
8 Practice 9. Use the vectors shown below to find the following sums and products. Show your work and use a separate color for your answer vector. Don t forget arrows! a. u r w ur b. 3* a r 8
9 10. Find the vertical and horizontal components of each vector shown. Show your work. a. b. 6 m a m 22 b Show work for part a here: Show work for part b here: Horizontal a r b r Vertical 11. Show all your work for the following sums and products. a) Find the horizontal and vertical components of a + b Horizontal: Vertical: b) Find the horizontal and vertical components of b a Horizontal: Vertical: c) Find the horizontal and vertical components of 3 a Horizontal: Vertical: 9
10 Answers 1 a m b m c seconds 2. a. 6 m b. -7 m/s c. 1.6 seconds 3. a. (x + 1)(x + 8) b. 2(x 5)(x 3) c. (x + 10)(x + 10) d. (2x 1)(x 2) e. (3x 2)(2x 3) f. x(3x + 1)(x 5) 4. a. x = 6, 1 b. x = 3.5, 0.5 c. x = 9, 2 d. x = 0, 7, 2 e. x = 4 5. Area = f. a = 1,!! 6. AB = m B = m C = , m B = , AC = a. b. 10. Horizontal Vertical 11. a. H: , V: b. H: 3.468, V: c. H: , V: a r b r
Review for Quarter 3 Cumulative Test
Review for Quarter 3 Cumulative Test I. Solving quadratic equations (LT 4.2, 4.3, 4.4) Key Facts To factor a polynomial, first factor out any common factors, then use the box method to factor the quadratic.
More informationMath Learning Center Boise State 2010, Quadratic Modeling STEM 10
Quadratic Modeling STEM 10 Today we are going to put together an understanding of the two physics equations we have been using. Distance: Height : Recall the variables: o acceleration o gravitation force
More informationMath 4: Advanced Algebra Ms. Sheppard-Brick B Quiz Review Sections and
3B Quiz Review Sections 2.8 2.10 and 3.1 3.6 Key Facts To add vectors, place the tail of one vector (the side without the arrow) at the head of the other vector (the side with the arrow). Draw the vector
More informationStep 2: Find the coordinates of the vertex (h, k) Step 5: State the zeros and interpret what they mean. Step 6: Make sure you answered all questions.
Chapter 4 No Problem Word Problems! Name: Algebra 2 Period: 1 2 3 4 5 6 A. Solving from Standard Form 1. A ball is thrown so its height, h, in feet, is given by the equation h = 16t! + 10t where t is the
More informationPrecalculus 2 Section 10.6 Parametric Equations
Precalculus 2 Section 10.6 Parametric Equations Parametric Equations Write parametric equations. Graph parametric equations. Determine an equivalent rectangular equation for parametric equations. Determine
More informationSection 5: Quadratics
Chapter Review Applied Calculus 46 Section 5: Quadratics Quadratics Quadratics are transformations of the f ( x) x function. Quadratics commonly arise from problems involving area and projectile motion,
More informationSince a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector: Horizontal Vertical
Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector: Horizontal Vertical With no gravity the projectile would follow the straight-line path (dashed line).
More informationLesson 3.1 Vertices and Intercepts. Important Features of Parabolas
Lesson 3.1 Vertices and Intercepts Name: _ Learning Objective: Students will be able to identify the vertex and intercepts of a parabola from its equation. CCSS.MATH.CONTENT.HSF.IF.C.7.A Graph linear and
More informationSample: Do Not Reproduce QUAD4 STUDENT PAGES. QUADRATIC FUNCTIONS AND EQUATIONS Student Pages for Packet 4: Quadratic Functions and Applications
Name Period Date QUADRATIC FUNCTIONS AND EQUATIONS Student Pages for Packet 4: Quadratic Functions and Applications QUAD 4.1 Vertex Form of a Quadratic Function 1 Explore how changing the values of h and
More informationTwo-Dimensional Motion
Two-Dimensional Motion Objects don't always move in a straight line. When an object moves in two dimensions, we must look at vector components. The most common kind of two dimensional motion you will encounter
More information2-D Motion: Projectiles at an Angle Physics
-D Motion: Projectiles at an Angle Physics Be sure your calculator is set to DEGREES! I. Trigonometry Reiew: 1. Find the alues of the following functions. (Use scientific calculator) i) sin45º ii) cos40º
More informationDo you need a worksheet or a copy of the teacher notes? Go to
Name Period Day Date Assignment (Due the next class meeting) Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday
More informationSemester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.
Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right
More informationStudent Exploration: Quadratics in Polynomial Form
Name: Date: Student Exploration: Quadratics in Polynomial Form Vocabulary: axis of symmetry, parabola, quadratic function, vertex of a parabola Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
More informationPreview. Two-Dimensional Motion and Vectors Section 1. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion
Two-Dimensional Motion and Vectors Section 1 Preview Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Two-Dimensional Motion and Vectors
More informationEdexcel Mechanics 2 Kinematics of a particle. Section 1: Projectiles
Edecel Mechanics Kinematics of a particle Section 1: Projectiles Notes and Eamples These notes contain subsections on Investigating projectiles Modelling assumptions General strateg for projectile questions
More informationPractice problems from old exams for math 233
Practice problems from old exams for math 233 William H. Meeks III October 26, 2012 Disclaimer: Your instructor covers far more materials that we can possibly fit into a four/five questions exams. These
More informationSPH3U1 Lesson 12 Kinematics
SPH3U1 Lesson 12 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the motion of an object thrown at arbitrary angles through the air. Describe the horizontal and vertical motions of
More informationVector Decomposition
Projectile Motion AP Physics 1 Vector Decomposition 1 Coordinate Systems A coordinate system is an artificially imposed grid that you place on a problem. You are free to choose: Where to place the origin,
More informationQuadratic Functions CHAPTER. 1.1 Lots and Projectiles Introduction to Quadratic Functions p. 31
CHAPTER Quadratic Functions Arches are used to support the weight of walls and ceilings in buildings. Arches were first used in architecture by the Mesopotamians over 4000 years ago. Later, the Romans
More information3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS
3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS Finding the Zeros of a Quadratic Function Examples 1 and and more Find the zeros of f(x) = x x 6. Solution by Factoring f(x) = x x 6 = (x 3)(x + )
More informationQuadratic Functions (Section 2-1)
Quadratic Functions (Section 2-1) Section 2.1, Definition of Polynomial Function f(x) = a is the constant function f(x) = mx + b where m 0 is a linear function f(x) = ax 2 + bx + c with a 0 is a quadratic
More informationYou ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46
Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often
More informationYou can take the arccos of both sides to get θ by itself.
.7 SOLVING TRIG EQUATIONS Example on p. 8 How do you solve cos ½ for? You can tae the arccos of both sides to get by itself. cos - (cos ) cos - ( ½) / However, arccos only gives us an answer between 0
More information3x 2 + 7x + 2. A 8-6 Factor. Step 1. Step 3 Step 4. Step 2. Step 1 Step 2 Step 3 Step 4
A 8-6 Factor. Step 1 3x 2 + 7x + 2 Step 2 Step 3 Step 4 3x 2 + 7x + 2 3x 2 + 7x + 2 Step 1 Step 2 Step 3 Step 4 Factor. 1. 3x 2 + 4x +1 = 2. 3x 2 +10x + 3 = 3. 3x 2 +13x + 4 = A 8-6 Name BDFM? Why? Factor.
