Standardized Test Practice

Standardized Test Practice. A store uses a matrix to show their inventory of jeans by waist size (in inches) and style of leg. What is a 3? A a. straight boot cut flared tapered 3 3 3 3 3 3 7 3 3 9 b. c. d. 7. What is A B? A 3 7, B 9 3 a. b. 7 3 Carnegie Learning, Inc. c. d. 7 3 Chapter l Assessments

Standardized Test Practice PAGE 3. What is 3C D? C 3 a. 7 b. 3 c. 3 d. 3 7 3, D 3. What is A 3B? A a. b. 3 c. 7, B 3 3 3 3 3 d. The expression cannot be evaluated because the matrices are different sizes.. What is CD? C a. b. c. 3 7, D 3 3 d. The matrices cannot be multiplied because the matrices are different sizes. Carnegie Learning, Inc. Chapter l Assessments

Standardized Test Practice PAGE 3. Matrix H shows the number of girls and boys in one high school from ninth through twelfth grades. What is H T? H 7 7 a. 7 7 b. 3 c. 3 79 7 d. 3 3 79 7 7 79 3 7 7 7 7 79 79 7 7 7 7 7. Which two matrices can be added? A 3 a. A and B b. A and D c. B and C d. B and E, B 7 3, C, D 3 3, E 3 9 Carnegie Learning, Inc.. Which two matrices cannot be multiplied with either matrix first? A 3 a. A and B b. A and D c. B and C d. B and E, B 7 3, C, D 3 3, E 3 9 Chapter l Assessments 7

Standardized Test Practice PAGE 9. What is the inverse of a. b. c. d.?. Solve the system of equations using Cramer s Rule. x y 7 x y a. x 3, y b. x, y 3 c. x, y 3 d. x 3, y. What is the product of A and A? a. b. c. d.. Determine the equation of a line passing through the points ( 3, ) and (, ) using a matrix equation. a. y 3 x 7 b. y 3 x 7 c. y 3 x 7 d. y 3 x 7 Carnegie Learning, Inc. Chapter l Assessments

Standardized Test Practice PAGE 3. What is the determinant of the matrix 9 a. 3? b. 9 c. 3 d. 7. Solve the system of equations using Cramer s Rule. x y 3z x y z x y z 7 a. x, y, z b. x, y, z c. x, y, z d. x, y, z. Determine the equation of a parabola that passes through the points (, ), (, ), and (3, ). The general form of the quadratic function whose graph is a parabola is y ax bx c. a. y x 3x b. y x x c. y x 3x d. y x x. What is the determinant of the matrix a. 3? Carnegie Learning, Inc. b. c. 3 d. 7. Solve the system of equations using Cramer s Rule..x.9y..3x 3.7y 3. a. x, y b. x, y 3 c. x, y d. x, y Chapter l Assessments 9

Standardized Test Practice The following table represents nutrition information about one serving of different protein sources. Use the table for Questions. Protein source Calories Fat (grams) Carbohydrates (grams) Protein (grams) Cod 9.7 9. Pot roast 3.. Black beans.. 7. Italian sausage 3 3.3.7.3. If matrix A represents the data in the table, what does element a 3 represent in the problem situation? a. the number of grams of carbohydrates in a serving of cod b. the number of calories in a serving of cod c. the number of grams of carbohydrates in a serving of black beans d. the number of calories in a serving of black beans. One day Sean ate serving of cod, servings of black beans, and serving of Italian sausage. Which row matrix B represents the number of servings of each protein source? a. [ ] b. [ ] c. [ ] d. [ ] 3. Use matrix A and matrix B. How many grams of protein did Sean consume that day? Carnegie Learning, Inc. a..3 grams b..9 grams c. 9. grams d. 3. grams. Use matrix A and matrix B. How many grams of fat did Sean consume that day from his protein sources? a. 3. grams b. 3. grams c. 33 grams d.. grams Chapter l Assessments 9

Standardized Test Practice PAGE. Which graph shows the solution set for the system of linear inequalities? y 3x x y a. y b. y x x c. y d. y x x Carnegie Learning, Inc. Chapter l Assessments

