A proportion is a statement equating two ratios. example: A proportion using the ratio above is 9:4 = 18:8 or
|
|
- Ursula Greer
- 5 years ago
- Views:
Transcription
1 FOUNDATIONS OF MATH 11 Ch. 8 Day 1: RATES RATIOS AND PROPORTIONS A ratio is a comparison between two amounts. example: A recipe uses nine cups of flour to make four cakes. In this cake recipe, the ratio of flour amount to number of cakes is 9: or 9 A proportion is a statement equating two ratios. example: A proportion using the ratio above is 9: = 18:8 or 9 = 18 8 RATES A rate is a comparison of two amounts that are measured in different units. example: In the cake recipe, the rate of flour amount in a number of cakes is 9 cups of flour 9 cups of flour per cakes or cakes A unit rate is a rate in which the numerical value of the second term is 1. example: In the cake recipe, the unit rate of flour amount in a cake is.5 cups of flour in a cake or.5 cups of flour/cake example: $50 can buy 36 litres of gasoline. What is the unit price? cost rate = 50 dollars 36 litres Answer: The price per litre is about $1.389/litre. unit cost rate dollars/litre example: A world-class sprinter can run 100 m in 9.8 seconds. At what rate can the sprinter run? Answer in m/s and km/h. unit rate in m/s = 100 metres 9.8 seconds unit rate in km/h m 1 s km/h m/s 1 km 1000 m 60 s 1 min 60 min 1 h Answer: The sprinter's speed is about 10.0 m/s or km/h.
2 Ch. 8: Day 1 notes Rates Page of On a straight-line graph, its slope is a rate of change. When the amount that y changed is compared to the amount that x changed: o rate = rise run = 6 3 o unit rate = slope = The slope is the rate at which the y-coordinate changes as the x-coordinate changes. y x example: This graph describes a training run. Describe what d distance from home could have happened during the run. distance (km) t time (min) From 0 to 10 min: speed = slope = 3 km 10 min From 10 to 15 min: speed = slope = 1 km 5 min From 15 to 0 min: speed = slope = 0 km 5 min From 0 to 60 min: speed = slope = km 0 min 60 min 1 h 60 min 1 h 60 min 1 h 60 min 1 h = 18 km/h = 1 km/h = 0 km/h = 6 km/h example: While driving at 70 km/h, a driver looks down to read a text message for 5 seconds. How far has the car travelled in that time? speed = 70 km 1 h 1000 m 1 km 1 h 60 min 1 min 60 s 19. m/s distance = speed time (19. m/s)(5 s) 97. m Answer: The car travelled about 97 m in 5 seconds.
3 FOUNDATIONS OF MATH 11 Ch. 8 Day : RATE PROBLEMS SOLVING PROBLEMS THAT INVOLVE RATE example: Gas in Surrey is $1.8/L, while gas in Blaine is $.38/gallon. Where is it cheaper to buy 75 litres of gas and what would be the savings? 1 US gallon 3.79 L and use 1 USD = 1.0 CAD o Convert the Blaine price to CAD/L..38 USD 1gal 1.0 CAD 1USD 1gal 3.79L CAD/L o Calculate the cost savings in CAD. cost in Surrey = 1.8 CAD/L 75 L = 111 CAD cost in Blaine CAD/L 75 L CAD difference in cost = 111 CAD 88.1 CAD =.59 CAD Answer: It is.59 CAD less to buy 75 litres of gas in Blaine. example: Amelia walks briskly for hours and burns 5 calories. Bruce walks at a slower rate, burning 6 calories in 30 minutes. If Amelia walks for 3 hours, how long will Bruce need to walk in order to burn the same amount of calories as Amelia? o Amelia: unit rate = 5 calories = 7 calories/h h number of calories = 7 calories/h 3 h = 681 calories o Bruce: unit rate = number of hours = 6 calories = 1 calories/h 0.5h 681 calories h 1 calories/h Answer: Bruce will need to walk about 5.5 hours to burn the same number of calories as Amelia.
4 Ch. 8: Day notes Rate Problems Page of example: The simple interest formula is I = Prt, where I is the amount of interest earned, P is the principal (the starting amount), r is the interest rate, and t is the time; time must be in years for an annual interest rate. Mia invested $3000 for months and earned $10 of simple interest. What was the annual interest rate? o Use the simple interest formula. I = Prt months is years 10 = (3000)r() o Solve for r. Answer: The annual interest rate was %. 10 = 6000r r = r = 0.0 example: The low temperature for a certain day was 5.3 C at 3:30 AM. The temperature then rose steadily that day until the high temperature was as 11.8 C at 5:5 PM. A weather forecaster predicted the same temperature increase rate for the next day, from a low of 7 C at 3:00 AM. Estimate the temperature at 7:00 AM the second day. o Calculate the temperature rate of increase. During the first day: temperature increase = 11.8 C ( 5.3 C) = 17.1 C hours after 3:30 AM = 17:5 3:30 = 1:15 = 1.5 hours temperature rate of increase = 17.1 C 1.5 h = 1. C/h o Calculate the temperature at 7:00 AM on the second day. hours after 3:00 AM = 7:00 3:00 = :00 = hours temperature increase = 1. C/h h =.8 C temperature at 7:00 AM = 7 C +.8 C =. C Answer: The temperature is. C below 0 at 7:00 AM on the nd day.
