ALGEBRA 1 CST Questions (2009)

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1 1 Is the equation 3(x ) = 18 equivalent to 6x 1 = 18? Yes, the equations are equivalent by the ssociative Property of Multiplication. Yes, the equations are equivalent by the ommutative Property of Multiplication. Yes, the equations are equivalent by the istributive Property of Multiplication over ddition. No, the equations are not equivalent. Which statement is false? The order in which two whole numbers are subtracted does not affect the difference. The order in which two whole numbers are added does not affect the sum. The order in which two rational numbers are added does not affect the sum. The order in which two rational numbers are multiplied does not affect the product = Which expression is equivalent to x 6 x? x x 3 x 7 x 3 x 5 x 3 x 9 x 3 6 What is the multiplicative inverse of 1? What is the solution for this equation? x 3 = 5 x = or x = x = 1 or x = x = or x = 3 x = 1 or x = 3 8 What is the solution set of the inequality 5 x + 3? x 6 1 x x or x 6 x 1 or x 9 Which equation is equivalent to 5x (7x + 1) = 1x? 9x = 1x 9x + 1 = 1x 9x + = 1x 1x 1 = 1x 10 Which equation is equivalent to ( 5x) = 6 3(1 3x)? 8x = 5 9x = 5 8x = 17 9x = 17 5 Which number does not have a reciprocal? Which equation is equivalent to 3[7x (x 3)] + 1 = 16? 9x = 16 17x = 16 9x + 37 = 16 17x + 13 = 16 Page 1 of 13

2 1 The total cost (c) in dollars of renting a sailboat for n days is given by the equation c = n. If the total cost was $360, for how many days was the sailboat rented? Solve: 3(x + 5) = x + 35 Step 1: 3x + 15 = x + 35 Step : 5x + 15 = 35 Step 3: 5x = 0 Step : x = Which is the first incorrect step in the solution shown above? Step 1 Step 3 Step Step 16 What is the solution to the inequality x 5 > 1? x > 9 x < 9 x > 19 x < The lengths of the sides of a triangle are y, y + 1, and 7 centimeters. If the perimeter is 56 centimeters, what is the value of y? eth is two years older than Julio. Gerald is twice as old as eth. ebra is twice as old as Gerald. The sum of their ages is 38. How old is eth? foot-long rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope? 0 feet 0 feet 60 feet 80 feet 19 Which number serves as a counterexample to the statement below? ll positive integers are divisible by or The cost to rent a construction crane is $750 per day plus $50 per hour of use. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed $500 per day? What is the conclusion of the statement in the box below? If x =, then x = or x =. x = x = x = x = or x = Page of 13

3 1 Which of the following is a valid conclusion to the statement If a student is a high school band member, then the student is a good musician? ll good musicians are high school band members. student is a high school band member. ll students are good musicians. ll high school band members are good musicians. The chart below shows an expression evaluated for four different values of x. x x + x Josiah concluded that for all positive values of x, x + x + 5 produces a prime number. Which value of x serves as a counterexample to prove Josiah s conclusion false? John s solution to an equation is shown. Given: x + 5x + 6 = 0 Step 1: (x + )(x + 3) = 0 Step : x + = 0 or x + 3 = 0 Step 3: x = or x = 3 Which property of real numbers did John use for Step? multiplication property of equality zero product property of multiplication commutative property of multiplication distributive property of multiplication over addition Stan s solution to an equation is shown. Given: n + 8(n +0) = 110 Step 1: n + 8n + 0 = 110 Step : 9n + 0 = 110 Step 3: 9n = Step : 9n = 90 Step 5: 9 9 n = 90 9 Step 6: n = 10 Which statement about Stan s solution is true? Stan s solution is correct. Stan made a mistake in Step 1. Stan made a mistake in Step 3. Stan made a mistake in Step 5. 5 When is this statement true? The opposite of a number is less than the original number. This statement is never true. This statement is always true. This statement is true for positive numbers. This statement is true for negative numbers. 6 What is the y-intercept of the graph of x + y = 1? 6 1 Page 3 of 13

4 7 Which inequality is shown on the graph below? 9 Which inequality does the shaded region of the graph represent? y < 1 x 1 y 1 x 1 y > 1 x 1 y 1 x 1 3x + y 3x + y 3x + y 3x + y 8 Which best represents the graph of y = x 30 Which equation best represents the graph above? y = x y = x y = x + y = x + Page of 13

