ECT Math Reviewer

1. Find the center and radius of the circle ( x2 + y 2 + 8x - 8y +23 = 0) on the coordinate coordinate plane.

2. What is the equation of the circle on the coordinate coordinate plane with a radius of 4 and its center ce nter at (4, -5)?

3. Evaluate: i4379

4. Evaluate: (12 + 3i) / (4  –  3i);  3i); 2 answers: in polar and rectangular form

5. Two lines: y = 5x - 10 ; y = 2x - 1 intersect each other on a coordinate plane. Find their point of intersection.

6. Convert to Roman Numerals: a. 3 456 b. 543 342 c. 2 043 598

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7. Convert to Arabic Numerals: a. XLVI b. MDCCXLIX c. DXXIV

8. Find the area of the circle inscribed in a square if the area of the latter is 49.

9. A Sphere with a volume of 36π is inscribed in a Cylinder. a. Find the Surface Area of the Sphere b. Find the Surface Area of the Cylinder c. Find the Volume of the Cylinder d. Find the height of the Cylinder e. Find the area of the top of the Cylinder

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Answers

1. C(-4, 4) ; radius = 3 2. x2 + y2 - 8x + 10y +25 = 0 3. -i 4. 1.56 + 1.92i ; 2.474<50.91 5. (3, 5)

6. a. MMMCDLVI b. DXLIII bar CCCXLII c. II (inside doorframe) XLIII bar DXCVIII

7. a. 46 b. 1749 c. 524

8. 38.48

9. a. 113.1 b. 169.65 c. 169.65 d. 6 e. 28.27

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