5 FOUNDATIONS OF MATH 11 Ch. 8 Day 3: SCALE DIAGRAMS SCALE FOR A REDUCTION DIAGRAM A scale diagram is a drawing in which measurements are proportionally reduced or enlarged from actual measurement. Scale is the ratio of a length on a diagram to the corresponding. The scale factor is k = example: The picture below is an aerial photo of NWSS; the photo is a reduction. What is the scale factor of the photo? How long is NWSS? 100 m o The 100 m length on the photo is measured to be.5 cm, so the scale factor, k = o Find the length of NWSS, L =.5 cm 100 m =.5 cm cm k = The school image is 9.5 cm long = L = 9.5 cm = cm 1 m 100 cm = 380 m Answer: NWSS is about 380 m long. = cm L
6 Ch. 8: Day 3 notes Scale Diagrams Page of exercise: What is the scale factor of this apartment floor plan? What are the dimensions of the rooms? Dining Room Den Living Room Kitchen Bath Bedroom 5 m [Answer: living room m by.8 m, dining room m by. m, den m by 1. m, kitchen -.7 m by 1.8 m, bath m by 1.8 m, bedroom m by 3.3 m] SCALE FOR AN ENLARGEMENT DIAGRAM example: The diagram of the wasp is an enlargement. What is the scale factor of this picture? How big is the wasp? o The 1 cm length on the diagram is measured to be cm, so the scale factor, k = cm 1 cm = 1 cm o Find the wasp length, L The wasp image is 6 cm long. k = Answer: The wasp is about 1.5 cm long. = 6 cm L L = 6 cm = 1.5 cm What conclusion can you make about the scale factor of a reduction? What conclusion can you make about the scale factor of an enlargement?
7 FOUNDATIONS OF MATH 11 Ch. 8 Day : SCALE FACTORS & AREAS OF -D SHAPES The scale factor, k = is the linear scale factor and would be applied to linear dimensions such as length, width, height,... SCALE FACTORS FOR AREA The smaller image is an computer chip at its actual size, a 1 cm square. Beside it is a 5 cm enlargement. The linear scale factor, k = 5 cm 1 cm = 5 The area scale factor is diagram area actual area = 5 cm 1 cm = 5 The area scale factor is diagram area actual area which is also equal to k, the square of the linear scale factor. example: A 6 m by 10 m room is drawn as a 3 cm by 5 cm rectangle on a floor plan. Find the scale factor and the area scale factor of the floor plan to determine the area of a kitchen that is 8 cm on the floor plan. o scale factor, k = = 3 cm 6 m = 3 cm 600 cm = o area scale factor = k = (0.005) = o Find the actual kitchen area, A. k = cm = 1 m 100 cm 1 m 100 cm Answer: The kitchen area is 3 m. A = = 3 m diagram area actual area 8 cm A 8 cm = cm
8 Ch. 8: Day notes Scale Factors & Areas of -D Shapes Page of exercise: The radius of a special giant-size pizza is twice the radius of a small pizza. How much bigger is the giantsize pizza when compared to a small pizza? x x o Define variable x to represent the radius of the smaller pizza. o Calculate the scale factor of the enlargement k = giant-sized radius small radius = x x = o The area scale factor of the enlargement, k = () = area scale factor = giant-sized area small area = π( x) πx = πx πx = OR Answer: The giant-sized pizza is times the size of the small pizza. exercise: The area of a computer display is 1 in. When the display is projected onto a screen, the image is 5ft. What is the scale factor of the projection? o The area scale factor of the projected image is k = image area display area = 5 ft 1 in 1 in 1 ft 1 in 1 ft = 3600 in 1 in = 5 o The scale factor of the projected image is k = 5 = 5 Answer: The scale factor of the projected image is 5.
9 FOUNDATIONS OF MATH 11 Ch. 8 Day 5: SCALE MODELS & SCALE DIAGRAMS Similar figures are proportionally sized; a two-dimensional objects and all its scale diagrams are similar. These triangles are similar If the grey triangle is the actual object, then the scale factor for the: the reduction drawing scale factor, k = the enlargement drawing scale factor, k = 8 1 = = 0.5 = 6 = 1.5 Similar figures can also be three-dimensional objects; it and all its scale models are similar. model length The scale factor, k = is the linear scale factor and would be applied to linear dimensions such as length, width, height,... These rectangular prisms are similar because they are proportionally sized If the grey prism is the actual object, then the scale factor for the: the reduction model scale factor, k = the enlargement model scale factor, k = model length = = 0.5 model length = 6 = 1.5
10 Ch. 8: Day 5 notes Scale Models & Scale Diagrams Page of example: A 1:50 die-cast model of the world's largest dump truck is shown. The model is 30.6 cm long, 0.0 cm wide, and 15. cm tall. How long, wide, and tall is the dump truck? o linear scale factor, k = 1 50 = 0.0 k = model length o Find the truck length, L L = 30.6 cm 0.0 = 1530 cm o Find the truck width, W W = 0.0 cm 0.0 = 1000 cm o Find the truck height, H H = 15. cm 0.0 = 770 cm 0.0 = 1 m 100 cm = 15.3 m 0.0 = 1 m 100 cm = 10.0 m 0.0 = 1 m 100 cm = 7.7 m 30.6 cm L 0.0 cm W 15. cm H Answer: The truck is about 15. m long, 10.0 m wide, and 7.7 m tall.