Standardized Test Practice PAGE 3. Which of the following points is not a solution to the system of linear inequalities? y 3x x y a. (, ) b. (3, ) c. (, ) d. ( 3, 3 ) Use the following system of inequalities for Questions 7 and. x 3 y x y 7. What is the best description of the intersection of the line x y and the solution region to the system of inequalities? a. The intersection is the line segment with endpoints (, ) and ( 3, ). b. The intersection is the line segment with endpoints (, ) and (, 3). c. The intersection is the point (, ). d. There is no intersection.. What is the maximum value of the expression x y in the solution region? a. b. c. Carnegie Learning, Inc. d. 9. Use the following system of inequalities. Evaluate 3x y at each of the vertices of the solution region. At which point in the solution region does the expression have a maximum value? x y x y y x a. (, ) b. (, ) c. (, ) d. (, ) Chapter l Assessments

Standardized Test Practice PAGE A company makes two different types of skis. One type of ski takes person-hours to make one pair. The other type of ski takes 3 person-hours to make one pair. The company has employees making the skis, each of whom works hours per day. Use this information to answer Questions through 3.. If x is the number of the first type of pairs of skis and y is the number of the second type of pairs of skis, which inequality represents the number of person-hours to produce both models? a. 3x y b. x 3y c. x y d. x y. The company s total manufacturing capacity is 3 pairs of skis per day. Which inequality represents this constraint? a. x y 3 b. x y 3 c. x y 3 d. x y 3. Use the inequalities from Questions and and the inequalities x and y as the system of possible solutions. What are the points of intersection of the boundary lines? a. (, ), (, 3), (7, ), (, ) b. (, ), (, 3), (3, ), (, ) c. (, ), (, 3), (7, ), (, ) d. (, ), (, 3), (3, ), (, ) 3. The company sells the first type of skis for $ per pair and the second type of skis for $3 per pair. Assume that all pairs of skis that are made are also sold. Which expression shows how many of each type of skis to make to maximize income? a. (3) 3(),3 b. () 3(3), c. () 3(),7 d. () 3(), Carnegie Learning, Inc. Chapter l Assessments

a a Standardized Test Practice PAGE. Use the digraph shown. What is the adjacency matrix for the digraph? A a B D a a. A B C D b. A B C D c. A B C D a 3 A B C D A B C D A B C D C d. A B C D A B C D Carnegie Learning, Inc. Chapter l Assessments

a a Standardized Test Practice PAGE 7 7. How many paths of length are there between A and C? A a B D a a 3 C a. b. c. d. 3 A new airline is starting flights between four cities, A, B, C, and D. The following adjacency matrix F represents the flight paths between cities. Use this information to answer Questions through. F A B C D A B C D. Which digraph models matrix F? a. b. Carnegie Learning, Inc. c. A D A B C B d. A D A B C B D C D C Chapter l Assessments

Standardized Test Practice. What is the equation of a circle with center at the origin and radius.? a. x y. b. x y. c. x y. d. x y.. Which conic section is formed when a plane parallel to the axis of a double-napped cone intersects both nappes of the cone? a. circle b. ellipse c. hyperbola d. parabola 3. At how many points do the circles with equations x y 3 and x ( y 3) 9 intersect? a. three b. two c. one d. zero. If a line with equation y 3x is tangent to a circle with center (, ), what is the point of tangency? Carnegie Learning, Inc. a. (, ) b. (, 3 ) c. (, 3 ) d. (, ). What is the center of the circle whose equation in general form is x y x y? a. (, 3) b. (, 3) c. (, ) d. (, ). Which is the equation of the circle with center (, ) that is tangent to the line y x? a. ( x ) ( y ) b. ( x ) ( y ) c. ( x ) ( y ) d. ( x ) ( y ) Chapter l Assessments 73

