I. Expressions/Equations/Inequalities: Show all work for each question.

Transcription

1 Name: Date: Algebra I Common Core: Midterm Review I. Expressions/Equations/Inequalities: Show all work for each question. 1) Solve for y: 5) Which value of x is in the solution set of the inequality 5 1? (1) -8 () -6 (3) -3 (4) 0 ) Solve for x: 1) 8 ) 13 3) 15 4) 3 6) Solve for x: 3 ax b c ) Solve for x: : ( x ) 0 7) Solve for h: A h( b 1 b ) 3 5 4) Name the smallest integer value for x: x ) Solve for h: A r h

2 9) Given + ax 5 > 10, determine the smallest integer value of x when a =? 13) Find the product of ( 6) and (5x x 7). 10) Simplify and express as a trinomial: 5( x 3) 6( x ) 3 14) If A= 5x 6x 3 and B= 4x 5x 7 ; find each of the following: a) A + B b) A - B 11) Given 5m + mn + 1 > 11, determine the largest integer value of n when m = -. 15) Which statement is not always true? 1) The sum of two rational numbers is rational. ) The product of two irrational numbers is rational. 3) The sum of a rational number and an irrational number is irrational. 4) The product of a nonzero rational number and an irrational number is irrational. 1) Determine if the product of and is rational or irrational. Explain your answer. 16) When multiplying polynomials for a math assignment, Pat found the product to be. He then had to state the leading coefficient of this polynomial. Pat wrote down as the leading coefficient, 5 as the constant and 3 as the degree. Do you agree with Pat's answer? Explain your reasoning.

3 II. Word Problems 17) The Ambrose family has two children whose ages can be represented by consecutive odd integers. If the sum of their ages is 37, which of the following equations could be used to find the age of the youngest child? (1) x + x + 1 = 37 () x(x + 1)= 37 (3) x + x + = 37 (4) x(x + ) = 37 18) Jonathan has been on a diet since January 013. So far, he has been losing weight at a steady rate. Based on monthly weigh-ins, his weight, w, can be modeled by the function w = -3m + 05 where m is the number of months after January ) Alex makes ceramic bowls to sell at a monthly craft fair in a nearby city. Every month, she spends $50 on materials for the bowls from a local art store. At the fair, she sells each completed bowl for a total of $5 including tax. Which equation expresses Alex s profit as a function of the number of bowls that she sells in one month? (1) p(x)=50x + 15 () p(x)=15x+ 5 (3) p(x)=5 (4) p(x)=5x-50 1) A parking garage charges a base rate of $3.50 for up to hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking. a) How much did Jonathan weigh at the start of the diet? b) How much weight has Jonathan been losing each month? c) How many months did it take Jonathan to lose 45 pounds? 19) The length of a rectangular sandbox is 4 more than twice the width, w. Write an equation that shows the perimeter of the playground is 98 feet. Solve the equation to determine the length of the sandbox. Write an equation that shows the area of the sandbox is equal to 510 square feet. Which linear equation can be used to find x, the additional hourly parking rate? 1) ) 3) 4) ) Jennifer and Kim both enjoy making bracelets. At the beginning of this year Jennifer had already made 5 bracelets. She continues to make eight bracelets every month, m. Kim just started making bracelets recently, so she had only made eleven at the beginning of the year. Kim is able to work more quickly, so she makes ten bracelets every month, m. Write an equation for the total number of bracelets, T, made by Jennifer. Write an equation for the total number of bracelets, T, made by Kim. Use your equations to determine how many months it will take for Jennifer and Kim to have made the same number of bracelets.

4 III. Graphs of Equations/Inequalities & Systems 3) What is the solution to the system of linear equations: y x 4 and y x 1? (1) (-1,3) () (0,4) (3) (1,-1) (4) (-3,3) 4) Which point is in the solution set to the system of inequalities y x 1 and 1 y x 5? (1) (-3,10) () (8,) (3) (-,1) (4) (4,1) 5) Which system of equations would have the same solution as the system: x y 5 y 10 y 5 (1) x y 10 () 3y 5 y 10 (3) 3y 15 y 10 (4) x y 5 y 10 6) Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.

5 IV. Statistics 7) The accompanying box-and-whisker plot represents the scores earned on a science test. 8) Which statistic would indicate that a linear function would not be a good fit to model a data set? Explain your response. 1) ) Answer each of the following questions about the box plot shown above: 3) 4) Minimum= Range= 1 st quartile= Median= Interquartile Range= Explain: 3 rd Quartile= Maximum= Percentage of scores between ) Since 1990, fireworks usage nationwide has grown, as shown in the accompanying table, where t represents the number of years since 1990, and p represents the fireworks usage per year, in millions of pounds. Create the residual plot using the table in question #9 on the set of axes given below. Number of years since 1990 Fireworks usage per year, in millions of pounds Residual Find the equation of the linear regression model for this set of data, round values to the nearest hundredth.

6 30) The relationship of a woman s shoe size and length of a woman s foot, in inches, is given in the accompanying table. 31) Based on the line of best fit drawn below, which value could be expected for the data in June 015? The linear correlation coefficient for this relationship is 1) 1 ) 3) 0.5 4) 0 1) 30 ) 310 3) 480 4) 540 V. Functions 3) A store sells self-serve frozen yogurt sundaes. The function represents the cost, in dollars, of a sundae weighing w ounces. An appropriate domain for the function would be 1) integers ) rational numbers 3) nonnegative integers 4) nonnegative rational numbers 33) If the function h(x) represents the number of full hours that it takes a person to assemble x sets of tires in a factory, which would be an appropriate domain for the function? (1) Set of real numbers () Set of negative integers (3) Set of integers (4) Set of non-negative integers