11 FOUNDATIONS OF MATH 11 Ch. 8 Day 6: SCALE FACTORS & 3-D OBJECTS SCALE FACTORS FOR SURFACE AREA Compare the surface areas of a 1-cm cube and a 5-cm cube. The linear scale factor, k = 5 cm 1 cm = 5 The surface area scale factor is ( ) ( ) = 5 larger surface area smaller surface area = 6 5 cm 6 1 cm The surface area scale factor is model surface area actual surface area which is equal to k, the square of the linear scale factor. SCALE FACTORS FOR VOLUME Compare the volume of a 1-cm cube and a 5-cm cube. The linear scale factor, k = 5 cm 1 cm = 5 The volume scale factor is larger volume smaller volume = cm 3 1 cm = 53 The volume scale factor is model volume actual volume which is equal to k 3, the cube of the linear scale factor.
12 Ch. 8: Day 6 notes Scale Factors & 3-D Objects Page of example: A 1:50 die-cast model of a dump truck is shown. The model can carry 100 cm 3 of sand. How much sand will the actual dump truck be able to carry? o linear scale factor, k = 1 50 = 0.0 volume scale factor, k 3 = (0.0) 3 = o Find the truck load capacity, C C = cm = cm3 = 150 m 3 k 3 = = model volume actual volume cm C 1 m 100 cm 1 m 100 cm 1 m 100 cm Answer: The dump truck will be able to carry about 150 m 3 of sand. exercise: A cylindrical soup can is 10 cm wide and 10 cm tall. The company wants to make a similar shaped can that will hold twice as much soup. What will the diameter and height of the new can be? o volume scale factor of the can k 3 = o linear scale factor of the can k = o diameter and height of the can, D D 10 cm D cm D cm Answer: The new can's diameter and height should be about 1.6 cm.
Chapter 8: Proportional Reasoning
Chapter 8: Proportional Reasoning Section 8.1 Chapter 8: Proportional Reasoning Section 8.1: Comparing and Interpreting Rates Terminology: Rate: A comparison of two amounts that are measured in different
More informationLesson Lesson Tutorials
7.4 Lesson Lesson Tutorials An equation in two variables represents two quantities that change in relationship to one another. A solution of an equation in two variables is an ordered pair that makes the
More information4. What is the area of a square that has a side length of 3x?
2013 6 th Grade Math Contest 1. Collin needs three wooden boards to repair his porch. The lengths he needs are 2.2 meters, 2.82 meters, and 4.25 meters. He purchases a board that is 10 meters long and
More informationSOL Review Items. 7.1 The student will. 7.1a 1. Which fraction and decimal are equivalent to A. and B. and C. and D. and 0.
7.1 The student will a) investigate and describe the concept of negative exponents for powers of ten; b) determine scientific notation for numbers greater than zero; c) compare and order fractions, decimals,
More informationName Class Date. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Practice - Solving Two-Step Equations Solve each equation. Check your answer.. a +. +. b +. 9 + t. a +. -t + Write an equation to model each situation. Then solve.. You want to buy a bouquet of yellow
More informationPLC Papers. Created For:
PLC Papers Created For: Compound Units 2 Grade 5 Objective: Convert standard compound units in numerical and algebraic contexts. Question 1. Ben goes on holiday to Hong Kong. In Hong Kong, Ben sees a camera
More informationSection A Coordinate Geometry Grade G / F
Name: Teacher Assessment Section A Coordinate Geometr Grade G / F. (a) On the grid plot the points with coordinates (, ), (, ) and (, ). x () (b) Join the points and give the mathematical name of the shape..
More informationArithmetic Review 1. Solve Solve: = =
Arithmetic Review 1 Simplify: 1. -15 (-6) Solve 1. 5.6 (.1)=. - * -7 1..4 (.)=. 7 9 14. 9 1 = 4. 16 (-4) * 6 15. 7 = 9 5. ( 49 * 6 * 16 ) 10 6. 17 0 = Solve: 1 1 16. 5 + = 7. 1 + 50 Solve 1. + = 15 5 9.
