The Cartesian Plane Practice Test

If necessary, review:

• The Cartesian Plane Help
• Relation versus Function Help
• Parabolas and Circles Help
• Solving Pairs of Equations Help 

The Cartesian Plane Practice Test

Directions: A good score is eight correct.

1. The ordinate in the xy -plane is the same as the value of the

(a) abscissa

(b) x coordinate

(c) dependent variable

(d) independent variable

2. The graph of y = 3 x ² − 5 is

(a) a straight line

(b) a parabola opening upward

(c) a parabola opening downward

(d) a circle

3. Suppose you see a graph of a straight line. The x -intercept point is (4,0) and the y -intercept point is (0,8). What is the equation of this line?

(a) y = −2 x + 8

(b) y = −4 x − 8

(c) y = 4 x + 8

(d) ( x − 4) ² + ( y − 8) ² = 0

4. At which points, if any, do the graphs of y = 2 x + 4 and y = 2 x − 4 intersect?

(a) (0, −2)

(b) (2, 0)

(c) (0, −2) and (2, 0)

(d) The graphs do not intersect

5. Suppose the equation of the circle is ( x − 1) ² + ( y + 2) ² = 100, and the equation of a line is y = 1. What can we say about the solutions to the pair of equations?

(a) There are none

(b) There is one

(c) There are two

(d) There are more than two

6. Examine Fig. 6-12 below. At what point does the straight line intersect the x axis?

(a) (0, 1)

(b) (1, 0)

(c) (−3, 4)

(d) It is impossible to precisely tell without more information

Fig. 6-12 . Graphs of two equations, showing solutions as intersection points.  Fig. 6-12 refers to Question 6 and 10.

7. What are the y -intercept points, if any, of the circle ( x + 5) ² + ( y + 4) ² = 1?

(a) It is impossible to tell without more information

(b) (0, 5) and (0, 4)

(c) (0, −5) and (0, −4)

(d) There are none

8. What is the distance d between the points (3, 5) and (5, 3)?

(a) d = 0

(b) d = 2

(c) d = 8 ^1/2

(d) d = 4

9. What is the slope of the line represented by the equation y − 2 = 3 x + 18?

(a) 2

(b) 3

(c) 18

(d) −18

10. Examine Fig. 6-12. Suppose that a third equation is graphed on this Cartesian plane, and its equation is y = x − 3. If the equations of the two existing graphs are considered together with this new equation, how many common solutions are there to all three equations considered simultaneously?

(a) None

(b) One

(c) Two

(d) Three

Fig. 6-12 . Graphs of two equations, showing solutions as intersection points.  Fig. 6-12 refers to Question 6 and 10.

Answers:

1. c

2. b

3. a

4. d

5. c

6. b

7. d

8. c

9. b

10. a