Standardized Test Practice PAGE 7. Which equations should be entered into a graphing calculator to graph the circle with equation ( x 3) ( y )? a. y ( x 3) y ( x 3) b. y ( x 3) y ( x 3) c. y ( x 3) y ( x 3) d. y ( x 3) y ( x 3). Which is an equation of a circle with its center at the origin? a. 3x y b. 3x y c. x y d. x x y 9. What are the points of intersection of the circles with equations x y x and x y 3? a. (7, 9) and (9, 7) b. (7, 9) and (7, 9) c. ( 7, 9) and (7, 9) d. (7, 9) and ( 7, 9). Which conic section is formed when a plane perpendicular to the axis of a double-napped cone intersects one nappe of the cone? a. circle b. ellipse c. hyperbola d. parabola Carnegie Learning, Inc. 7 Chapter l Assessments

Standardized Test Practice PAGE 3. A high school marching band director is arranging formations for the halftime show at the next home football game. The band members will form two circles, each spanning 3 yards. Half the band members will form a circle centered on the -yard line, and the other half will form a circle centered on the -yard line. Both centers of the circles will be set at the hash marks at the middle of the football field. The drum major and the drum majorette will be positioned at the points of intersection of the two circles. How far apart will they be standing to the nearest tenth of a yard? a.. yards b.. yards c. yards d. 3 yards. What is the equation of the line tangent to the circle with equation x y at the point (, 3)? a. y x b. y 3 x 3 c. y 3 x 3 d. y 3 x 3 3. How many points do the circle x y 3 and the line y x have in common? a. 3 b. c. d.. What is the standard form of the equation of a circle with center (, 7) and radius? Carnegie Learning, Inc. a. ( x ) ( y 7) b. ( x ) ( y 7) c. ( x ) ( y 7) d. ( x ) ( y 7). What are the points of intersection of the circle with equation ( x 3) ( y ) 9 and the line with equation y x? a. (, ) b. (, ) and (, ) c. (, ) and (, ) d. no points of intersection Chapter l Assessments 7

Standardized Test Practice. What is the length of the semi-major axis of the ellipse represented by the equation x y? a.. units b. 9 units c. units d. units. Which equation represents the ellipse with vertices at (, 3) and (, 9) and with a minor axis of length units? (x ) a. ( y 3) 3 b. c. d. (x ) 3 (x ) 3 (x ) ( y 3) ( y 3) ( y 3) 3. What is the eccentricity of the ellipse with equation x y to the nearest thousandth? 3 a..3 b.. c.. d..7. What is the general form of the ellipse x y? 3 7 a. 7x 3y b. 7x 3y Carnegie Learning, Inc. c. x y d. 3x 7y. What is the center of the ellipse represented by the equation a. (, 9) b. (, ) c. (, 9) (x ) ( y 9)? 3 d. (, ) Chapter l Assessments 93

Standardized Test Practice PAGE. Which equation represents the ellipse with one vertex at (, ) and foci at (, ) and (, )? (x ) a. y (x ) b. y 39 (x ) c. ( y ) 9 (x ) d. ( y ) 9 7. What are all intercepts of the ellipse represented by the equation x 9 a. x-intercepts: (, ) and (, ); y-intercepts: (, 7) and (, 7) b. x-intercept: (, ); y-intercept: (, 7) c. x-intercepts: ( 7, ) and (7, ); y-intercepts: (, ) and (, ) d. x-intercepts: ( 7,) and ( 7, ); y-intercepts: (, ) and (, ) y?. For the ellipse modeling the orbit of Jupiter, the length of the major axis is approximately. AU (astronomical units). The eccentricity of the orbit is approximately.9. What is the distance between the foci to the nearest thousandth? a..7 AU b..9 AU c.. AU d.. AU 9. Which is the equation in general form of the ellipse a. 9x y 7x y b. x 9y x y (x ) ( y )? 9 c. 9x y d. 9x y 7x y. What are the coordinates of the co-vertices of the ellipse represented by the equation x y? 9 a. (, ) and (, ) b. (, 3) and (, 3) c. (, ) and (, ) d. (, ) and (, ) Carnegie Learning, Inc. 9 Chapter l Assessments

