[Math Center]

1. In the [latex]xy[latex]-plane, the equation of line [latex]k[latex] is [latex]3x-2y=0[latex].

Quantity A Quantity B
The [latex]x[latex]-intercept of line [latex]k[latex] The [latex]y[latex]-intercept of line [latex]k[latex]


2. In the [latex]xy[latex]-plane, line [latex]k[latex] is a line that does not pass through the origin.
Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line [latex]k[latex] is negative?
Indicate all such statements.

(A) The [latex]x[latex]-intercept of line [latex]k[latex] is twice the [latex]y[latex]-intercept of line [latex]k[latex]. 
(B) The product of the [latex]x[latex]-intercept and the [latex]y[latex]-intercept of line [latex]k[latex] is positive. 
(C) Line [latex]k[latex] passes through the points ( and where [latex]a,b)( r,s), (a-r)(b-s)<0[latex].


3. [latex]P, Q[latex], and [latex]R[latex] are three points in a plane, and [latex]R[latex] does not lie on line [latex]PQ[latex]. Which of the following is true about the set of all points in the plane that are the same distance from all three points? 

(A) It contains no points. 
(B) It contains one point. 
(C) It contains two points. 
(D) It is a line. 
(E) It is a circle.


4. In the [latex]xy[latex]–plane, the point with coordinates is the center of circle [latex]C(-6,-7)[latex] The point with coordinates lies inside [latex]C[latex]( , and the point with [latex]-6,5[latex]) coordinates lies outside C. If [latex]m[latex] is the radius of [latex]C[latex] and [latex]m[latex] ([latex]8[latex], is an [latex]-7[latex]) integer, what is the value of [latex]m[latex] ?



#GREpracticequestion What is the slope of line k in the xy-plane above.jpg

What is the slope of line [latex]k[latex] in the [latex]xy[latex]-plane above? 

(A) [latex]-5[latex] 
(B) [latex]-1[latex] 
(C) [latex]0[latex] 
(D) [latex]1[latex]  
(E) [latex]5[latex] 


6. Eight points are equally spaced on a circle. If [latex]4[latex]  of the [latex]8[latex]  points are to be chosen at random, what is the probability that a quadrilateral having the [latex]4[latex]  points chosen as vertices will be a square? 

(A) [latex]\frac{ 1 }{ 70 }[latex]
(B) [latex]\frac{ 1 }{ 35 }[latex] 
(C) [latex]\frac{ 1 }{ 7 }[latex]  
(D) [latex]\frac{ 1 }{ 4 }[latex]  
(E) [latex]\frac{ 1 }{ 2 }[latex] 


7. In the figure, the horizontal and vertical lines divide the square [latex] ABCD[latex] into [latex]16[latex] equal squares as shown. What is the area of the shaded region?


(A) [latex]4[latex]
(B) [latex]4.5[latex]
(C) [latex]5[latex]
(D) [latex]6.5[latex]
(E) [latex]7[latex]


8. In the rectangular coordinate plane shown, what are the coordinates of point [latex]E[latex] ?

#GREpracticequestion In the rectangular coordinate.jpg

(A) [latex](2, 0)[latex]
(B) [latex](2, 3)[latex]
(C) [latex](6, 2)[latex]
(D) [latex](6, 6)[latex]
(E) [latex](6, 8)[latex]


9. In the two figures shown, line [latex]l[latex] represents the function [latex]f[latex] and line [latex]m[latex] represents the function [latex]g[latex].

#GREpracticequestion In the two figures shown.jpg

Quantity A Quantity B
[latex]f(10)[latex] [latex]g(10)[latex]


10. Which of the following statements is true about the line segment with endpoints [latex](-1, 1)[latex] and [latex](1, -1)[latex]?

(A) Crosses the [latex]x[latex]-axis only.
(B) Crosses the [latex]y[latex]-axis only.
(C) Crosses the [latex]y[latex]-axis on its positive side.
(D) Passes through the origin [latex](0, 0)[latex].
(E) Crosses the [latex]x[latex]- and [latex]y[latex]-axes on their negative sides.


11. Which of the following could be the equation of line [latex]l[latex] in the figure above?


(A) [latex]2x = 3y – 2[latex]
(B) [latex]2x = 3y – 6[latex]
(C) [latex]3x = 2y – 6[latex]
(D) [latex]\frac {2}{3}*x = 2y –2[latex]
(E) [latex]\frac {2}{3}*2x = 3y – 6[latex]


Quantity A Quantity B
The slope of a line passing through [latex](-3, -4)[latex] and the origin The slope of a line passing through [latex](-5, -6)[latex] and the origin


13. A line has the equation [latex]2y-4x-8 = 0[latex].

Quantity A Quantity B
The slope of the line [latex]4[latex]



14. What is the equation of the line that passes through [latex](-1,-3)[latex] and has a slope of [latex]-2[latex]?

(A) [latex]y = -2x-1[latex]
(B) [latex]y = -2x-2[latex]
(C) [latex]y = -2x-5[latex]
(D) [latex]y = -4x-2[latex]
(E) [latex]y = -5x + 2[latex]


15. In the coordinate plane, line [latex]p[latex] has an equation of [latex]3y-9x = 9[latex]

Quantity A Quantity B
The slope of line [latex]p[latex] The [latex]x[latex]-intercept of line [latex]p[latex]




1 C
2 A, B, C
3 B
4 13
5 D
6 B
7 E
8 E
9 A
10 D
11 B
12 A
13 B
14 C
15 A