More informationALGEBRA 2 W/ TRIGONOMETRY MIDTERM REVIEW
Name: Block: ALGEBRA W/ TRIGONOMETRY MIDTERM REVIEW Algebra 1 Review Find Slope and Rate of Change Graph Equations of Lines Write Equations of Lines Absolute Value Functions Transformations Piecewise Functions
More informationLab 4 Projectile Motion
b Lab 4 Projectile Motion What You Need To Know: x = x v = v v o ox = v + v ox ox + at 1 t + at + a x FIGURE 1 Linear Motion Equations The Physics So far in lab you ve dealt with an object moving horizontally
More informationLecture 5. If, as shown in figure, we form a right triangle With P1 and P2 as vertices, then length of the horizontal
Distance; Circles; Equations of the form Lecture 5 y = ax + bx + c In this lecture we shall derive a formula for the distance between two points in a coordinate plane, and we shall use that formula to
More informationAlgebra II Quadratic Functions and Equations - Extrema Unit 05b
Big Idea: Quadratic Functions can be used to find the maximum or minimum that relates to real world application such as determining the maximum height of a ball thrown into the air or solving problems
More informationQuadratic Functions, Part 1
Quadratic Functions, Part 1 A2.F.BF.A.1 Write a function that describes a relationship between two quantities. A2.F.BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation
More informationRationalize the Denominator: Get the root the denom. Multiply by more roots to cancel. w/ and w/
Name Unit 2 Day 1 Simplifying Square Roots Properties: 1. = Examples: 2. = 12 4 9 4 9 4 + 9 4 + 9 Rationalize the Denominator: Get the root the denom. Multiply by more roots to cancel. w/ and w/ Conjugate:
More information(ii) Calculate the maximum height reached by the ball. (iii) Calculate the times at which the ball is at half its maximum height.
1 Inthis question take g =10. A golf ball is hit from ground level over horizontal ground. The initial velocity of the ball is 40 m s 1 at an angle α to the horizontal, where sin α = 0.6 and cos α = 0.8.
More informationOCR Maths M2. Topic Questions from Papers. Projectiles
OCR Maths M2 Topic Questions from Papers Projectiles PhysicsAndMathsTutor.com 21 Aparticleisprojectedhorizontallywithaspeedof6ms 1 from a point 10 m above horizontal ground. The particle moves freely under
More informationWriting Equivalent Forms of Quadratic Functions Adapted from Walch Education
Writing Equivalent Forms of Quadratic Functions Adapted from Walch Education Recall The standard form, or general form, of a quadratic function is written as f(x) = ax 2 + bx + c, where a is the coefficient
More information7-5 Parametric Equations
3. Sketch the curve given by each pair of parametric equations over the given interval. Make a table of values for 6 t 6. t x y 6 19 28 5 16.5 17 4 14 8 3 11.5 1 2 9 4 1 6.5 7 0 4 8 1 1.5 7 2 1 4 3 3.5
More informationYou ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46
Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often
More informationCP1 Math 2 Cumulative Exam Review
Name February 9-10, 2016 If you already printed the online copy of this document, there are answer corrections on pages 4 and 8 (shaded). Deductive Geometry (Ch. 6) Writing geometric proofs Triangle congruence
More information20/06/ Projectile Motion. 3-7 Projectile Motion. 3-7 Projectile Motion. 3-7 Projectile Motion
3-7 A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola. 3-7 It can be understood by analyzing the horizontal and vertical motions separately.
More informationUnit 2: Functions and Graphs
AMHS Precalculus - Unit 16 Unit : Functions and Graphs Functions A function is a rule that assigns each element in the domain to exactly one element in the range. The domain is the set of all possible
More information2.3 Projectile Motion
Figure 1 An Olympic ski jumper uses his own body as a projectile. projectile an object that moves along a two-dimensional curved trajectory in response to gravity projectile motion the motion of a projectile
More informationSummer Review for Students Entering Pre-Calculus with Trigonometry. TI-84 Plus Graphing Calculator is required for this course.
Summer Review for Students Entering Pre-Calculus with Trigonometry 1. Using Function Notation and Identifying Domain and Range 2. Multiplying Polynomials and Solving Quadratics 3. Solving with Trig Ratios
More informationContents 10. Graphs of Trigonometric Functions
Contents 10. Graphs of Trigonometric Functions 2 10.2 Sine and Cosine Curves: Horizontal and Vertical Displacement...... 2 Example 10.15............................... 2 10.3 Composite Sine and Cosine
More informationIntroduction to Graphing Quadratics
Graphing Quadratic Functions Table of Contents 1. Introduction to Graphing Quadratics (19.1) 2. Graphing in Vertex Form Using Transformations (19.2) 3. Graphing in Standard Form (19.3) 4. Graphing in Factored
More informationSemester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.
Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right
More informationTRIGONOMETRY. Meaning. Dear Reader
TRIGONOMETRY Dear Reader In your previous classes you have read about triangles and trigonometric ratios. A triangle is a polygon formed by joining least number of points i.e., three non-collinear points.
More informationChapter 3 Practice Test
1. Complete parts a c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b. Make a table of values that includes the vertex.
More informationCHAPTER 2. Polynomials and Rational functions
CHAPTER 2 Polynomials and Rational functions Section 2.1 (e-book 3.1) Quadratic Functions Definition 1: A quadratic function is a function which can be written in the form (General Form) Example 1: Determine
More informationQuiz 1 Review: Quadratics through 4.2.2
Name: Class: Date: ID: A Quiz 1 Review: Quadratics 4.1.1 through 4.2.2 Graph each function. How is each graph a translation of f(x) = x 2? 1. y = x 2 + 2 2. y = (x 3) 2 3. y = (x + 3) 2 + 4 4. Which is
More informationProjectile Motion SECTION 3. Two-Dimensional Motion. Objectives. Use of components avoids vector multiplication.
Projectile Motion Key Term projectile motion Two-Dimensional Motion Previously, we showed how quantities such as displacement and velocity were vectors that could be resolved into components. In this section,
More informationPolynomial and Rational Functions. Copyright Cengage Learning. All rights reserved.
2 Polynomial and Rational Functions Copyright Cengage Learning. All rights reserved. 2.1 Quadratic Functions Copyright Cengage Learning. All rights reserved. What You Should Learn Analyze graphs of quadratic
More informationIntroduction to Trigonometry
NAME COMMON CORE GEOMETRY- Unit 6 Introduction to Trigonometry DATE PAGE TOPIC HOMEWORK 1/22 2-4 Lesson 1 : Incredibly Useful Ratios Homework Worksheet 1/23 5-6 LESSON 2: Using Trigonometry to find missing
More informationLesson 20: Graphing Quadratic Functions
Opening Exercise 1. The science class created a ball launcher that could accommodate a heavy ball. They moved the launcher to the roof of a 23-story building and launched an 8.8-pound shot put straight
More informationSlide 2 / 222. Algebra II. Quadratic Functions
Slide 1 / 222 Slide 2 / 222 Algebra II Quadratic Functions 2014-10-14 www.njctl.org Slide 3 / 222 Table of Contents Key Terms Explain Characteristics of Quadratic Functions Combining Transformations (review)
More informationSummer Review for Students Entering Pre-Calculus with Trigonometry. TI-84 Plus Graphing Calculator is required for this course.