More informationSect 4.2 Applications of Ratios and Proportions
15 Sect 4.2 Applications of Ratios and Proportions Objective 1: Scale Drawings In designing blueprints for a house or creating a model airplane, the measurements on the blueprints or on the model airplane
More informationPractice A. Name Date. Evaluate the expression for the given value of the variable. Match the equation with its solution. Solve the equation.
mm mm OFF ON ZERO Name Date Practice A For use with pages 390 395 Evaluate the expression for the given value of the variable.. 2 x 2 3 4; 25 2. 3 2x 8 2 0; 3 3. 24 x 2 9 ; 26 Match the equation with its
More informationSTRAND: GRAPHS Unit 1 Straight Lines
CMM Subject Support Strand: GRAPHS Unit Straight Lines: Text STRAND: GRAPHS Unit Straight Lines TEXT Contents Section. Gradient. Gradients of Perpendicular Lines. Applications of Graphs. The Equation of
More informationLesson 6: Graphs of Linear Functions and Rate of Change
Lesson 6 Lesson 6: Graphs of Linear Functions and Rate of Change Classwork Opening Exercise Functions 1, 2, and 3 have the tables shown below. Examine each of them, make a conjecture about which will be
More information4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want
More informationPre-Algebra Semester 1 Practice Exam B DRAFT
. Evaluate x y 5 6 80 when x = 0 and y =.. Which expression is equivalent to? + + + +. In Pre-Algebra class, we follow the order of operations in evaluating expressions. Which operation should a student
More informationUnit 3, Lesson 1: How Well Can You Measure?
Unit 3, Lesson 1: How Well Can You Measure? 1. Estimate the side length of a square that has a 9 cm long diagonal. 2. Select all quantities that are proportional to the diagonal length of a square. A.
More information2.4 Slope and Rate of Change
2.4 Slope and Rate of Change Learning Objectives Find positive and negative slopes. Recognize and find slopes for horizontal and vertical lines. Understand rates of change. Interpret graphs and compare
More informationCAHSEE MR & Alg. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: ate: I: HSEE MR & lg Multiple hoice Identify the choice that best completes the statement or answers the question. 1. What is the reciprocal of 4 7? 7 4 4 7 7 4 1 7 4 2. What is the solution
More information3 x 2 x 2. Algebraic Equation
33337_020.qxp 2/27/06 :0 AM Page 66 66 Chapter 2 Solving Equations and Inequalities 2. Linear Equations and Problem Solving Equations and s of Equations An equation in x is a statement that two algebraic
More informationMinnesota K-12 Academic Standards in Mathematics (2007)
8.1.1.1 Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number an irrational
More informationSummer Math Packet Grade 8 / Course 3
SHOW WORK FOR EVERY PROBLEM 1. If Michelle rollerblades around a circular track with a radius of 80 meters, how far does she skate? Use 3.14 for π. Round to the nearest tenth. 4. The weight of an object
More informationReleased 2010 Achievement Test. Mathematics GRADE
Released 2010 Achievement Test Mathematics GRADE 9 Use the following information to answer question 1. The letters on the number line below represent rational numbers. 1. The approximate value of 15 is
More informationWhat value of x satisfies the equation = 1? 2
Math 8 EOG Review Problems Name # If a question is marked, you need to solve the problem without using a calculator. If a problem is not marked, you may use a calculator to solve to the problem. If a question
More informationshape Area Perimeter Circle Square rectangle Parallelogram Triangle Surface area to volume ratio = Savings Plan Formula A = P M T (1+ AP R N Loan Paym
APY compounded continuously APY= APY compounded n times APY= Compounded Continuously A= Compounded n times A= Simple Interest A= Three Exponential models Q= using T half Q= using T double Q= using r r=
More informationBEMIDJI AREA SCHOOLS Outcomes in Mathematics Grade 7
Outcomes in Mathematics Grade Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but.1.1.1 that it can
More information3. A beam or staircase frame from CSP costs $2.25 for each rod, plus $50 for shipping and handling.
Pg. 13: #3 3. A beam or staircase frame from CSP costs $2.25 for each rod, plus $50 for shipping and handling. a. Complete the following table to show the costs for beams of different lengths. Beam Length
More informationUsing Graphs to Relate Two Quantities
- Think About a Plan Using Graphs to Relate Two Quantities Skiing Sketch a graph of each situation. Are the graphs the same? Explain. a. your speed as you travel from the bottom of a ski slope to the top
More informationMaterials for assessing adult numeracy
Materials for assessing adult numeracy Number Task The population of Wales is approximately Write this in numbers in the box. million. What is the value of the 7 in this number? Write your answer in words.
More informationFair Game Review. Chapter. Complete the statement qt L cm = in grams oz ml cups
Name Date Chapter 1 Complete the statement. Fair Game Review 1. 5 qt L. 5 cm = in. 3. 00 ml cups 4. 600 grams oz 5. A can of orange juice is 1 ounces. How many grams is the can of orange juice? 6. A recipe
More informationABC is a triangle. The point D lies on AC. Angle BDC = 90 BD = 10 cm, AB = 15 cm and DC = 12.5 cm.
1. Mr McGrath s special questions FOUNDATION Paper B ABC is a triangle. The point D lies on AC. Angle BDC = 90 BD = 10 cm, AB = 15 cm and DC = 12.5 cm. (a) Calculate the length of AD. Give your answer
More informationName: Pd: Score: Weekly Checkup Mixed Review. 1. The pictures below show how two different groups of shapes balance a scale.