5 31 Which equation represents the line shown in the graph below? 35 The data in the table show the cost of renting a bicycle by the hour, including a deposit. Hours (h) Renting a icycle ost in dollars (c) y = 3 x + y = 3 x + y = 3 x 6 y = 3 x 6 If hours, h, were graphed on the horizontal axis and cost, c, were graphed on the vertical axis, what would be the equation of a line that fits the data? c = 5h c = 5h + 5 c = 1 5 h + 5 c = 5h 5 3 What is the x-intercept of the line defined by x + 3y = 1? Which point lies on the line defined by 3x + 6y =? (0, ) (1, 1 6 ) (0, 6) (1, 1 3 ) 36 Some ordered pairs for a linear function of x are given in the table below. x y Which of the following equations was used to generate the table above? y = x + 1 y = 3x y = x 1 y = x 3 3 What is the equation of the line that has a slope of and passes through the point (3, 10)? y = x y = x 3 y = x + y = x Which point lies on the line represented by the equation below? 5x + y = (, 11 ) (, 3) ( 1, 17 ) (6, ) Page 5 of 13

6 38 The equation of line l is 6x + 5y = 3, and the equation of line q is 5x 6y = 0. Which statement about the two line is true? Lines l and q have the same y-intercept. Lines l and q are parallel. Lines l and q have the same x-intercept. Lines l and q are perpendicular. 39 Which equation represents al line that is parallel to y = 5 x +? y = 5 x + 1 y = 5 x + 3 y = 5 x + y = 5 x + 0 Which graph best represents the solution to this system of inequalities? x y1 x5y10 1 What is the solution to this system of equations? y 3x 6x y (6, ) (1, 5) no solution infinitely many solutions Which ordered pair is the solution to the system of equations below? x3y7 x y 10 7, 13 (, 3) 7 17, 5 (16, 3) 3 Marcy has a total of 100 dimes and quarters. If the total value of the coins is $1.05, how many quarters does she have? Which of the following best describes the graph of this system of equations? y x 3 5y 10x 15 two identical lines two parallel lines two lines intersecting in only one point two lines intersecting in only two points Page 6 of 13

7 5 Members of a senior class held a car wash to raise funds for their senior prom. They charged $3 to wash a car and $5 to wash a pick-up truck or a sport utility vehicle. If they earned a total of $75 by washing a total of 75 vehicles, how many cars did they wash? t what point do the lines represented by the equations x + y + 1 = 0 and x + y 3 = 0 intersect? 7 (, 5) ( 1, 1) (, 5) (1, 1) 5x x x 1 5x 1 x x 5 50 Which of the following expressions is equal to (x + ) + (x )(x + 1)? x x x x x + x x + x 51 volleyball court is shaped like a rectangle. It has a width of x meters and a length of x meters. Which expression gives the area of the court in square meters? 3x 3x x x 3 5 What is the perimeter of the figure shown below, which is not drawn to scale? 5x x x x (x x + 8) (x + 3x ) = 3x + x + 6 3x 5x + 6 3x + x x 5x The sum of two binomials is 5x 6x. If one of the binomials is 3x x, what is the other binomial? x x x 8x 8x + x 8x 8x 53 Which is the factored form of 3a ab + 8b? (3a 8b)(a 6b) (3a 16b)(a 3b) 3(a b)(a b) 3(a 8b)(a 8b) 5 Which is a factor of x 11x +? x + 3 x + x 3 x Page 7 of 13

8 55 Which of the following shows 9t + 1t + factored completely? (3t + ) (9t + )(t + 1) (3t + )(3t + 1) 9t + 1t + 56 What is the complete factorization of 3 8z? 8( + z)( z) 8( + z) 8( + z)( z) 8( z) 57 If x is added to x, the sum is. Which of the following could be the value of x? What quantity should be added to both sides of this equation to complete the square? x 8x = arter is solving this equation by factoring. 10x 5x + 15 = 0 Which expression could be one of his correct factors? x + 3 x + 3 x 3 x 3 6 What are the solutions for the quadratic equation x 8x = 9? 3 1, 9 3, 3 1, 9 63 Toni is solving this equation by completing the square. ax + bx + c = 0 (where a 0) Step 1: ax + bx = c Step : x + a b x = c a Step 3:? Which should be Step 3 in the solution? x = c b b a x x + b a = c ax x + b a x + b a = a c + b a 59 What are the solutions for the quadratic equation x + 6x = 16?, 8, 8, 8, 8 60 Leanne correctly solved the equation x + x = 6 by completing the square. Which equation is part of her solution? (x + ) = 8 (x + ) = 10 (x + ) = 10 (x + ) = x + b a x + ( b a ) = a c + ( b a ) *6 Which is one of the solutions to the equation x x = 0? Page 8 of 13

