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Name: ________________________ Class: ___________________ Date: __________ MID-TERM TEST Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A Identify the mapping diagram that represents the relation and determine whether the relation is a function. ÏÔ ¸Ô ÔÌÓ (−3, −6), (−1, −6), (5, −6), (8, −6) Ô˝˛ A The relation is not a function. B B The relation is a function. C The relation is a function. D The relation is not a function. 2 Which graph represents the following system of equations? y = 3x + 3 y = –2x – 3 1 ID: A Name: ________________________ ID: A C 3 4 5 D Which equation is an identity? A 5w + 6 − w = 6w − 2(w − 3) B 9 − (5v + 7) = −5v − 2 C 5y + 3 = 5y − 3 D 6m − 6 = 7m + 9 − m Which equation is an identity? A 5m − 4 = 6m + 6 − m B 4y + 5 = 4y − 8 C 3w + 6 − w = 4w − 2(w − 3) D 12 − (6v + 8) = −6v − 4 Evaluate f (x ) = −x 2 + 1 for x = –3. A –9 B –4 C –8 D 4 Write a function rule for the table. 6 x 2 3 4 5 A B C D 2 f(x) –8 –12 –16 –20 f(x) f(x) f(x) f(x) = = = = −4x 4x x−4 x+4 Name: ________________________ ID: A Short Answer Write the slope-intercept form of the equation for the line. Find the slope of the line. 7 17 Find the slope of the line that passes through the pair of points. 8 (2, 8), (7, –3) 9 (2, 6), (7, 0) Find the x- and y-intercept of the line. Find the slope and y-intercept of the line. 10 7 y= x+2 5 11 15x + 3y = 18 12 1 y = x – 10 4 13 10x + 6y = 78 14 16x + 2y = –110 18 2x + 3y = –18 19 3x -4y = –12 20 The grocery store sells kumquats for $4.00 a pound and Asian pears for $2.75 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $12. Write an equation in point-slope form for the line through the given point with the given slope. Write an equation of a line with the given slope and y-intercept. 21 (4, –6); m = 15 m = –5, b = 5 22 16 m = –4, b = –7 A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. 3 3 5 Name: ________________________ ID: A Are the graphs of the lines in the pair parallel? Explain. 23 1 y= x+5 3 4x – 12y = –11 Write an equation for the line that is parallel to the given line and that passes through the given point. 24 y = –5x + 3; (–6, 3) 26 –x + 12y = 5; (0, 8) 27 Evaluate f (x ) = 3x + 2 for x = 3. 28 Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $.51. 29 Find a solution to the following system of equations. −2x + 3y = −1 4x + 2y = 10 30 What is the solution of the system of equations? y=x+1 y = 2x – 4 33 Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs. Huang can use them. To apply herbicide to a large field she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution. How much of the 67% solution must she use? 34 A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the current. Write the equation of a line that is perpendicular to the given line and that passes through the given point. 25 x + 9y = –7; (8, –3) Solve the system of equations using substitution. 31 3x + 2y = 7 y = –3x + 11 32 A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by elimination to find the number of nickels and dimes that are in the jar. Graph the inequality. 35 y < 5x − 2 37 p<2 36 y ≥ 2x − 2 38 x ≤ −2 4 Name: ________________________ ID: A Write the linear inequality shown in the graph. 39 40 Find a solution of the linear inequality. y ≥ 4x − 5 Write the inequality in words. 41 3n < 52 Solve the inequality. Then graph your solution. 42 x − 4 ≤ −8 47 | 5x + 10 | < 20 43 w −5 ≤ 5 48 | d + 2| ≥ − 6 44 –6g < –12 49 | d − 10 | < − 11 45 –17 < 3x – 8 < 4 50 –2 < 3x – 5 < 7 46 | d + 2| ≥ 6 51 –5 < 2x – 9 < 19 57 4x – 8 = 3x – 4 Solve the inequality. 52 4(x – 12) > 8 Solve the equation. 53 2 x–5=3 9 54 12 = –d + 20 55 5(y + 6) = 70 56 3x – 4 = 2x – 8 5 Name: ________________________ 58 67 a. 23 = −11 − 4x 68 b. 23 = −11 + (−4x) What is the solution of the system of equations? y = –2x + 2 y = –x – 10 c. 23 + 11 = −11 + (−4x) + 11 69 d. 23 + 11 = −11 + 11 + (−4x) What is the solution of the system of equations? y = 3x + 3 y = –5x – 5 −4x 70 Evaluate f (x ) = x + 3 for x = –2. −4 71 Evaluate f (x ) = 2x + 7 for x = 2. 72 Find a solution to the following system of equations. −3x + 3y = −9 2x + 3y = 6 73 Find a solution to the following system of equations. −5x + 3y = 8 −x + y = 4 74 Find the range of f (x ) = −x + 4 for the domain {–3, –2, –1, 1}. 34 = −4x 34 f. g. −4 = −8.5 = x A van travels 320 miles on 16 gallons of gas. Write and solve a function to find how many gallons the van needs to travel 480 miles. Write an algebraic expression for the phrase. 60 the sum of h and 11 Define a variable and write an expression for the phrase. 61 the quotient of 8 times a number and 9 62 What equation models the data in the table if d = number of days and c = cost? Days 2 3 5 6 63 (−9)(2) (−2) Which properties of equality justify steps c and f? e. 59 ID: A Use the vertical line test to determine whether the relation is a function. 75 Cost 8 12 20 24 Evaluate u + xy, for u = 11, x = 9, and y = 5. Simplify the expression. 64 –8 + 7 65 |−5 − 16| 66 (−4) 4 6 ÔÏ Ô¸ ÌÔ (−1, −2), (3, −1), (−5, 2), (−3, −5) ˝Ô Ó ˛ ID: A MID-TERM TEST Answer Section MULTIPLE CHOICE 1 B 2 D 3 A 4 C 5 C 6 A SHORT ANSWER 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 −1 11 − 5 6 − 5 7 ;2 5 −5; 6 1 ; –10 4 5 − ; 13 3 −8; −55 y = –5x + 5 y = –4x – 7 y=x−1 x-intercept is –9; y-intercept is –6. x-intercept is –4; y-intercept is 3. 4k + 2.75p = 12 3 y + 6 = (x − 4) 5 y + 5 = –3(x – 1); y = –3x – 2 Yes, since the slopes are the same and the y-intercepts are different. y = –5x – 27 y = 9x – 75 y = −12x + 8 11 1 ID: A 28 29 30 31 32 33 34 c(p ) = 0.51p (2, 1) (5, 6) (5, –4) 31 nickels and 29 dimes 18 L 4 mph 35 36 37 38 39 40 41 y ≤ −5x + 2 (1, 1) Three times n is less than fifty-two. 2 ID: A 42 x ≤ −4 43 w ≤ 10 44 g>2 45 –3 < x < 4 46 d ≤ − 8 or d ≥ 4 47 –6 < x < 2 48 all real numbers 49 no solution 50 1<x<4 51 2 < x < 14 52 x > 14 53 36 8 8 –4 4 Addition Property of Equality; Division Property of Equality 24 gallons of gas h + 11 8x 9 c = 4d 56 –1 54 55 56 57 58 59 60 61 62 63 64 3 ID: A 65 21 66 256 67 9 68 (12, –22) 69 (–1, 0) 70 1 71 11 72 (3, 0) 73 (2, 6) 74 {7, 6, 5, 3} 75 The relation is a function. 4