Senshu Mathematics Exam 2008

1  Fill in the following blanks with correct answers

(1)  \(2\sqrt{12} \:-\:3\sqrt{6} \div \sqrt{18}\)

 

(2)  \(\dfrac{x^2 \:-\:x \:-\:6}{x^2 + x \:-\:2} \:-\: \dfrac{2x\:-\:4}{x\:-\:1}\)

 

2  On the plane \(xy\), there are three points: O (0, 0), A (2, 4), B (3, 0). Fill in the following blanks with correct answers.

(1)  Taking point D in the fourth quadrant and when the quadrilateral ODBA is parallelogram, the coordinates of point D is…

 

(2)  When a straight line \(x = p\) bisects the area of \(\triangle \text{OAB}\), \(p = \dotso\)

 

(3)  When a straight line \(y = q\) bisects the area of \(\triangle \text{OAB}\), \(q = \dotso\)

 

(4)  When the straight line L drawn from point B bisects the area of \(\triangle \text{OAB}\), the equation of the straight line L is \(y = \dotso\)

 

(5)  The equation of a parabola which passes three points: O, A, B is \(y = \dotso\)