1. Using Function Notation and Identifying Domain and Range 2. Multiplying Polynomials and Solving Quadratics 3. Solving with Trig Ratios and Pythagorean Theorem 4. Multiplying and Dividing Rational Expressions
More informationTable of Contents Volume I
Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3rd Edition Sullivan SOLUTIONS MANUAL Full download at: https://testbankreal.com/download/precalculus-concepts-throughfunctions-a-unit-circle-approach-to-trigonometry-3rd-edition-sullivansolutions-manual/
More informationSolving Simple Quadratics 1.0 Topic: Solving Quadratics
Ns Solving Simple Quadratics 1.0 Topic: Solving Quadratics Date: Objectives: SWBAT (Solving Simple Quadratics and Application dealing with Quadratics) Main Ideas: Assignment: Square Root Property If x
More informationAlgebra 1 Notes Quarter
Algebra 1 Notes Quarter 3 2014 2015 Name: ~ 1 ~ Table of Contents Unit 9 Exponent Rules Exponent Rules for Multiplication page 6 Negative and Zero Exponents page 10 Exponent Rules Involving Quotients page
More informationCatholic Central High School
Catholic Central High School Algebra II Practice Examination II Instructions: 1. Show all work on the test copy itself for every problem where work is required. Points may be deducted if insufficient or
More informationLesson 8 Introduction to Quadratic Functions
Lesson 8 Introduction to Quadratic Functions We are leaving exponential and logarithmic functions behind and entering an entirely different world. As you work through this lesson, you will learn to identify
More informationMid-Chapter Quiz: Lessons 4-1 through 4-4
1. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex for f (x) = 2x 2 + 8x 3. Then graph the function by making a table of values. 2. Determine whether f (x)
More informationLesson 17: Graphing Quadratic Functions from Factored Form,
: Graphing Quadratic Functions from Factored Form, ff(xx) = aa(xx mm)(xx nn) 2 Opening Exercise 1. Solve the following equation. xx 2 + 6xx 40 = 0 0-12 -10-8 -6-4 -2-2 0 2 4 6-4 -6-8 -10 2. Consider the
More informationTypes of Functions Here are six common types of functions and examples of each. Linear Quadratic Absolute Value Square Root Exponential Reciprocal
Topic 2.0 Review Concepts What are non linear equations? Student Notes Unit 2 Non linear Equations Types of Functions Here are six common types of functions and examples of each. Linear Quadratic Absolute
More informationCollege Algebra. Quadratic Functions and their Graphs. Dr. Nguyen October 12, Department of Mathematics UK
College Algebra Quadratic Functions and their Graphs Dr. Nguyen nicholas.nguyen@uky.edu Department of Mathematics UK October 12, 2018 Agenda Quadratic functions and their graphs Parabolas and vertices
More informationSPH3U1 Lesson 09 Kinematics
VECTORS IN TWO-DIMENSIONS LEARNING GOALS Students will Draw vector scale diagrams to visualize and analyze the nature of motion in a plane. Analyze motion by using scale diagrams to add vectors. Solve
More informationTest 3 review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Test 3 review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Approximate the coordinates of each turning point by graphing f(x) in the standard viewing
More informationMathematical Techniques Chapter 10
PART FOUR Formulas FM 5-33 Mathematical Techniques Chapter 10 GEOMETRIC FUNCTIONS The result of any operation performed by terrain analysts will only be as accurate as the measurements used. An interpretation
More informationSolve the following system of equations using either substitution or elimination:
Mathematics 04 Final Eam Review Topic : Solving a system of equations in three variables. 009 Solve the following system of equations using either substitution or elimination: + y + z 0 + y z y + z Select
More informationChapter 3: Vectors & 2D Motion. Brent Royuk Phys-111 Concordia University
Chapter 3: Vectors & 2D Motion Brent Royuk Phys-111 Concordia University Vectors What is a vector? Examples? Notation:! a or! a or a 2 Vector Addition Graphical Methods Triangle, parallelogram, polygon
More informationLesson Title 2: Problem TK Solving with Trigonometric Ratios
Part UNIT RIGHT solving TRIANGLE equations TRIGONOMETRY and inequalities Lesson Title : Problem TK Solving with Trigonometric Ratios Georgia Performance Standards MMG: Students will define and apply sine,
More informationThe ball is at a height of 8 m at x = and x = b. Substitute that value into the equation:
MPMD Day : Intro to Quadratic Equations... and solving them graphically. Task : The Quadratic Equation Warm-Up: The equation h = -0.05x + x represents the height, h, in metres of one kick of a soccer ball
More information6. Find the equation of the plane that passes through the point (-1,2,1) and contains the line x = y = z.
