Name Date Part 1 (Multiple Choice): Please show ALL work! ALGEBRA MIDTERM REVIEW SHEET 1) The equations 5x 2y 48 and 3x 2y 32 represent the money collected from school concert ticket sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket? 2) A line with a slope of 1 passes through the 3 point (3,6). Which point also lies on this line? (1) $20 (3) $8 (2) $10 (4) $4 (1) (6,3) (3) (-3,-3) (2) (7,6) (4) (-6,3) 3) If 5 1 3 n 2 6n, what is the value of n? 4) A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? (1) -2 (3) 2 7 (2) 2 (4) 9 (1) 6 (3) 3 (2) 8 (4) 19
5) Solve for x: 6) If the population in 1999 for a Town C is 95,000, and is decreasing at a rate of 2.5% every 2 years, what is the projected population of the Town C in 2003? (1) 5 (2) 2 (3) 8 (4) 20 (1)104,046 (3) 99,809 (2) 85,850 (4) 90,309 7) Which inequality is shown in the accompanying diagram? 8) Which equation expresses the relationship between x and y, as shown in the accompanying table? 3 3 (1) y x 2 (3) y x 2 2 2 3 3 (2) y x 2 (4) y x 2 2 2 (1) y x 3 (3) y 3x 2 (2) y 2x 3 (4) y x 2
9) Identify the parts of the exponential formula f t 3,000 1.24 t 10) Is the following sequence arithmetic or geometric, and what is the common difference (d) or the common ratio (r) of the sequence? (1) Initial amount=$3,000, Exponential Decay, Percent of Decrease=24% (2) Initial amount=$3,000, Exponential Growth, Percent of Increase=24% (3) Initial amount=$24, Exponential Decay, Percent of Increase=3000% (1) Arithmetic, d = 3 (2) Geometric, r = 3 (3) Geometric, r = (4) Arithmetic, r = (4) Initial amount=$3,000, Exponential Growth, Percent of Increase=76% 11) If a n( n 1), determine the value of a 8 n 12) Which ordered pair is the solution of the following system of equations? 3x + 2y = 4 2x + 2y = 24 (1) 64 (2) 72 (3) 81 (4) 8 (1) (2, 1) (3) ( 4,8) (2) (2, 5) (4) ( 4, 8)
13) The slope of a line is ½ and the y-intercept is 4. Which choice is the x-intercept of this line? 14) During the 2012 season, football player McGee s earnings, m, were.005 million dollars more than those of his teammate Fitzpatrick s earnings, f. The two players earned a total of 3.95 million dollars. Which system of equations could be used to determine the amount each player earned, in millions of dollars? (1) m + f = 3.95 (3) f 3.95 = m m +.005 = f m +.005 = f (1) -8 (3) -4 (2) 8 (4) 4 (2) m 3.95 = f (4) m + f = 3.95 f +.005 = m f +.005 = m 15) Ralph keeps quarters, nickels, and dimes in his change jar. He has a total of 52 coins. He has three more quarters than dimes and five fewer nickels than dimes. How many dimes does Sal have? 16) Which is an equation for the nth term of the sequence below? -6, 2, 10, 18, 26 (1) 13 (2) 20 (3) 21 (4) 18 (1) an= 8n + 10 (3) an= 16n + 10 (2) an= 8n - 14 (4) an= 16n 38
17) Which table represents a linear function? 18) What is the value of x in the equation (1) (2) (3) (4) (1) 4 (3) 8 (2) 6 (4) 11 19) What is the range of the function + 3? 20) Which point is in the solution set of the following system of inequalities? y < 2x + 1 y - x + 4 (1) All Real Numbers (2) {{ } (3) {{ } (4) {{ } (1) (5, 0) (2) ( 2, 1) (3) (6, 6) (4) (1, 9)
21) Function g(x) is defined as: 22) If f(x) = 2 x + 4 and g (x) = x 2 4, the value of f(5) + g(-3) is : { Find g(-2). (1) 1 (2) 6 (3) -4 (4) 4 (1) 16 (2) 23 (3) 34 (4) 41 23) At a yearly basketball tournament, 64 different teams compete. After each round of the tournament, half of the teams remain, as shown in the accompanying table. Rounds, r Number of teams, t, remaining 0 64 1 32 2 16 3 8 Which equation models the relationship between the round and the number of teams remaining? (1) t = 64(0.5) r (2) t = 64(2) r (3) t = 64(0.5) r-1 (4) t = 64(2) r-1 24) Rashawn recently spent $100 to open a store selling t-shirts. At his business, he purchases plain t-shirts for $11 each, prints graphics on them, and sells them for $26 each. What is the minimum number of t-shirts that he must sell in order to make a profit (total income minus expenses) of at least $400? (1) 26 (2) 27 (3) 33 (4) 34