Standardized Test Practice PAGE. Which equation represents the ellipse shown? y x a. x ( y 3) b. ( y x 3) (x 3) c. y (x 3) d. y. What are the coordinates of the vertices of the ellipse represented by the equation a. (, ) and (, ) (x ) 9 ( y )? 3 b. (, ) and (, 7) c. (, ) and (, ) d. (, ) and (, 7) 7. Which equation has the same graph as the equation x 9y x 9y? (x ) a. ( y ) 9 (x ) b. ( y ) 9 (x ) c. ( y ) 9 (x ) d. ( y ) 9. Which are the coordinates of one of the foci of the ellipse represented by the equation a. (, 3 3 ) (x ) ( y 3)? Carnegie Learning, Inc. b. (, 3) c. (, 3 ) d. ( 3, 3) 9 Chapter l Assessments

Standardized Test Practice. To the nearest thousandth, what is the eccentricity of the hyperbola represented by the equation y 7 a.. b..79 c..3 d.. x?. Which is the equation of an asymptote of the hyperbola represented by the equation x 3 a. y 3 x b. y x y? c. y 3x d. y 9 x 3. Which equation represents the hyperbola shown in the graph? ( y ) a. x ( x ) b. y c. ( y ) x d. y (x ) y (, ) (, ) x 3 Carnegie Learning, Inc.. What are the co-vertices of the hyperbola represented by the equation y x? 9 a. (, 3) and (, 3) b. ( 3, ) and (3, ) c. (, ) and (, ) d. (, ) and (, ). Which is the equation in standard form of the hyperbola x y x 3y 9? ( x 3) a. ( y ) ( x 3) b. ( y ) ( y ) c. ( x 3) ( y ) d. ( x 3) Chapter 3 l Assessments 33

Standardized Test Practice PAGE. Which graph represents the equation ( x y 3)? a. b. y y (, 3) (, 3) x (, 3) (, 3) x c. y d. y (, 3) (, 3) x (, ) (, ) x 3 7. The curve of the surface of a floodlight is designed in the shape of a hyperbola with the light source positioned at one focus. For one floodlight model, the surface can be represented by the equation x y, with dimensions in inches. How far should the light source be placed from the vertex of the hyperbolic surface to create a floodlight? a. inch b. inches Carnegie Learning, Inc. c. 7 inches d. inches 3 Chapter 3 l Assessments

Standardized Test Practice PAGE 3. What is the center of the hyperbola represented by the equation a. ( 3, ) b. (3, ) c. (, 3) d. (, 3) ( y 3) (x )? 9 9. Which are the coordinates of a focus of the hyperbola represented by the equation (x 3) ( y )? 3 a. (, 3) b. ( 7, ) c. (3, ) Carnegie Learning, Inc. d. (9, ). Which is the equation of an asymptote of the hyperbola represented by the equation y a. y x b. y x (x )? c. y x d. y x. Which equation represents a hyperbola with vertices at ( 7, ) and (, ) and with eccentricity 3? (x ) a. ( y ) 3 b. c. d. (x ) 9 ( y ) 9 ( y ) 3 ( y ) 7 ( x ) 7 (x ). Which are the coordinates of a focus of the hyperbola represented by the equation x y y 39? a. (, ) b. (, ) c. (, ) d. (, ) 3 Chapter 3 l Assessments 3

Standardized Test Practice PAGE 3. Which are the coordinates of a vertex of the hyperbola represented by the equation a. (, ) b. (, ) c. (, ) d. (, ) (x ). Which are the coordinates of a focus of the hyperbola represented by the equation y x? a. (,.) b. (,.) c. (., ) d. (., ) ( y )? 9 3. Which equation represents a hyperbola centered at (, 3), with one vertex at (, ), and with asymptotes y 3 x and y 3 x? (x ) a. ( y 3) 9 ( y 3) b. (x ) 9 (x ) c. ( y 3) 9 (x ) d. ( y 3) 9. Which is the equation in general form of the hyperbola x a. x y y? b. x y c. x y d. x y 7. Which equation represents a hyperbola with center at (, ), one vertex at (, ), and one focus at (, 3)? a. x y y b. x 9 c. y d. y x x Carnegie Learning, Inc. 3 Chapter 3 l Assessments

