1. L1 is a straight line passing through (0,0),and its slope is=-1
The equation of another straight line L2 is2x-y+3=0.
A is the intersection of L1 and L2.Please find the coordinates of A.
1.Let f(x)=x^2-4x-5 and g(x)=f(x-2),find the x-intercepts of the graph of y=g(x)
2.P(2,8) lies on the graph of y=2x+b,If f(x)=(2x+b^2),slove f(x)=12(Leave the ans in surd form.)
3a.Slove the following simultaneous equations: x-4y=-3 & x^2-2xy=5
3b.Let m and n be positive integers.slove the following simultaneous equations: logm/n^4=-3 & (log m)^2-2 log m log n=5(leave the ans in index form)
4.Let f(x)=2x^3-x^2-5x-2 and g(x)=x^3-4x+x+6.x+1 is a common factor of f(x) and g(x).It is given that h(x)=3x^3-5x^2-4x+4=f(x)+g(x).Please slove the equation 3x^3-5x^2-4x+4=0.
1.Let f(x)=x^3+2x^2+ax+b.If f(x) is divisible by x+1 and x-2,f(x) can be factorized as?
2.Let f(x)=x^2-x-3.If f(k)=k,then k=?
3.2^x times 8^y=?
4.The remainder when x^2+ax+b is divided byx+2 is-4.the remainder when ax^2+bx+1 is divided by x-2 is 9.The value of a is?
5.If log x^2=Log3x+1,then x=?
1.If f(x)=x^2-1,then f(a-1)=
2.John goes to school and returns home at speeds x km/h and (x+1)km/h respectively.The school is 2Km from John's home and the total time for the two journeys is 54 minutes.Which of the following equations can be used to find x?
4.Let f(x)=x^3-2x^2-5x+6.It's known that f(1)=0.f(x) can be factorized as?
6.Let f(x)=(2x-1)(x+1)+2x+1.Find the remainder when f(x) is divided by 2x+1.
1.The equation8x^2-(k+2)x+2=0 has a double root.
a)Find the possible values of k.
b)If k takes the possitive value obtained in a),slove the given equation.
2.Let f(x)=2x^3-x^2-5x-2 and g(x)=x^3-4x^2+x+6.
a)Show that x+1 is a common factor of f(x) and g(x)
b)Factorize f(x) and g(x) completly.
c)(i)It is given that h(x)=3x^3-5x^2-4x+4.Express h(x) in terms of f(x) and g(x).(ii)Solve the equation 3x^3-5x^2-4x+4=0
1. It's given that g(x)=f(x-1)&h(x)=g(x+3).
a.Describe the effect of the transformation on the graph of y=f(x) when f(x) is transformes to g(x).
b.Describe the effect of the transformation on the graph of y=g(x) when g(x) is transformes to h(x).
c.Hence ,solve h(x)=0