F.4數學功課 (20分!)(I)

1. When 3x²+px-1 is divided by x-2a,the remainder is 15.When px²+5x-4 is divided by 2x+a,the remainder is -6.Find the values of a and p.

2. a/(a-b)(a-c) + b/(b-c)(b-a) + c/(c-a)(c-b)

3. When ax^2+bx+c is divided by ax+b , the quotient is ...?

4. If x^3+2 is congruent to (x+1)Q(x)+R,where Q(x) is a quadratic polynomial and R is a constant,R=?

5. The graphs of y=2x^2-6x+1 and y=mx intersect at one and only one point.A possible value of m is ...?

6. Find the H.C.F. of m^4-n^4 and m^3+n^3.

7. Without using calculators,determine the sign of each of the following ratios.
(a) tan137°
(b) cos128°
(c) cos333°
(d) sin248°

8. Find the maximum and minimum values of the following functions for the following functions of 0° </= x </=360°.
(a) y=2+sinx
(b) y=2/5 cos2x

9. Find the maximum and minimum values of the following functions for the following functions of 0° </= x </=180°.
(a) y=-sinx
(b) y=1+3cos3x