Q3:1 - CALCULATOR and turned in the following week with your new check- up. 1. The pictures below show how two different groups of shapes balance a scale. a. If 1 block weights 10 pounds, what is the weight
More informationBenchmark Test Second Quarter
Benchmark Test Second Quarter 1. The table shows the prices of different sized jars of peanut butter. Which of the jars has the least unit price? A. 1-oz jar B. 1-oz jar Prices of Peanut Butter Size Price
More information( )( 2x + 1) = 2x 2! 5x! 3
USING RECTANGLES TO MULTIPLY 5.1.1 through 5.1. Two ways to find the area of a rectangle are: as a product of the (height)! (base) or as the sum of the areas of individual pieces of the rectangle. For
More informationDear Parents, Guardians, and Students:
Dear Parents, Guardians, and Students: During the summer, students who will be enrolled in Algebra net year are required to complete a portfolio of mathematics problems. The purpose of this eperience is
More informationAssessment Test for Singapore Primary Mathematics 3B This test covers material taught in Primary Mathematics 3B (
Assessment Test for Singapore Primary Mathematics 3B This test covers material taught in Primary Mathematics 3B (http://www.singaporemath.com/) 1. Which is heavier, A or B? [1] 2. Fill in heavier than,
More informationMinnesota 7 th Grade 2007 Math Strands & Standards
Minnesota 7 th Grade 2007 Math Strands & Standards Number & Operation Algebra Geometry & Measurement Data Analysis Read, write, represent and compare positive and negative rational numbers, expressed as
More informationINTRODUCTION TO MATHEMATICAL MODELLING
306 MATHEMATICS APPENDIX 2 INTRODUCTION TO MATHEMATICAL MODELLING A2.1 Introduction Right from your earlier classes, you have been solving problems related to the real-world around you. For example, you
More information1 Which expression represents 5 less than twice x? 1) 2) 3) 4)
1 Which expression represents 5 less than twice x? 2 Gabriella has 20 quarters, 15 dimes, 7 nickels, and 8 pennies in a jar. After taking 6 quarters out of the jar, what will be the probability of Gabriella
More informationGraphical Solution Y 3. and y 2 = 3 intersect at (0.8, 3), so the solution is (3-2x) - (1 - x) = 4(x - 3) (5 - x) - (x - 2) = 7x - 2
660_ch0pp076-68.qd 0/6/08 : PM Page 6 6 CHAPTER Linear Functions and Equations continued from previous page The following eample illustrates how to solve graphically, and numerically. 5 - = symbolically,
More informationRATES AND UNIT RATES
RATES AND UNIT RATES 7.. 7.. Rate of change is a ratio that describes how one quantity is changing with respect to another. Unit rate is a rate that compares the change in one quantity to a one-unit change
More informationInstructor: TODD CONKLIN Course: 3rd hour Math
Student: Date: Instructor: TODD CONKLIN Course: 3rd hour Math Assignment: Samples and Populations Practice/ End of Year Review 1. You ask 8 classmates how many pencils they have in their bags. The mean
More informationAlgebra 1 Honors First Semester Review
Permitted resources: Algebra 1 Honors First Semester Review TI-108 (or similar basic four function calculator) Algebra 1 and Geometr EOC Reference Sheet 4. Identif the mapping diagram that represents the
More informationDay 1(Answers) NS Solve: 2 2 (- 5) -12
Day 1(Answers) NS Solve: 2 2 (- 5) -12 5 John wanted a skate board that cost $65. It went on sale for 20% off. How much money will John save? How much will the skate board cost? Save $ 13.00,Cost $52.00
More information8 th Grade Academic: Fall 2014 Semester Exam Review-Part 1
Name Date Period 8 th Grade cademic: Fall 2014 Semester Exam Review-Part 1 1. Four schools,,, C, and D, all played the same number of football games this season. School won 70% of its games. School won
More informationReleased Assessment Questions, 2017 QUESTIONS. Grade 9 Assessment of Mathematics Academic LARGE PRINT
Released Assessment Questions, 2017 QUESTIONS Grade 9 Assessment of Mathematics Academic LARGE PRINT page 2 Read the instructions below. Along with this booklet, make sure you have the Answer Booklet and
More informationPaper 2. Mathematics test. Calculator allowed. First name. Last name. School. Pupil number KEY STAGE TIER
Ma KEY STAGE 3 TIER 6 8 2002 Mathematics test Paper 2 Calculator allowed Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your
More informationChapter 1 ( )? Chapter 1 Opener. Section 1.1. Worked-Out Solutions. 2π π = π. Try It Yourself (p. 1) So, x = 95.3.
Chapter Chapter Opener Try It Yourself (p. ). + ( ) 7.. + 8. ( ) +. 7. ( 7) + 7 7. 8 () 0 + 8. 7. ( 7) 8 0.. 8. Section.. Activity (pp. ). Triangle Angle A (degrees) Angle B (degrees). a. The sum of the
More informationGCSE MATHEMATICS 43603F. Foundation Tier Unit 3 Geometry and Algebra. Morning. (NOV F01) WMP/Nov16/E4. Materials.
Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature GCSE F MATHEMATICS Foundation Tier Unit 3 Geometry and Algebra Tuesday 8 November 2016 Morning
More informationChapter 1: Introduction to Real Numbers and Algebraic Expressions
Chapter 1: Introduction to Real Numbers and Algebraic Expressions 1.1 EXERCISE SET a. Substitute to find values of the expressions in each of the following applied problems. 1. Commuting Time. It takes
More informationInstructions. Information. Advice
Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided
More informationChapter 7: Practice/review problems The collection of problems listed below contains questions taken from previous MA123 exams.
Word problems Chapter 7: Practice/review problems The collection of problems listed below contains questions taken from previous MA3 exams. Max-min problems []. A field has the shape of a rectangle with
More information8th Grade Math Summer (8thGradeMathSummer)
Name: Date: 1. The cube shown has an edge length of x inches. The equation can be used to determine the length, in inches, of each edge of the cube. What is the value of x? Explain your answer or show
More informationName: Date: Period: Study Guide: Final Exam Wednesday, June 19th
Part A: Multiple Choice (1 point) * Directions: Circle the correct answer choice for the following multiple choice problems. 1. 5. The graph below shows the relationship between velocity and time for a
More informationFirst Name: Last Name:
5 Entering 6 th Grade Summer Math Packet First Name: Last Name: 6 th Grade Teacher: I have checked the work completed: Parent Signature 1. Find the products. This page should be completed in 3 minutes
More informationDiagnostic Test. Month Balance Change February $ March $ $13.10 April $1, $ May $ $ June $ $163.
Diagnostic Test Select the best answer for questions 1 60. Fill in the correct bubble on your answer sheet. 1. The chart shows the balance in Neil s savings account and the change from the previous month.
More informationChapter 3 The Integral Business Calculus 197
Chapter The Integral Business Calculus 97 Chapter Exercises. Let A(x) represent the area bounded by the graph and the horizontal axis and vertical lines at t=0 and t=x for the graph in Fig.. Evaluate A(x)
More information3 2 (C) 1 (D) 2 (E) 2. Math 112 Fall 2017 Midterm 2 Review Problems Page 1. Let. . Use these functions to answer the next two questions.
Math Fall 07 Midterm Review Problems Page Let f and g. Evaluate and simplify f g. Use these functions to answer the net two questions.. (B) (E) None of these f g. Evaluate and simplify. (B) (E). Consider
More informationMath 074 Final Exam Review. REVIEW FOR NO CALCULATOR PART OF THE EXAM (Questions 1-14)
Math 074 Final Exam Review REVIEW FOR NO CALCULATOR PART OF THE EXAM (Questions -4) I. Can you add, subtract, multiply and divide fractions and mixed numbers?. Perform the indicated operations. Be sure
More information2. In Exercise 1, suppose the two pricing plans changed as follows. Complete parts (a) (d) based on these two plans.
A C E Applications Connections Extensions Applications 1. A school is planning a Saturday Back-to-School Festival to raise funds for the school art and music programs. Some of the planned activities are
More informationThe Top 11 Keystones of Algebra 1
The Top 11 Keystones of Algebra 1 The Top Eleven Keystones of Algebra 1 You should be able to 1) Simplify a radical expression. 2) Solve an equation. 3) Solve and graph an inequality on a number line.
More informationState the condition under which the distance covered and displacement of moving object will have the same magnitude.
Exercise CBSE-Class IX Science Motion General Instructions: (i) (ii) (iii) (iv) Question no. 1-15 are very short answer questions. These are required to be answered in one sentence each. Questions no.
More informationLearning Outcome 4 Measurement
Maths in Context Learning Outcome 4 Measurement Exercise Book Learning Outcome 4 Exercise 1 Select the most appropriate metric units for measuring each item. 1. The height of a person: (A) mm (B) cm (c)
More information13. Convert to a mixed number: Convert to an improper fraction: Are these two fractions equivalent? 7
FINAL REVIEW WORKSHEET BASIC MATH Chapter 1. 1. Give the place value of 7 in 3, 738, 500. 2. Give the word name for 302, 525. 3. Write two million, four hundred thirty thousand as a numeral. 4. Name the
More informationName Per. Keystone Exams Practice Test A.) $300,000 B.) $400,000 C.) $500,000 D.) $600,000
Name Per Basic Skills Keystone Exams Practice Test 1.) A theme park charges $52 for a day pass and $110 for a week pass. Last month, 4,432 day passes and 979 week passes were sold. Which of the following
More informationSample. Test Booklet. Subject: MA, Grade: HS PSSA 2013 Keystone Algebra 1. - signup at to remove - Student name:
Test Booklet Subject: MA, Grade: HS PSSA 2013 Keystone Algebra 1 Student name: Author: Pennsylvania District: Pennsylvania Released Tests Printed: Friday May 31, 2013 1 Which of the following inequalities
More informationLecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 2nd edition. Miller, O'Neill, & Hyde. Victor Valley College
Lecture Guide Math 90 - Intermediate Algebra to accompan Intermediate Algebra, 2nd edition Miller, O'Neill, & Hde Prepared b Stephen Toner Victor Valle College Last updated: 11/24/10 0 1.1 Sets of Numbers
More informationSection A Plotting Straight Line Graphs Grade D / C
Name: Teacher Assessment Section A Plotting Straight Line Grade D / C. The diagram shows the points P (0, 4) and Q (5, 2). Q O Find the coordinates of the mid-point of the line segment PQ. P Answer (...,...