25) Which choice satisfies the inequality y + 2 < -2x? 26) The formula for the volume of a cone is The radius, r, of the cone may be expressed as: (1) (-2, -2) (3) (0, 0) (2) (2, -2) (4) (2, 2) (1) (3) 3 (2) (4) 27) Which of these relation choices represents a function? (1) {(1,1), (2,1), (3,1), (4,1), (5,1)} (2) {(2,1), (2,2), (2,3), (2,4), (2,5)} (3) {(0,2), (0,3), (0,4), (0,5), (0,6)} (4) {(0,1), (0, 2), (0,3), (0,4), (0,5)} 28) The accompanying table represents Emilio s savings account Month Balance for the last full year. 1 62 Which function represents the account 2 74 balance in terms of his 3 86 monthly savings? 4 98 5 110 6 122 7 134 8 146 9 158 10 170 11 182 12 194 (1) f(x)= 12x + 50 (2) f(x)= 50x 12 (3) f(x)= 12x - 50 (4) f(x)= 12x
29) At a school play, one family bought 3 student tickets and 2 adult tickets for $20.50. Another family bought 4 student tickets and 1 adult ticket for $19.00. What was the cost of one student ticket? 30) After examining the table of values below, which statement is a false statement? x -2 0 1 2 4 5 y 8 6 5 4 1 0 (1) $1.50 (2) $2.50 (3) $3.50 (4) $3.90 (1) The domain is {-2, 0, 1, 2, 4, 5} (2) The average rate of change is -2 (3) The range is {0, 1, 4, 5, 6, 8} (4) The relation is a function 31) If s(x) = is graphed, which statement is true about s(x)? 32) Which function represents exponential decay? (1) s(x) is not a function (2) The vertex is (0,1) (3) It is increasing on the interval (0, ) (4) The domain and range are both (- (1) f(x) = 100(.9) x (2) f(x) = 10(1.09) x (3) f(x) = 1.9 x (4) f(x) = ½ (9) x
33) Decide whether the relation is a function, and give the domain and range. 34) Kathy plans to purchase a car that depreciates (loses value) at a rate of 14% per year. The initial cost of the car is $21,000. Which equation represents the value, v, of the car after 3 years? (1) Function; Domain: [-2,8]; Range: [3,5] (2) Function; Domain: [3,5]; Range: [-2,8] (3) Not a Function; Domain: [-2,8]; Range: [3,5] (1) v = 21,000(0.14) 3 (2) v = 21,000(0.86) 3 (3) v = 21,000(1.14) 3 (4) v = 21,000(0.86)(3) (4) Not a Function; Domain: [3,5]; Range: [-2,8] 35) Which equations is represented by the accompanying graph? 36) What is the formula for the n th term of the sequence 54, 18, 6,? (1) (1) f(x) = x + 1 (2) f(x) = x 1 (3) f(x) = x + 1 (4) f(x) = x 1 (2) (3) (4)
37) In the graph of y -x, which quadrant is completely shaded? 38) The flight paths of two Thunderbird jets are plotted on a Cartesian coordinate plane, and the equations of the jets' flight paths are represented by y = 2 x + 3 and y = 0.5 x. The best approximation of the intersection of the flight paths is: (1) I (3) III (1) (-1.50, 2.82) (3) (0,1) (2) II (4) IV (2) (-1.72, 3.3) (4) (-2, -1) 39) Mrs. Jones is describing a function to her students. She says the output is equal to 7 less than twice the input. Which of the following equations models this relationship? 40) Which equation illustrates the associative property? (1) (x + y) + z = (x + y) + z (1) f(x) = 7 2x (3) f(x) = 2x 7 (2) f(x) = 2(7 x) (4) f(x) = 2(x 7) (2) x(y + z) = xy + xz (3) x + y + z = z + y + x (4) (x + y) + z = x + (y + z)
41) Which of the following equations are identities? 42) Which equation is represented by the accompanying graph? (1) f x -1 x < -2 2 x > -2 (1) (2) (3) (4) (2) f x -1 x -2 2 x > -2 (3) f x (4) f x -1 x < -2 2 x -2-1 x -2 2 x -2 Part 2 (Short Response): Please show ALL work! 43) Solve the following equation for p:
44) Graph this system of inequalities: 3y > 2x 6 x + y > 7 Which of the following points is part of the solution set of the system of inequalities above? (1) (5, 0) (2) (7, 4) (3) (4, 2) (4) (7, 1) 45) Solve for m:
46) What is the value of x in the equation? 4(2x + 1) = 27 + 3(2x - 5) 47) Solve and graph the following compound inequality: 2x - 4 8 and x + 5 7? 48) Determine the domain and range in interval notation form of the function represented in the graph below.
49) If h(x) = 2x 2 + 3x + 1, find h(-2). 50) Which is steeper and why? y = ½ x + 2 y = 2x 3 51) The growth of bacteria in a dish is modeled by the function. For what value of t is f (t) = 32? 52) When the teacher asked for examples of rational numbers, Ted s response was and Tanya s response was 5.. Who is correct?
53) Graph: 3x 2y = 12 54) Write the equation of a line that passes through (-4, -2) and (-3, 5). Then name another point that also lies on this line. 55) Explain why or why not the set of rational numbers closed under: a) subtraction b) division