Week 1 Worksheet Sections from Thomas 13 th edition: 12.4, 12.5, 12.6, 13.1 1. A plane is a set of points that satisfies an equation of the form c 1 x + c 2 y + c 3 z = c 4. (a) Find any three distinct
More informationOpenStax-CNX module: m Quadratic Functions. OpenStax OpenStax Precalculus. Abstract
OpenStax-CNX module: m49337 1 Quadratic Functions OpenStax OpenStax Precalculus This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section, you
More informationContents 10. Graphs of Trigonometric Functions
Contents 10. Graphs of Trigonometric Functions 2 10.2 Sine and Cosine Curves: Horizontal and Vertical Displacement...... 2 Example 10.15............................... 2 10.3 Composite Sine and Cosine
More informationMPM 2DI EXAM REVIEW. Monday, June 25, :30 am 10:00 am ROOM 116 * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED *
NAME: MPM DI EXAM REVIEW Monday, June 5, 018 8:30 am 10:00 am ROOM 116 * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED * Please Note: Your final mark in this course will be calculated as the better
More informationQUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x p 2 16p. 3. 6x 2 13x 5 4.
QUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x 2 48 2. 25p 2 16p 3. 6x 2 13x 5 4. 9x 2 30x + 25 5. 4x 2 + 81 6. 6x 2 14x + 4 7. 4x 2 + 20x 24 8. 4x
More informationName Period. (b) Now measure the distances from each student to the starting point. Write those 3 distances here. (diagonal part) R measured =
Lesson 5: Vectors and Projectile Motion Name Period 5.1 Introduction: Vectors vs. Scalars (a) Read page 69 of the supplemental Conceptual Physics text. Name at least 3 vector quantities and at least 3
More informationLesson 6 - Practice Problems
Lesson 6 - Practice Problems Section 6.1: Characteristics of Quadratic Functions 1. For each of the following quadratic functions: Identify the coefficients a, b and c. Determine if the parabola opens
More informationSPH3U1 Lesson 05 Kinematics
VECTORS IN TWO-DIMENSIONS LEARNING GOALS Students will Draw vector scale diagrams to visualize and analyze the nature of motion in a plane. Analyze motion by using scale diagrams to add vectors. Solve
More informationPRECALCULUS MATH Trigonometry 9-12
1. Find angle measurements in degrees and radians based on the unit circle. 1. Students understand the notion of angle and how to measure it, both in degrees and radians. They can convert between degrees
More informationProjectile Motion. Honors Physics
Projectile Motion Honors Physics What is projectile? Projectile -Any object which projected by some means and continues to moe due to its own inertia (mass). Projectiles moe in TWO dimensions Since a projectile
More informationAdding vectors. Let s consider some vectors to be added.
Vectors Some physical quantities have both size and direction. These physical quantities are represented with vectors. A common example of a physical quantity that is represented with a vector is a force.
More informationUNIT 3 Quadratic Relations JOURNAL
1 U n i t 10D Date: Name: UNIT Quadratic Relations JOURNAL Big idea/learning Goals Not everything in real life can be modeled by a linear relations which look like:. Non-linear relations can look like
More informationWarm Up. Factor the following numbers and expressions. Multiply the following factors using either FOIL or Box Method
Warm Up Factor the following numbers and expressions 1. 36 2. 36x 3 + 48x 2 + 24x Multiply the following factors using either FOIL or Box Method 3. (3x 2)(x 1) 4. (x 2)(x + 3) Objectives Recognize standard
More informationWHAT ARE THE PARTS OF A QUADRATIC?
4.1 Introduction to Quadratics and their Graphs Standard Form of a Quadratic: y ax bx c or f x ax bx c. ex. y x. Every function/graph in the Quadratic family originates from the parent function: While
More informationFalling Balls. Names: Date: About this Laboratory
Falling Balls Names: Date: About this Laboratory In this laboratory,1 we will explore quadratic functions and how they relate to the motion of an object that is dropped from a specified height above ground
More informationNO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED
Algebra II (Wilsen) Midterm Review NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED Remember: Though the problems in this packet are a good representation of many of the topics that will be on the exam, this
More informationWelcome Back from March Break! (Easter break in 2 weeks + 4 days if you care)
Welcome Back from March Break! (Easter break in 2 weeks + 4 days if you care) Events for the Week: Mon: Lesson 2.8 Solving Quadratic Equations: Word Problems (pretty much the same as Gr. 10) Please show
More informationThen you can create an object like a sphere or a box. A sphere is easy: And here s what you see:
Visual Python Visual Python is a library of 3D objects you can program in Python to do all kinds of cool stuff using the tools you ve learned. Download and install the version for your computer at Vpython.org.
