Systems of Equations and Inequalities
Geometry & Trigonometry
Equivalent Expressions & FOIL/Distribution
Non-linear Equations & Functions
100
This is the value of x in the solution for the system below.
3/y=1/4
2/(3x)=2y-1/x
What is x=10?
100
This is the value of
sin^2(A°)+sin^2(B°)
for the triangle with vertices A,B,and C such that the measures (in degrees) of A,B,and C satisfy
A-32B=C=90.
What is 1?
100
The equation ax+4=2(x-b) has this many solutions for values of a and b that satisfy the system of equations below:
10a-4=16
a-b=4
A. Zero
B. One
C. Infinity
D. None of the above (determine the correct number to earn these points)
What is C. Infinity?
100
This is the vertex of the parabola whose equation is y=-2(x-4)(x+2).
What is (1,18)?
200
x-2y+2z=-8
x+y-4z=10
3x+y+2z=13
The solution to this system is (x,y,z). This is the value of x+2y+4z.
What is 11?
200
The sum of the areas of both rectangles in the figure below is 8 square inches. The sum of the lengths of all 7 line segments is 19 inches. The value of x+y, in inches, is NOT an integer; it is this value.
What is 73/12 or 6.08\bar3?
200
The equation x^2+6x+2=0 has solutions r and s such that r<s.
The equation x^2-14x+42=0 has solutions a and b such that a<b.
The solutions to the equation x^2-8x+m=0 are (a+r) and (b+s). This is the value of m.
What is m=-12?
200
Point M(10,3) is the midpoint of points S and T. Points S and T both lie on the curve y=sqrt(x).
The distance between S and T is 4sqrt37.
This is the sum of the sum of the x-coordinates of S and T and the sum of the y-coordinates of S and T.
What is 26?
300
This is the value of A in the system of linear equations
Ax+By=5
6x+3By=33
which intersect at the point (-4,y).
What is A=7/2
or A=3.5?
300
A "teardrop" figure is constructed by deleting one-quarter of the area of a circle, and replacing the deleted portion with a square whose side length is equal to the radius of the original circle. An isosceles right triangle is inscribed in such a teardrop as depicted in the figure such that the right angle occurs at the center of the original circle. The area of the triangle is 3 square units.
The area of the teardrop is api+b square units, where a and b are constants. This is the value of a+b.
What is 21/2 or 10.5?
300
There are 2 pairs (x,y) with non-negative integer values of x and y such that x<y solve the equation
xy+x+y+1=187.
This is the sum of all 4 of the coordinates of those 2 solutions.
What is 212?
300
This is the x-coordinate at the point of intersection of the graphs of
x^2-4xy+4y^2-3x+y=0
and
y=1/2x-50000.
What is 3999980000 or
3.99998 \times 10^9?
400
The graph of linear function f(x)=mx+b and the graph of non-linear function g(x)=f(x)/(x-c) intersect at two points.
The x-coordinates at their points of intersection consist of this set of values.
A. {-m/b,c}
B. {-b/m,c}
C. {-m/b,c+1}
D. {-b/m,c+1}
What is D.{-b/m,c+1}?
400
In the figure below, equilateral triangle ABC has a perimeter of 6 cm. Points D and E are the midpoints of their respective sides, and \bar{EF} has length 1 cm.
The area in square centimeters of the quadrilateral CDFE is (h+sqrtk)/4 where h and k are integer constants. This is the product hk.
What is 3?
400
The expression
(xsqrt2+2)(tx+q)
can be rewritten as
2(x-h)^2+k.
If t+q=2, this is the value of k.
What is -1/2 or -0.5?
400
(x+1)^2+(y+1)^2=9 defines a circle whose center point is O in the xy-plane.
(x-14)^2+(y-7)^2=16 defines a circle whose center point is P in the xy-plane.
Point A lies on the intersection of circle O with \overline{OP}. Point B lies on the intersection of circle P with \overline{OP}. The midpoint of \overline{OP} is point M, and the midpoint of \overline{AB} is point L. This is the length of the line segment formed by \overline{ML}.
What is 1/2 or 0.5?