More information1.5. Slopes of Secants and Average Rate of Change. _ Δd _ 400
1.5 Slopes of Secants and Average Rate of Change Change occurs in many aspects of everyday life. A person s height and mass change from birth to adulthood. The distance that a car travels in a period of
More informationcan be used to represent this situation.
Question 1. Solve the real-world situation by using the substitution method. A cable television provider has a $70 setup fee and charges $82 per month, while a satellite television provider has a $175
More informationUNIT 2 REASONING WITH LINEAR EQUATIONS AND INEQUALITIES Lesson 1: Creating Linear Equations and Inequalities in One Variable
Guided Practice Example 1 James earns $15 per hour as a teller at a bank. In one week he pays 17% of his earnings in state and federal taxes. His take-home pay for the week is $460.65. How many hours did
More informationCourse 1 Benchmark Test End of Year
Course 1 Benchmark Test End of Year 1. Which rule best describes the relationship shown in the function table below? Input A. subtract 2 Output 1 3 2 6 3 9 4 12 5 15 4. What is the least common multiple
More informationSt. Michael s Episcopal School. Summer Math
St. Michael s Episcopal School Summer Math for rising 7th & 8 th grade Algebra students 2017 Eighth Grade students should know the formulas for the perimeter and area of triangles and rectangles, the circumference
More informationMATH 081. Diagnostic Review Materials PART 2. Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED.
MATH 08 Diagnostic Review Materials PART Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED DO NOT WRITE IN THIS MATERIAL Revised Winter 0 PRACTICE TEST: Complete as
More informationPre-Algebra 8 Semester 1 Practice Exam
. Evaluate xy when x = 0 and y = 6. 6 80. Which expression is equivalent to x + x x + x+ x+ x+ x x x x x x x?. In math class, we follow the order of operations when evaluating expressions. Which is the
More informationA C E. Applications. Applications Connections Extensions. Student 1 Student Below are some results from the bridge experiment in a CMP class.
A C E Applications Connections Extensions Applications 1. Below are some results from the bridge experiment in a CMP class. Bridge-Thickness Experiment Number of Layers 2 4 6 8 Breaking Weight (pennies)
More informationNTI Work Day #1 Math. 4. What is the slope of the line that passes through the origin and (-3, -2)? a. 3 2 b. 2 3 c. 0 d. 2 3 e.
NTI Work Day #1 Math 1. 2 0 + 2 3 2 2 =? a. 4 b. 6 1 4 c. 7 d. 8 3 4 e. 9 3 4 2. The figure below is a graph of which of the following equations? a. y = -3x + 5 b. y = -2x + 2 c. y = 3 2 x 2 d. y = 2 3
More informationMTH 103 Group Activity Problems (W1B) Name: Types of Functions and Their Rates of Change Section 1.4 part 1 (due April 6)
MTH 103 Group Activity Problems (W1B) Name: Types of Functions and Their Rates of Change Section 1.4 part 1 (due April 6) Learning Objectives Identify linear and nonlinear functions Interpret slope as
More informationNUMERACY TOOLKIT TOOLKIT NUMERACY
NUMERACY TOOLKIT TOOLKIT NUMERACY Addition Calculating methods Example 534 + 2678 Place the digits in the correct place value columns with the numbers under each other. Th H T U Begin adding in the units
More informationYear 4 Term 3 Homework
Yimin Math Centre Year 4 Term 3 Homework Student Name: Grade: Date: Score: Table of contents 4 Year 4 Term 3 Week 4 Homework 1 4.1 Topic 1 Volume.................................... 1 4.2 Topic 2 Mass......................................
More informationChapter 3: Linear Functions & Their Algebra
Chapter 3: Linear Functions & Their Algebra Lesson 1: Direct Variation Lesson 2: Average Rate of Change Lesson 3: Forms of a Line Lesson 4: Linear Modeling Lesson 5: Inverse of Linear Functions Lesson
More informationSAT SHEET (calculators allowed)
. If! 15 = 15! x, then x = A) -0 B) -15 C) 0 D) 15 E) 0 4. A dozen roses cost $15.60 and the cost of one rose and one lily together cost $4.50. What is the cost of one lily? A) $1.0 B) $.0 C) $5.80 D)
More information3) What is the sum of the measures of all of the interior angles of the triangle?
1) Define an equilateral triangle. 2) Draw a diagram to illustrate this triangular garden and hose, and label the vertices A, B, C and let segment AD represent the hose. 3) What is the sum of the measures
More informationREVIEW: HSPA Skills 2 Final Exam June a) y = x + 4 b) y = 2x + 5 c) y = 3x +2 d) y = 2x + 3
Part I- Multiple Choice: 2 points each: Select the best possible answer. 1) The nutrition label of cookies states that there are 20 servings in a box and that one serving contains 1.5 grams of fat. Kyle
More informationToday s Date: Finished by: 7 th Grade Math Final Exam Study Guide Exams: May 27-29
NAME: Today s Date: Finished by: 7 th Grade Math Final Exam Study Guide Unit 7.1: Operations with Rational Numbers 1. Which number property describes the number sentence (17 x 3) x 20 = 17 x (3 x 20)?