More informationII. Functions. 61. Find a way to graph the line from the problem 59 on your calculator. Sketch the calculator graph here, including the window values:
II Functions Week 4 Functions: graphs, tables and formulas Problem of the Week: The Farmer s Fence A field bounded on one side by a river is to be fenced on three sides so as to form a rectangular enclosure
More informationChapter Nine Notes SN P U1C9
Chapter Nine Notes SN P UC9 Name Period Section 9.: Applications Involving Right Triangles To evaluate trigonometric functions with a calculator, there are a few important things to know: On your calculator,
More information2. The diagram shows part of the graph of y = a (x h) 2 + k. The graph has its vertex at P, and passes through the point A with coordinates (1, 0).
Quadratics Vertex Form 1. Part of the graph of the function y = d (x m) + p is given in the diagram below. The x-intercepts are (1, 0) and (5, 0). The vertex is V(m, ). (a) Write down the value of (i)
More information6.3 Creating and Comparing Quadratics
6.3 Creating and Comparing Quadratics Just like with exponentials and linear functions, to be able to compare quadratics, we ll need to be able to create equation forms of the quadratic functions. Let
More informationQUADRATIC FUNCTIONS: MINIMUM/MAXIMUM POINTS, USE OF SYMMETRY. 7.1 Minimum/Maximum, Recall: Completing the square
CHAPTER 7 QUADRATIC FUNCTIONS: MINIMUM/MAXIMUM POINTS, USE OF SYMMETRY 7.1 Minimum/Maximum, Recall: Completing the square The completing the square method uses the formula x + y) = x + xy + y and forces
More informationGCSE-AS Mathematics Bridging Course. Chellaston School. Dr P. Leary (KS5 Coordinator) Monday Objectives. The Equation of a Line.
GCSE-AS Mathematics Bridging Course Chellaston School Dr (KS5 Coordinator) Monday Objectives The Equation of a Line Surds Linear Simultaneous Equations Tuesday Objectives Factorising Quadratics & Equations
More informationChapter 2: Polynomial and Rational Functions Power Standard #7
Chapter 2: Polynomial and Rational s Power Standard #7 2.1 Quadratic s Lets glance at the finals. Learning Objective: In this lesson you learned how to sketch and analyze graphs of quadratic functions.
More information+ bx + c = 0, you can solve for x by using The Quadratic Formula. x
Math 33B Intermediate Algebra Fall 01 Name Study Guide for Exam 4 The exam will be on Friday, November 9 th. You are allowed to use one 3" by 5" index card on the exam as well as a scientific calculator.
More informationAA Simulation: Firing Range
America's Army walkthrough AA Simulation: Firing Range Firing Range This simulation serves as an introduction to uniform motion and the relationship between distance, rate, and time. Gravity is removed
More informationQuadratics. March 18, Quadratics.notebook. Groups of 4:
Quadratics Groups of 4: For your equations: a) make a table of values b) plot the graph c) identify and label the: i) vertex ii) Axis of symmetry iii) x- and y-intercepts Group 1: Group 2 Group 3 1 What
More informationLesson 17: Graphing Quadratic Functions from the Standard Form,
: Graphing Quadratic Functions from the Standard Form, Student Outcomes Students graph a variety of quadratic functions using the form 2 (standard form). Students analyze and draw conclusions about contextual
More informationUse of Number Maths Statement Code no: 1 Student: Class: At Junior Certificate level the student can: Apply the knowledge and skills necessary to perf
Use of Number Statement Code no: 1 Apply the knowledge and skills necessary to perform mathematical calculations 1 Recognise simple fractions, for example 1 /4, 1 /2, 3 /4 shown in picture or numerical
More information