Which of the following must be negative whenever x>y>0?
A) x^2 -4xy + y^2
B) x^2 -2xy – y^2
C) x^2 – xy -2y^2
D) y^2 -x^2 -xy
E) y^2 -x^2 +xy
Which of the following must be negative whenever x>y>0?
A) x^2 -4xy + y^2
B) x^2 -2xy – y^2
C) x^2 – xy -2y^2
D) y^2 -x^2 -xy
E) y^2 -x^2 +xy
For an real number k, which of the following must be a real number?
A)1/k
B)k/k+1
C)1/k-1
D) k/k^2+1
E) 1/k^2-1
Thank you
If points (6,0), (0,0), (0,2), and (a,2) are consecutive vertices of a trapezoid of area 7.5, what is the value of a?
A) 1.5
B) 2
C) 2.5
D) 5
E) 9
In figure 5, rectangle ABCD is inscribed in a circle. If the radius of the circle is 1 and AB = 1, what is the area of the shaded region?
A) 0.091
B) 0.285
C) 0.614
D) 0.705
E) 0.732
A cube with edge of length 4 is divided into 8 identical cubes. How much greater is the combined surface area of the 8 smaller cubes than the surface area of the original cube?
A) 48
B) 56
C) 96
D) 288
E) 384
A square and a regular hexagon have the same perimeter. If the area of the square is 2.25, what is the area of the hexagon?
A) 2.250
B) 2.598
C) 2.838
D) 3.464
E) 3.375
In figure 2, AB=BC. If the area of triangle ABE is x, what is the area of triangle ACD?
A) x sqrt2
B) x sqrt3
C) 2x
D) 3x
E) 4x
If f(x+1) = 3x^2 + 6x + 3, then f(x) =
A)3x
B)3x+3
C)3x^2
D)3x^2 + 3
E) 3x^2 + 6x + 2
Which of the following is NOT a graph of y as a function of x?
If a and c are real numbers such that 0<a<c, which of the following must be true?
A) -a<-c
B) 2a sqrt c
D) a^2 > c^2
2) a/c > 1
In the x-y plane, the x-axis and the graphs of the lines y = x, y = 1, and y+x=4 intersect to form a trapezoid. What is the sum of the slopes of the two nonparallel sides of the trapezoid?
A) -2
B) -1
C) 0
D) 1
E) 2
In the figure above, the length of each edge of the cube is 2. If P, Q, R, and S are the centres of faces ABFE, BCGF, DCGH, and ADHE, respectively, what is the perimeter of quadrilateral PQRS?
A) 4
B) 4 sqrt2
C) 6
D) 4 sqrt 3
E) 8
Math1 question:
In right triangle ABC in the figure above, if sin A = 0.6, what is sin B?
A) 0.36
B) 0.40
C) 0.60
D) 0.64
E) 0.80
What is the area of a triangle whose sides are 5,5, and 6?
A) 6
B) 12
C) 16
D) 18
E) 24
if x^2 – y^2 = x- y and x<y, what is the average (arithmetic mean) of x and y?
A) 0
B) 1/2
C) 1
D) x/2
E) y/2