Practice Test - Chapter 3. TEMPERATURE The equation to convert Celsius temperature C to Kelvin temperature K is shown.
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1 TEMPERATURE The equation to convert Celsius temperature C to Kelvin temperature K is shown. a. State the independent and dependent variables.explain. b. Determine the C- and K-intercepts and describe what the intercepts mean in this situation. a. The Kelvin temperature is dependent on the Celsius temperature. So, the Celsius temperature is the independent variable and the Kelvin temperature is the dependent variable. b. The C-intercept is (273, 0) and it means that a Celsius temperature of 273 degrees is equal to a Kelvin temperature of 0 degrees. The K-intercept is (0, 273) and it means that a Celsius temperature of 0 degrees is equal to a Kelvin temperature of 273 degrees. esolutions Manual - Powered by Cognero Page 1
2 Graph each equation. y = x + 2 To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. So, the x-intercept is 2 and the y-intercept is 2. y = 4x The slope of y = 4x is 4. Graph (0, 0). From there, move up 4 units and right 1 unit to find another point. Then draw a line containing the points. esolutions Manual - Powered by Cognero Page 2
3 x + 2y = 1 To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. So, the x-intercept is 1 and the y-intercept is. 3 = 5 esolutions Manual - Powered by Cognero Page 3
4 3x = 5 y To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. So, the x-intercept is y-intercept is 5. esolutions Manual - Powered by Cognero Page 4
5 Solve each equation by graphing. 4x + 2 = 0 The related function is y = 4x + 2. x f (x) = 4x + 2 f (x (x, f(x) ) 4 f (4) = 4(4) (4, 14) 2 f (2) = 4(2) (2, 6) 0.5 f(0.5) = 4(0.5) (0.5, 0) 0 f (0) = 4(0) (0, 2) 2 f (2) = 4(2) (2, 10) 4 f (4) = 4(4) (4, 18) The graph intersects the x-axis at. So, the solution is. 0 = 6 3x The related function is y = 3x + 6. x f (x) = 3x + 6 f (x (x, f(x) ) 4 f (4) = 3(4) (4, 18) 2 f (2) = 3(2) (2, 12) 0 f (0) = 3(0) (0, 6) 2 f (2) = 3(2) (2, 0) 3 f (3) = 3(3) (3, 3) 4 f (4) = 3(4) (4, 6) The graph intersects the x-axis at 2. So, the solution is = 3 esolutions Manual - Powered by Cognero Page 5
6 5x + 2 = 3 The related function is y = 5x + 5. x f (x) = 5x + 5 f (x (x, f(x) ) 4 f (4) = 5(4) (4, 15) 2 f (2) = 5(2) (2, 5) 1 f (1) = 5(1) (1, 0) 0 f (0) = 5(0) (0, 5) 2 f (2) = 5(2) (2, 15) 4 f (4) = 5(4) (4, 25) The graph intersects the x-axis at 1. So, the solution is 1. 12x = 4x + 16 The related function is y = 8x x f (x) = 8x + 16 f (x (x, f(x) ) 4 f (4) = 8(4) (4, 48) 2 f (2) = 8(2) (2, 32) 0 f (0) = 8(0) (0, 16) 2 f (2) = 8(2) (2, 0) 3 f (3) = 8(3) (3, 8) 4 f (4) = 8(4) (4, 16) The graph intersects the x-axis at 2. So, the solution is 2. esolutions Manual - Powered by Cognero Page 6
7 Find the slope of the line that passes through each pair of points. (5, 8), (3, 7) So, the slope is. (5, 2), (3, 2) So, the slope is 0. (4, 7), (8, 1) So, the slope is. (6, 3), (6, 4) esolutions Manual - Powered by Cognero Page 7
8 (6, 3), (6, 4) So, the slope is undefined. MULTIPLE CHOICE Which is the slope of the linear function shown in the graph? A B C D The line passes through the points (2, 3) and (3, 1). The slope is, so the correct choice is B. esolutions Manual - Powered by Cognero Page 8
9 Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve. If y = 6 when x = 9, find x when y = 12. So, the direct variation equation is Substitute 12 for y and find x. So, x = 18 when y = 12. When y = 8, x = 8. What is x when y = 6? So, the direct variation equation is y = xsubstitute 6 for y and find x. So, x = 6 when y = 6. If = 5 when = 2, what is when = 14? esolutions Manual - Powered by Cognero Page 9
10 If y = 5 when x = 2, what is y when x = 14? So, the direct variation equation is Substitute 14 for x and find y. So, y = 35 when x = 14. If y = 2 when x = 12, find y when x = 4. So, the direct variation equation is Substitute 4 for x and find y. So, y = x = 4. esolutions Manual - Powered by Cognero Page 10
11 BIOLOGY The number of pints of blood in a human body varies directly with the persons weight. A person who weighs 120 pounds has about 8.4 pints of blood in his or her body. a. Write and graph an equation relating weight and amount of blood in a persons body. b. Predict the weight of a person whose body holds 12 pints of blood. a. To write a direct variation equation, find the constant of variation k. Let x = 120 and y = 8.4. So, the direct variation equation is y = 0.07x. b. Using the direct variation equation from part a, let y = 12. So, a person who holds 12 pints of blood would weigh about 171 pounds. esolutions Manual - Powered by Cognero Page 11
