Algebra I. Midterm Review

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1 Algebra I Midterm Review

2 Class: Date: Algebra 1 Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 Use the vertical-line test to determine which graph represents a function. A C B D 1

3 2 What is the graph of y + 2 =! 2 3 ( x + 6)? F H G J 2

4 3 Find the rate of change. What does rate of change mean in this situation? A B C D 60; 1 hour to move 60 miles. 60; the speed is 60 miles per hour. 30; 1 hour to move 15 miles. 30; the speed is 30 miles per hour. 3

5 What is the graph of the equation? 4!4x + y =!2 F H G J 4

6 5 3x! y = 1 A C B D 6 A plumber s assistant charges a service fee of $40 plus $25 per hour for labor. Write a function rule for the total cost of hiring the assistant for a job that takes x hours. How much would it cost to hire him for a job that takes 4 hours? F y = x; $140 H y = 40x + 25; $185 G y = 25x! 40; $60 J y = 40x! 25; $135 5

7 What is the solution of each equation? z = z A! 5 6 B C D infinitely many solutions no solution 8 The formula for the area of a triangle is A = 1 bh. Solve the formula for h. What is the height h of a 2 triangle with area A = 40 square inches and base b = 20 inches? F h = A 2b, 1 inch H h = 2A b, 4 inches G h = 2A b, 2 inches J h = A! 1 2! b, h = inches Which number is a solution of the inequality? 9 8 " 8k A 1 B 11 C 3 D What are the solutions and graph of the compound inequality below? 3n! 1 > 8 or 4n + 3 <!1 F < n < 1 2 H n < 1 or n > 3 G n <!1 or n > 3 J n < 1 2 or n > If the data in the table are linear, what is the slope of the line that contains the data? x!2!1 0 1 y A 1 B! 2 3 C 1 D! 3 2 6

8 Write the equation in slope-intercept form. What are the slope and y-intercept? 12!5x! 8y = 1 F y = 5 8 x ; slope: G y = 5 8 x! 1 8 ; 1 8 ; y-intercept: 5 8 H y =! 5 8 x! 1 8 ; slope:! 5 8 ; y-intercept:! 1 8 slope: 5 8 ; y-intercept:! 1 8 J y =! 5 8 x slope: 5 8 ; y-intercept: !8x + 3y =!10 A y = 8 3 x ; 10 slope: 3 ; y-intercept: 8 3 B y = 8 3 x! 10 3 ; slope: 8 10 ; y-intercept:! 3 3 C y =! 8 3 x! 10 3 ; 8 slope: 3 ; y-intercept: 10 3 D y =! 8 3 x slope: 3 ; y-intercept: What are the names of the properties shown in steps 3 and 4? Step 1 10x! 3 + 5x = 10x + (!3) + 5x Step 2 = 10x + 5x + (!3) Step 3 = ( )x + (!3) Step 4 = 15x + (!3) Step 5 = 15x! 3 F G H J Commutative Property of Addition and Distributive Property Distributive Property and Substitution Commutative Property of Addition and Associative Property of Addition Substitution and Identity Property of Addition What property is illustrated by each statement? (4 + 4) = (7 + 4) + 4 A Inverse Property of Addition B Associative Property of Addition C Commutative Property of Multiplication D Commutative Property of Addition 7

9 16 Use the Distributive Property to rewrite the following expression. 8(4 +5x) F x G 32 40x H x J 32 3x What is the simplified form of each expression? 17 4 ( 12! 6) 2 3 A 12 B 48 C 8 D What is the solution of the proportion? 3y! 8 = y 12 5 F!10 G!7 H 3 40 J What is the value of x when!3x + 16 =!23? A 13 C 13 B 6 D 6 20 What is the solution of the equation? 12 =!2(!9!3z) F!36 G!1 H 12 J The distance traveled by a rock rolling down a hill is shown in the table below. Which equation best represents the relationship between x and y? Time (x) Distance (y) A y = 2x + 2 C x = y! 2 B y = 3x D x = 3y 8

