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Mock GRE Quiz for Students
What is the slope of the line represented by the equation x + 2y = 1?
a) -3/2
b) -1
c) -1/2
d) 0
e) 1/2
Option c – -1/2
A square is to be drawn on a coordinate plane with one vertex at the origin and an area of 100 square units. If all vertex coordinates must be integers, how many different ways can the square be drawn?
a) 4
b) 6
c) 8
d) 12
Option d – 12
The line 3x + 4y = 8 passes through all quadrants except
a) I
b) II
c) III
d) IV
e) II & IV
Option c – III
In the xy-coordinate plane, rectangle ABCD is inscribed in a circle given by x² + y² = 25. Diagonal AC lies on the x-axis, with vertex B in quadrant II and vertex D in quadrant IV. If side BC lies on the line y = 3x + 15, what is the area of rectangle ABCD?
a) 15
b) 30
c) 40
d) 45
e) 50
Option b – 30
The line y = 4 – 2x is the perpendicular bisector of segment RP. If point R is (4, 1), find the coordinates of point P.
a) (-4, 1)
b) (-2, 2)
c) (0, 1)
d) (0, -1)
e) (2, 0)
Option d – (0, -1)
A line passes through the points (0, 5) and (7, 0). Which of the following points must also lie on this line?
a) (-14, 10)
b) (-7, 5)
c) (12, -4)
d) (14, -5)
e) (21, -9)
Option d – (14, -5)
What is the slope of the line passing through the origin that is equidistant from points P(1, 11) and Q(7, 7)?
a) 2
b) 2.25
c) 2.5
d) 2.75
e) 3
Option b – 2.25
Which equation represents a line perpendicular to the line 3x + 4y = 8?
a) 3x + 4y = 18
b) 3x – 4y = 24
c) 4x – 3y = 26
d) 8x – 6y = 24
Option d – 8x – 6y = 24
In the xy-plane, line m has a positive slope and an x-intercept of 4. If the area of the triangle formed by line m and the coordinate axes is 12, find the y-intercept of the line.
a) 6
b) 4
c) -6
d) -8
e) 9
Option c – -6
Line P is given by y – 5x = 4 and line M by 10y + 2x + 20 = 0. If line N does not intersect line P, determine the angle in degrees between line N and line M.
a) 0
b) 30
c) 60
d) 90
e) Cannot be determined
Option d – 90
For any triangle T in the xy-plane, the center of T is the point whose coordinates are the averages of the corresponding coordinates of its vertices. A triangle has vertices (0, 0) and (6, 0) with its center at (3, 2). Find the coordinates of the third vertex.
a) (3, 4)
b) (3, 6)
c) (4, 9)
d) (6, 4)
e) (9, 6)
Option b – (3, 6)
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