Standardized Test Practice. Which is the equation in standard form of a parabola with a vertex at (, 3) and a directrix at y 3? a. (x ) ( y 3) b. ( y 3) (x ) c. (x ) ( y 3) d. ( y 3) (x ). Which is another way to write the equation of the parabola y y x 9? a. ( y 7) (x ) b. (x ) ( y 7) c. ( y 7) (x ) d. (x ) ( y 7) 3. What are the coordinates of the focus of the parabola represented by the equation y x? a. ( 3., ) b. ( 7, ) c. (, 3.) d. (3., ). Radio stations use parabolic dishes to transmit radio waves. Station KEEP uses a dish with a focus. feet from the vertex. Assume that the dish is positioned with the axis of symmetry along the y-axis and the vertex at the origin. Which is an equation of the parabola that represents the dish? Carnegie Learning, Inc. a. y x b. y x c. y.x d. x y. What are the coordinates of the focus of a parabola represented by the equation (x 3) ( y )? a. (, ) b. (3, ) c. (, ) d. (3, ) Chapter l Assessments 39

Standardized Test Practice PAGE. Which describes the concavity of a parabola represented by the equation ( y 3) 9(x )? a. concave up b. concave down c. concave left d. concave right 7. Which is the graph of the equation x y? a. y b. y x x c. y d. y x x. What is the equation of the directrix of the parabola represented by the equation x y? a. x b. y Carnegie Learning, Inc. c. x d. y 33 Chapter l Assessments

Standardized Test Practice PAGE 7. Which is the equation of the axis of symmetry of the parabola represented by the equation (x ) ( y )? a. y b. x c. y d. x. A parabolic archway was constructed so that the highest point is feet above the ground. The distance between the two endpoints of the archway (the points at which it touches the ground) is feet. If the archway is placed in a coordinate system so that the highest point lies on the positive y-axis and the lowest points lie on the x-axis, which equation will describe the parabola? a. x.( y ) b. x 3.( y ) Carnegie Learning, Inc. c. x.( y ) d. x ( y ) 9. Which is the equation in standard form of a parabola with a vertex at (, 3), a horizontal axis of symmetry, and including the point (, )? a. ( y 3) 3 (x ) b. (x ) 3 ( y 3) c. (x ) ( y 3) 3 d. ( y 3) 3 (x ). Which are the coordinates of the focus of the parabola represented by the equation x x y 3? a. (,.) b. (, 3) c. (,.) d. (3., 3) Chapter l Assessments 333

Standardized Test Practice PAGE. What are the center and radius of the sphere represented by the equation x y z x y z? a. center (,, ), radius 9 b. center (,, ), radius c. center (,, ), radius 9 d. center (,, ), radius 77 7. Which type of conic section is represented by the equation 3x 3y x y? a. circle b. ellipse c. hyperbola d. parabola. Which describes the intersection of the sphere x y z and the plane z? a. a single point b. a great circle c. a circle that is not a great circle d. no intersection 9. When the equation of a certain conic section is written in the general form, Ax By Cx Dy E, the relationship between the coefficients A and B can be described by the equation A B. What type of conic section is this? a. circle b. ellipse c. hyperbola d. parabola. The focal length of a parabolic mirror is the distance from the vertex to the focus of the mirror. Consider a concave mirror that is inches tall and is inches from the top to the bottom edge of the mirror. What is the focal length of the mirror? a. inches b. inches Carnegie Learning, Inc. c. inches d. inches 3 Chapter l Assessments

Standardized Test Practice PAGE 9. Which describes the intersection of the sphere (x 7) ( y ) (z 3) and the plane x? a. a circle with center ( 7,, 3) and radius b. a circle with center (,, 3) and radius c. the point ( 7,, 3) d. the point (,, 3). Which describes the concavity of the parabola represented by the equation 3y x y 3? a. concave up b. concave down c. concave left d. concave right Carnegie Learning, Inc. 7 Chapter l Assessments 33