# HSC Maths Sample Question Paper- Part 2 - AA2

Final part of the Question Paper set AA2 on StateBoard/ HSC Mathematics. You may wish to refer to Part 1 of the Question Paper Series before attempting this part. Again, if you know the answers, share it
21) The complex number form of $3-\sqrt{-7}$ is:

a) $-3+i\sqrt{7}$                              b) $–3-i\sqrt{7}$

c) $3-i7$                                         d) $3+i7$

22) Real and imaginary parts of $\frac{3}{2i}$ are:

a) $0, \;\frac{3}{2}$                        b) $\frac{3}{2}, \;0$

c) 2, 3                                                          d) 3,2

23) The standard form (a+ ib) of 3+2i+(-7-i) is:

a) 4-i                  b) -4+i                  c) 4+i                  d) 4+4i

24) The modulus values of -2+2i and 2-3i are:

a) $\sqrt{5}, \;5$                         b) $2\sqrt{5}, \;\sqrt{13}$

c) 2\sqrt{2}, \;\sqrt{13}                              d) –4, 1

25) The cube roots of unit are:

a) In G.P. with common ratio $\omega$

b) In G.P. with common difference $\omega^{2}$

c) In A.P. with common difference $\omega$

d) In A.P. with common difference $\omega^{2}$

26) Which of the following statements is correct?

a) Negative complex numbers exist                             b) order relation does not exist in real numbers

c) order relation exist in complex numbers                  d) (1+i) > (3-2i) is meaningless

27) The value of $z\overline{z}$ is:

a) $|z|$                  b) $|z|^2$                  c) $2|z|$                  d) $2|z|^2$

28) If $|z-z_{1}| = |z-z_{2}|$ then the locus of z is:

a) A circle with centre at the origin                             b) A circle with centre at $z_{1}$

c) A straight line passing through the origin                d) Is a perpendicular bisector of the line joining $z_{1}$ and  $z_{2}$

29) The axis of the parabola $y^2=4x$ is:

a) x=0           b) y=9           c) x=1           d) y=1

30) The equation of the latus rectum of $y^2=4x$ is:

a) x=1           b) y=1           c) x=4           d) y=-1

31) The equations of the major and minor axes of $\frac{x^2}{9}\;+\;\frac{y^2}{4}=1$ are:

a) x=3, y=2                b) x=-3, y=-2                c) x=0, y=0                d) y=0, x=0

32) The equations of the minor and major axes of $\frac{x^2}{9}\;+\;\frac{y^2}{4}=1$ are:

a) 6, 4                b) 3, 2                c) 4,6                d) 2, 3

33) The equation of the latus rectum of $\frac{x^2}{16}\;+\;\frac{y^2}{9}=1$ are:

a) $y= \pm \sqrt{7}$                                      b) $x= \pm \sqrt{7}$

c) $x= \pm 7$                                               d) $y= \pm 7$

34) The eccentricity of the ellipse $16x^2+25y^2=400$ is:

a) $\frac{4}{5}$                                            b) $\frac{3}{5}$

c) $\frac{3}{4}$                                            d) $\frac{2}{5}$

35) The equation of the tangent at (-3, 1) to the parabola $x^2=9y$ is:

a) 3x-2y-3=0                  b) 2x-3y+3=0                   c) 2x+3y+3=0                  d) 3x+2y+3=0

36) The equations of the directrices of the hyperbola $\frac{x^2}{9}\;-\;\frac{y^2}{4}=1$ are:

a) $y=\pm \frac{9}{\sqrt{13}}$                               b) $x=\pm \frac{13}{9}$

c) $y=\pm \frac{\sqrt{13}}{9}$                               d) $x=\pm \frac{9}{\sqrt{13}}$

37) The vertices of the hyperbola $25x^2-16y^2=400$ are:

a) $(0, \; \pm4)$        b) $(\pm4, \;0)$        c) $(0, \; \pm5)$        d) $(\pm5, \;0)$

38) The equation of chord of contact of tangents from (2, 4) to the ellipse $2x^2+5y^2=20$ is:

a) x-5y+5=0            b) 5x-y+5=0            c) x+5y-5=0            d) 5x-y-5=0

39) Find the angle between the asymptotes of the hyperbola $24x^2-8y^2=27$ is:

a) $\frac{\pi}{3}$                            b) $\frac{\pi}{3}$ or $\frac{2\pi}{3}$

c) $\frac{2\pi}{3}$                          d)  $\frac{-2\pi}{3}$

40) The point of contact of the tangent y=mx+c and the hyperbola $\frac{x^2}{a^2}\;-\;\frac{y^2}{b^2}=1$ is:

a) $(\frac{am^2}{c},\; \frac{b^2}{c})$                                    b) $(\frac{a^2m}{c},\; \frac{b^2}{c})$

c) $(\frac{-a^2m}{c},\; \frac{-b^2}{c})$                                  d) $(\frac{-am^2}{c},\; \frac{-b^2}{c})$