12 Find the next three terms of each arithmetic sequence. 0, 15, 30, 45, 60, Find the common difference by subtracting two consecutive terms = The common difference between terms is next term, subtract 15 from the resulting number, and so on = = = 105 So, the next three terms of this arithmetic sequence are 75, 90, , 8, 11, 14, Find the common difference by subtracting two consecutive terms. 8 The common difference between terms is 3. So, to find the next term, add 3 from the last term. To find the next term, add 3 from the resulting number, and so on = = = 23 So, the next three terms of this arithmetic sequence are 17, 20, 23. Determine whether each sequence is an arithmetic sequence. If it is, state the common difference. 40, 32, 24, 16, 40, 32, 24, 16, An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called the common difference. To find the common difference, subtract two consecutive numbers in the sequence. 32 (40) = 8 24 (32) = 8 16 (24) = 7 The common difference is , 1.5, 3, 6, 12, esolutions Manual - Powered by Cognero Page 12
13 0.75, 1.5, 3, 6, 12, An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called the common difference. To find the common difference, subtract two consecutive numbers in the sequence = = = = 6 The difference between terms is not constant, so the sequence is not an an arithmetic sequence and does not have a common difference 5, 17, 29, 41, An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called the common difference. To find the common difference, subtract two consecutive numbers in the sequence = = = 12 The common difference is 4. esolutions Manual - Powered by Cognero Page 13
14 MULTIPLE CHOICE In each figure, only one side of each regular pentagon is shared with another pentagon. Each side of each pentagon is 1 centimeter. If the pattern continues, what is the perimeter of a figure that has 6 pentagons? F 15 cm H 20 cm G 25 cm J 30 cm Number of Perimeter Pentagons The perimeter increases by 3 as the number of polygons increases by 1. Continue the sequence to find the perimeter of a figure that has 6 pentagons. Number of Perimeter Pentagons So, a figure that has 6 pentagons has a perimeter of 20 centimeters. The correct choice is H. esolutions Manual - Powered by Cognero Page 14
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Solution of the System of Linear Equations: any ordered pair in a system that makes all equations true.
Definitions: Sstem of Linear Equations: or more linear equations Sstem of Linear Inequalities: or more linear inequalities Solution of the Sstem of Linear Equations: an ordered pair in a sstem that makes
Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.
Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear
a. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F
FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter 1. 1. Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all
ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only Student Name: School Name:
Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper
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Zeros of Polynomial Functions
Review: Synthetic Division Find (x 2-5x - 5x 3 + x 4 ) (5 + x). Factor Theorem Solve 2x 3-5x 2 + x + 2 =0 given that 2 is a zero of f(x) = 2x 3-5x 2 + x + 2. Zeros of Polynomial Functions Introduction
Successful completion of Math 7 or Algebra Readiness along with teacher recommendation.
MODESTO CITY SCHOOLS COURSE OUTLINE COURSE TITLE:... Basic Algebra COURSE NUMBER:... RECOMMENDED GRADE LEVEL:... 8-11 ABILITY LEVEL:... Basic DURATION:... 1 year CREDIT:... 5.0 per semester MEETS GRADUATION
Title Location Date Start Time End Time Description
Title Location Date Start Time End Time Description Operations w/ Integers SJC Rm 1457B Aug. 29 12:30 PM 2:00 PM Beginning with an introduction to integers, this workshop will review the four basic operations
WARM UP EXERCSE. 2-1 Polynomials and Rational Functions
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1 Determine whether an. 2 Solve systems of linear. 3 Solve systems of linear. 4 Solve systems of linear. 5 Select the most efficient
Section 3.1 Systems of Linear Equations in Two Variables 163 SECTION 3.1 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES Objectives 1 Determine whether an ordered pair is a solution of a system of linear
Students will use various media (computer, graphing calculator, paper and pencil) to graph/sketch linear equations.
Title: Lines, Lines, Everywhere!! A discovery/exploration lesson investigating equations of the form y = mx + b to see how the values of b and m affects the graph. Link to Outcomes: Communication/ Cooperation
Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan
Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan I. Topic: Slope-Intercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.
Aim: How do we find the slope of a line? Warm Up: Go over test. A. Slope -
Aim: How do we find the slope of a line? Warm Up: Go over test A. Slope - Plot the points and draw a line through the given points. Find the slope of the line.. A(-5,4) and B(4,-3) 2. A(4,3) and B(4,-6)
Name: Class: Date: ID: A
Class: Date: Slope Word Problems 1. The cost of a school banquet is $95 plus $15 for each person attending. Write an equation that gives total cost as a function of the number of people attending. What
GRADES 7, 8, AND 9 BIG IDEAS
Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for
1.1 Practice Worksheet
Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)