2012_Question1e 2012_Question1f

A. The circle has radius 2
Answer is not (a) as the point (1,1) lies in the circle
Answer is definitely not © by observation
Answer is not (d) as (sqrt 2,0) lies in the circle

Answer is (b)

B. N= 2^(k+2m+3n)
N is a square number if k + 2m + 3n is even
2n+2m must be even
so k+ n is even

Answer is (d)

C. The option (b) equals to 4
For (a), (sqrt 3)^3 > 4 as sqrt 3 > 4/3, (b) < (a)
For ©, the answer is 27/4 > 4, (b) < ©
For (d), the answer is log (base 2) (15) < 4, (d) < (b)

Answer is (d)

D. When c=0, y=x, Area is 0.5, not (d)
Answer is (a)

E. There are 5 roots in total
Answer not (b) because it doesn’t pass through (0,0)
When x=0, y is positive so answer not ©
Answer not (a) because the two smaller roots are repeated roots

Answer is (d)

F. All three integrals are defined so answer is not (d)
For the cos x integral, it’s antiderivative is sin x so calculating the integral we have the integral = 2 > 0
For the sin x integral, its antiderivative is -cos x and the integral = -1 < 0
For the last integral, it is positive

so answer is (b)

G. 2x + 2y = 2k
we see k = 2 has infinitely many solutions
We also see k =0 has no solution where x, y > 0
For k =1, we can solve y =3 but x = -1

Answer is ©