10 22 The scatter plot shows the trend for the number of cars a company rents during a two-week period. Which equation best models the data in the scatter plot? F y =! 2 5 x + 70 H y = 2 5 x + 70 G y = 5 2 x! 70 J y =! 5 2 x What is the solution of the equation?!2 = 3 + z!2 A!2 B 1 C 4 D 7 What is the solution of the equation? 24 5 ( 10x! 10) =!5 (!4x + 4) F 1 G 1 H 0 J 2 25 A dress that normally costs $69.50 is on sale for 45% off. What is the sale price of the dress? A $38.23 C $24.50 B $31.28 D $ The circulation of a newsletter decreased from 5200 to Find the percent of decrease in circulation to the nearest percent. F 66% G 40% H 166% J 6% 9

11 27 What value of x makes the equation below true? 1 10 x! 5 = 65 A 650 C 700 B 600 D A sound studio charges a $100 reservation fee and $52 per hour. Felipe paid a total of $360 to use the sound studio. Write an equation that can be used to find the total number of hours (h) during which Felipe used the studio. F h = 360 G h = 360 H 100(52+ h) = 360 J 52(h + 100) = Ed is saving his money in a savings account. She started the account with $150. Each week he will deposit $50. In how many weeks will he have saved $400? A 5 C 20 B 10 D During Ivan s last vacation, he used 10 gallons of gas to travel 220 miles. Which proportion can he use to predict the number of gallons g he will use to travel 1,000 miles? To the nearest tenth, what is g? g F 10 = ; 22.0 gallons 220 H = 1000 ; 78.0 gallons 10 g G = 1000 ; 45.5 gallons J g g 10 = 220 ; 45.5 gallons This table represents how a group of elementary students in a school in Boston get to school. Transportation Mode Number of Elementary Students bus 28 subway 20 car 16 foot 11 Approximately what precent of the respondents take the subway to school? A 25% C 52% B 45% D 33% 10

12 32 This table represents how a group of elementary students in a school in Boston get to school. Transportation Mode Number of Elementary Students bus 28 subway 20 car 16 foot 11 Of 5,000 elementary students in Boston, what is the best estimate of the number of students who will ride the bus to school? F 1150 H 1750 G 1600 J 1850 What is the graph of the inequality? 33 h > 7 2 A B C D 34 Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. How many cans are needed to meet or surpass your goal? F c > 325; c > 101 H c " 325; c " 101 G " c; c " 549 J c " 325; c #

13 What compound inequality represents the phrase? Graph the solutions. 35 all real numbers that are greater than 8 and less than 8 A 8 < x < 8 B 8 < x < 8 C 8 < x # 8 D 8 # x # 8 36 What are the solutions and graph of the inequality?!12 # 2x! 4 < 8 F x #!4 or x > 6 G!4 # x < 6 H!2 # x < 8 J!8 # x < 2 Let X = {x x is a whole number less than 15}, Y = { y y is a multiple of 3}, Z = {z z is a real number greater than or equal to 5.5}. 37 What is X $ Z? A {6,7,8,9,10,11,12,13,14} B {6,9,12,15} C {5,6,7,8,9,10,11,12,13,14,15} D % 12

14 38 A doctor is examining 3 patients. Which symptoms do all three patients have in common? F {headaches, hair loss, congestion} H {spasms, memory loss, appetite loss} G {cold sweats, congestion, memory loss} J {fever, joint pain, tiredness} 39 Identify whether the relation between the domain (time) and range (height) is or is NOT a function. a. b. A B C D a is a function, b is not a function a is not a function, b is a function both a and b are functions neither a or b are functions 13

14 40 As a homework assignment, Amy has done a study on the number of hours spent on homework a week and the average grade in a particular math class.

15 14 40 As a homework assignment, Amy has done a study on the number of hours spent on homework a week and the average grade in a particular math class. She found the relationship to be G = h, where G represents the grade earned and h represents the number of hours spent on homework. If a student spends 6 hours doing math homework each week, what grade can that student expect? F 90 H 86 G 88 J What is the domain and the range of the function represented by the list of ordered pairs? (!2, 5), (0, 4), (3, 6), (5, 1) A The domain is 1,4,5,6 and the range is!2, 0, 3, 5 C The domain is!2, 0, 1, 3 and the range is!2,0,1,6 B The domain is!2,0,3,6 and the range is!2, 0, 2, 6 D The domain is!2,0,3,5 and the range is 1, 4, 5, 6 42 What is the range of f(x) = 4 3 x + 4 for the domain {!1, 3, 7, 9}? F 8 3, 10, 40 3, 16 H 8 3, 8, 40 3, 16 G 8 3, 7, 40 3, 15 J 8 3, 8, This graph shows the height and distance traveled by a tennis ball. What is the maximum height of the tennis ball? A 0 feet B about 4.5 feet C about 5.5 feet D about 9 feet

