Problem 1 :
In the figure above ABC and CDE are right triangles. If ∠ACE is a right angle, which of the following is equal to sin∠ACB?
Solution :
Problem 2 :
The expression 3x2 + bx – 56, where b is a constant, can be written as (mx + n)(x + p) where m, n and p are integer constants. Which of the following must be integer?
Solution :
Problem 3 :
In the figure above, what is the value of x?
Solution :
Problem 4 :
In the xy-plane, a parabola has a vertex (7, 12) and intersects the x-axis at two points. If the equation of the parabola is written in the form y = ax2 + bx + c, where a, b and c are constants, which of the following could be the value a + b + c?
A) 36
B) 18
C) 14
D) 10
Solution :
Problem 5 :
In the circle with center O, the central angle has a measure of 2𝜋/3 radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?
Solution :
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