Unit #3 Linear Algebra Review

Transcription

1 Name: Unit # Linear Algebra Review Date: 1. The expression x + 5y 7x+ 4y is equivalent to which of the following? (1) 4x 9y () 4x y () 9y 4x (4) 10x + 9y. Written without parentheses, the expression 5 ( x ) ( x 8) + is equal to (1) 8 x + 1 () 1x + 1 () 1 x 1 (4) 8x 1. Which of the following is the solution to the equation 5x+ 9= x+ 4? (1) () () (4) For which of the following values of m will the line whose equation is y = mx+ pass through the point ( 8, 15)? (1) m = 8 () () m = (4) 5 4 m = m = 5. Which of the following values of x solves the equation 1.5 ( ) x + = 1.05? (1) x = 4.7 () x = 1.6 () x =.7 (4) x =.

2 6. Ellen is charged a flat monthly fee of $10 plus an additional 5 cents per phone call she makes. Which of the following equations gives the dollar cost of her bill, C, as a function of the number of calls she makes, n? (1) C = 10n+ 5 () C = 0.5n+ 10 () C = 5n+ 10 (4) C = 10n Which of the following expressions most correctly represents the phrase three less than seven times a number? (1) 7 n () 7 n () 7( n ) (4) ( n 7 ) ) ) 8. When ( 5x 9 is subtracted from (x + the resulting binomial can be written as (1) x 1 () 7x 6 () 7x 6 (4) x If n +1 represents an even integer, which of the following represents the next smaller consecutive even integer? (1) n () n 1 () n (4) n The area of any triangle is given by 1 A = bh. Solved for h this formula is (1) 1 Ab () Ab () A b 1 A (4) b 11. Which of the following values of x lies in the solution set of x + 7< 1? (1) x = 0 () x = 5 () x = 1 (4) x = 4

3 1. Which of the following values of x solves the equation 5( x ) ( x 9) =? (1) 11 () 6 () 8 (4) 1. Maria went to the store and bought pounds of green beans and a loaf of bread that cost $.5. If Maria spent $4.9 in total, which of the following equations could be used to determine the price per pound, p, of the green beans? (1) () p +.5 = 4.9 () p +.5 = ( 4.9) (4) p +.5 = 4.9 p + = ( ) 14. The physics classes at Arlington are taking a field trip to Great Adventure. There are a total of 60 students and chaperones going on the trip. Each bus holds a maximum of 40 students. What is the least number of busses needed for the trip? (1) 14 () 18 () 16 (4) The length of a rectangle is 6 more than twice its width, w. Which of the following expressions gives the perimeter of the rectangle in terms of w? (1) 6 w + 1 () 4w + 1 () w + 6 (4) 8w Mrs. Wright starts her Algebra class with a warm-up problem. She states I am thinking of a number such that eight less than three times is number is 49. What number is Mrs. Wright thinking of? (1) 10 () 14 () -4 (4) 19

4 17. Which of the following values of x solves the equation 15 x + =? (1) 9 () - () 7 (4) What is the largest integer value that lies in the solution set of the inequality x + 1 5? (1) x = 1 () x = () x = (4) x = Maria went to the store and bought four pounds of potatoes and a turkey that cost $1.50. If she spent $15.10, then the price, per pound, of the potatoes was (1) $0.65 () $0.95 () $0.50 (4) $ Two consecutive integers have the property that if twice the smaller is added to the larger the resulting sum is equal to 40. Which of the following represents the larger consecutive integer? (1) 0 () 18 () 1 (4) Which of the following values of x is the smallest integer in the solution set of the inequality shown below? 8 x < 1 (1) () () 0 (4) 4. Which of the following values of x solve the equation x+ 0= x 15? (1) 5 () 7 () 11 (4) 5

5 Part II Answer all questions in this part. Each correct answer will receive credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.. When three times a number is added to eight times the same number, the result is 10 less than six times that same number. Algebraically determine the number. 4. Maria recently went to the store and bought 8 rolls and a pound of hamburger and spent a total of $6.85. If the hamburger cost $.5, how much did an individual roll cost? Only an algebraic solution will be accepted. 5. Solve the equation shown below. ( x ) ( = 8x+ ) Part III - Answer all questions in this part. Each correct answer will receive credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 6. Solve the following equation. ( ) x 7= 7x+ 1 5x+

6 7. A rectangle has a length that is 5 less than three times its width, w. On the diagram below, write an expression for the length in terms of the width, w. Then, find the perimeter of the rectangle in simplest terms of w. length = w Part IV - Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 8. Three sisters have ages that are consecutive odd integers. When twice the youngest sister s age is added to the oldest sister s age, the result is 11 less than four times the middle sister s age. Algebraically determine the three sisters ages. 9. Solve the inequality below. Graph the solution set on the number line below. 5x + 9< 8x