16 44 Use integer coefficients. What is the standard form of the equation below? (y! 3) = 2 (x + 6) 3 F 2x + 3y = 7 H 2x 3y = 9 G 3x 2y = 21 J 2x 3y = Find the domain and range of the relation and determine whether it is a function. A B C D 1 domain: positive integers; range: positive integers; No, it is not a function. domain: x > 1; range: y > 0; Yes, it is a function. domain: all real numbers; range: all real numbers; Yes, it is a function. domain: x " 0; range: y > 1; No, it is not a function. 15

17 46 Terry pays $210 in advance into her health savings account. She used the account 1 time, and $10 was deducted from the account. After using it 4 times, $40 was deducted from the account. Which graph would you use to represent this situation? F B = 210! 2n H B = n G B = n J B = n 47 Suppose you have two distinct lines. One has slope m, one contains points A and B. Are the lines parallel, perpendicular, or neither? If neither, what is the correct explanation? m = 1 ; A = (0, 0), B = (1,! 2) 2 A B parallel perpendicular C Neither; the slopes are NOT equal, and the product of the slopes does NOT equal 1. D Neither; the slopes are equal, and the product of the slopes does NOT equal 1. 16

18 48 What is the equation for the line that is parallel to the given line and that passes through the given point? y =!3x + 6; (0, 1) F y = 3x + 1 H y =!3x + 1 G y =!3x! 1 J y =!3x What is the equation of a line that is perpendicular to the given line and that passes through the given point? y = 1 3 x + 5 ; (2, 1) 3 A y = 3x + 7 C y =!3x + 7 B y = 3x D y =!3x The table shows the height of a slowly descending air balloon over time. Let y stand for the height of the balloon in feet and let x stand for the time in minutes. Which equation best models the data? Time (minutes) Height (feet) F y = 250x! 1.6 H y =!1.6x G y =!1.6x J y = 10x

19 Algebra 1 Midterm Review Answer Section MULTIPLE CHOICE 1 ANS: A STA: MA.912.A ANS: G STA: MA.912.A ANS: D STA: MA.912.A ANS: G STA: MA.912.A ANS: B STA: MA.912.A ANS: F STA: MA.912.A ANS: D STA: MA.912.A.3.1 MA.912.A ANS: H STA: MA.912.A ANS: A STA: MA.912.A ANS: G STA: MA.912.A ANS: C STA: MA.912.A ANS: H STA: MA.912.A ANS: B STA: MA.912.A ANS: G STA: MA.912.A ANS: B STA: MA.912.A ANS: G STA: MA.912.A ANS: B STA: MA.912.A ANS: J STA: MA.912.A ANS: C STA: MA.912.A ANS: G STA: MA.912.A ANS: B STA: MA.912.A ANS: J STA: MA.912.A ANS: B STA: MA.912.A ANS: F STA: MA.912.A.3.1 MA.912.A ANS: A STA: MA.912.A ANS: G STA: MA.912.A ANS: C STA: MA.912.A ANS: G STA: MA.912.A ANS: D STA: MA.912.A ANS: G STA: MA.912.A ANS: D STA: MA.912.A ANS: J STA: MA.912.A ANS: A STA: MA.912.A ANS: H STA: MA.912.A ANS: A STA: MA.912.A ANS: G STA: MA.912.A ANS: A STA: MA.912.D.7.1 MA.912.D.7.2 1

20 38 ANS: J STA: MA.912.D.7.1 MA.912.D ANS: B STA: MA.912.A ANS: G STA: MA.912.A ANS: D STA: MA.912.A ANS: H STA: MA.912.A ANS: B STA: MA.912.A ANS: J STA: MA.912.A ANS: B STA: MA.912.A.2.3 MA.912.A ANS: F STA: MA.912.A ANS: B STA: MA.912.G ANS: H STA: MA.912.A ANS: C STA: MA.912.A ANS: H STA: MA.912.A

Name: Period: QVMS GTA FALL FINAL EXAM REVIEW PRE-AP ALGEBRA 1

Name: Period: QVMS GTA FALL FINAL EXAM REVIEW PRE-AP ALGEBRA ) When simplifing an epression, ou perform operations inside grouping smbols first. a. alwas b. sometimes c. never ) The opposite of a negative