More informationKansas City Area Teachers of Mathematics 2016 KCATM Math Competition
Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 5 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 15 minutes You may
More informationx 2 + x + x 2 x 3 b. x 7 Factor the GCF from each expression Not all may be possible. 1. Find two numbers that sum to 8 and have a product of 12
Factor the GCF from each expression 4 5 1. 15x 3x. 16x 4 Name: a. b. 4 7 3 6 5 3. 18x y 36x y 4x y 5 4. 3x x 3 x 3 c. d. Not all may be possible. 1. Find two numbers that sum to 8 and have a product of
More informationSemester 1 Final Review. c. 7 d.
Solve the equation in questions 1-4. 1. 7 x + 5 = 8 a. 7 b. 1 7 c. 7 d. 7. 7 = d + 0 a. 10 b. 0 c. 1 d. 1. p 1 = 5(p 1) (7 p) a. b. 0 c. 9 d. 10 4. 5x 5 = x 9 a. b. 1 c. 1 d. 5. A customer went to a garden
More informationGrade 7/8 Math Circles Fall Nov. 4/5 Solution Set - The Pythagorean Theorem
1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 014 - Nov. 4/5 Solution Set - The Pythagorean Theorem 1. Let a and b be the lengths
More informationThis is Solving Linear Systems, chapter 4 from the book Beginning Algebra (index.html) (v. 1.0).
This is Solving Linear Systems, chapter 4 from the book Beginning Algebra (index.html) (v. 1.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
More informationMATH 410 Notes Simplifying Algebraic Expressions
MATH 410 Notes 2016 1.9 - Simplifying Algebraic Expressions Commutative Property: a + b = b + a and a b = b a Associative Property: a + (b + c) = (a + b) + c and a (b c) = (a b) c Distributive Property:
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1332 Exam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the cardinal number for the set. 1) {8, 10, 12,..., 66} 1) Are the sets
More informationObjective 8 - Page 1 of 6
Objective 8 - Page of 6 The drama department at McHenry High School has built a stage floor in the shape of a regular octagon. The length of each side of the octagon is 4 yards. is the apothem. What is
More informationDISTANCE, RATE, AND TIME 7.1.1
DISTANCE, RATE, AND TIME 7.1.1 Distance (d) equals the product of the rate of speed (r) and the time (t). This relationship is shown below in three forms: d = r!t!!!!!!!!!r = d t!!!!!!!!!t = d r It is
More informationGive your answer to part (a) to an appropriate degree of accuracy. 2. This is a list of ingredients for making a pear & almond crumble for 4 people.
1. Work out 2.56 3.50 8.765 6.78 (a) Write down all the figures on your calculator display.... (b) Give your answer to part (a) to an appropriate degree of accuracy.... (1) (Total 3 marks) 2. This is a
More information8, x 2. 4and. 4, y 1. y 2. x 1. Name. Part 1: (Skills) Each question is worth 2 points. SHOW ALL WORK IN THE SPACE PROVIDED. 1.
MATH 099 PRACTICE FINAL EXAMINATION Fall 2016 Name Part 1: (Skills) Each question is worth 2 points. SHOW ALL WORK IN THE SPACE PROVIDED. 1. Determine whether 4, 3 is a solution to the equation 3x 3y 21
More informationName: Class: Date: Unit 1. Thinking with Mathematical Models Investigation 2: Linear Models & Equations. Practice Problems
Unit 1 Thinking with Mathematical Models Investigation 2: Linear Models & Equations Practice Problems Directions: Please complete the necessary problems to earn a maximum of 7 points according to the chart
More information7 th Grade MCA3 Standards, Benchmarks, Examples, Test Specifications & Sampler Questions
7 th Grade 3 Standards, Benchmarks, Examples, Test Specifications & Sampler Questions Strand Standard No. Benchmark (7 th Grade) Sampler Item Number & Operation 12-16 Items Modified 7-9 Items Read, write,
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *6527724295* MATHEMATICS 0580/33 Paper 3 (Core) May/June 2017 Candidates answer on the Question Paper.
More informationBUMPER BETWEEN PAPERS PRACTICE PAPER. SET 2 (of 3) Foundation Tier (Summer 2017) QUESTIONS. Not A best Guess paper.
BUMPER BETWEEN PAPERS PRACTICE PAPER SET 2 (of 3) Foundation Tier (Summer 2017) QUESTIONS Not A best Guess paper. Neither is it a prediction... only the examiners know what is going to come up! Fact! You
More informationReview Unit 4: Linear Functions
Review Unit 4: Linear Functions You may use a calculator. Unit 4 Goals Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships
More informationSection 2.5 Ratios and Proportions
Section. Ratios and Proportions Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Apply cross-multiplication to Simplifying fractions (R.) to
More information