9 *65 Four steps to derive the quadratic formula are shown below. I x + a b x = c a II x + b a x + ( b a ) = c a + ( b a ) III x = b ac b a a IV x + bx a + ( b a ) = c a + ( b a ) What is the correct order for these steps? I, IV, II, III I, III, IV, II II, IV, I, III II, III, I, IV 68 What are the solutions to the equation 3x + 3 = 7x x 7 85 or x x 7 85 or x x 7 13 or x x 7 13 or x The graph of the equation y = x 3x is shown below. 66 Which statement best explains why there is no real solution to the quadratic equation x + x + 7 = 0? The value of 1 7 is positive. The value of 1 7 is equal to 0. The value of 1 7 is negative. The value of 1 7 is not a perfect square. 67 What is the solution set of the quadratic equation 8x + x + 1 = 0? 1, 1 1, 1 1 7, No real solution For what value or values of x is y =0? x = 1 only x = 1 and x = x = only x = 1 and x = *70 Which quadratic function, when graphed, has x-intercepts of and 3? y = (x 3)(x + ) y = (x + 3)(x 8) y = (3x 1)(x + 1) y = (3x + 1)(8x ) Page 9 of 13

10 *71 Which best represents the graph of y = x How many times does the graph of y = x x + 3 intersect the x-axis? none one two three 7 n object that is projected straight downward with initial velocity v feet per second travels a distance s = vt + 16t, where t = time in seconds. If Ramón is standing on a balcony 8 feet above the ground and throws a penny straight down with an initial velocity of 10 feet per second, in how many seconds will it reach the ground? seconds 3 seconds 6 seconds 8 seconds 7 What are the real roots of the function in the graph? 75 The height of a triangle is inches greater than twice its base. The area of the triangle is 168 square inches. What is the base of the triangle? 7 in. 8 in. 1 in. 1 in and 3 6, 1, and 3 76 rectangle has a diagonal that measures 10 centimeters and a length that is cm longer than the width. What is the width of the rectangle in centimeters? Page 10 of 13

11 x xy y 77 What is 3xy 6y terms? x y 3 x y 3y reduced to lowest x y 3 x y 3y 81 What is the simplest form of the fraction x 1 x x? 1 x 1 x x x 1 x 1 x x 78 Simplify 6x 1x9 x 1 to lowest terms. 3( x 1) 3(x 3) x 1 ( x 1) 3( x 3) 3( x 3) x 1 x 1 8 z z 3 z 8 z z z = 7z 7 7( z ) 7 zz ( 1) ( z 1) ( z ) 7( z ) 7 zz ( 1) ( z 1) ( z ) 79 What is x x terms. x x 1 x x 1 x 3x reduced to lowest x x 1 x x 1 83 Which fraction equal the product x5 x3 3x x 5? 3 x x 5 3x 6x 5x6 3 x x 7x15 x 3 3x 13x10 80 What is 1a 0a 16a 8a terms? a 3 a 5 a 1 3 reduced to lowest a a a(3a 5) (a 1) 8 ivide: x ( x ) ( x3)( x 3) ( x3)( x3) x 8x16 x 3 x 8 x 9 = ( x)( x3) ( x)( x3) ( x 3) Page 11 of 13

12 85 Which fraction is equivalent to x 5 5 3x 5 x x? 89 Two airplanes left the same airport traveling in opposite directions. If one airplane averages 00 miles per hour and the other airplane averages 50 miles per hour, in how many hours will the distance between the two planes be 165 miles? x pharmacist mixed some 10%-saline solution with some 15%-saline solution to obtain 100 ml of a 1%-saline solution. How much of the 10%-saline solution did the pharmacist use in the mixture? 60 ml 5 ml 0 ml 5 ml 87 ndy s average driving speed for a -hour trip was 5 miles per hour. uring the first 3 hours he drove 0 miles per hour. What was his average speed for the last hour of his trip? 50 miles per hour 60 miles per hour 65 miles per hour 70 miles per hour 88 One pipe can fill a tank in 0 minutes, while another takes 30 minutes to fill the same tank. How long would it take the two pipes together to fill the tank? 50 min 5 min 15 min 1 min 90 Lisa will make punch that is 5% fruit juice by adding pure fruit juice to a -liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add? 0. liter 0.5 liter liters 8 liters 91 Jena s Vacation Miles Traveled Gallons of Gasoline x Jena s car averaged 30 miles per gallon of gasoline on her trip. What is the value of x in gallons of gasoline? Page 1 of 13

13 9 Which relation is a function? {( 1, 3), (, 6), (0, 0), (, )} {(, ), (0, 0), (1, 1), (, )} {(, 0), (, 1), (, ), (, 3)} {(7, ), (8, 8), (10, 8), (10, 10)} 9 For which equation graphed below are all the y-values negative? 93 Which relation is a function? 95 What is the domain of the function shown on the graph below? { 1,, 3, } { 1,,, 5} {1,, 3, } {1,,, 5} Page 13 of 13

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