HSC Maths Practice Question Paper - Part3 - AA1

This is part 3 of the Question paper set AA1 on HSC Mathematics. You may wish to refer to Part1-Questions and Part2-Questions before starting with this section. The Part 3 section comprises of 15 questions, from 31 to 45.

31) The quadratic equation whose roots are $ \pm i\sqrt7 $ is ………..

a) $ x^2+7=0 $

b) $ x^2-7=0 $

c) $ x^2+x+7=0 $

d) $ x^2-x-7=0 $

32) If $ \omega $ is the cube root of unity, then the value of $ (1-\omega)(1-\omega^2)(1-\omega^4)(1-\omega^8)$ is ………….

a) 9

b) –9

c) 16

d) 32

33) If the line 4x+2y=c is a tangent to the parabola $ y^2=16x $ then c is ……..

a) –1

b) –2

c) 4

d) –4

34) The focus of the parabola $ x^2=16y $ is ………

a) (4, 0)

b) (0, 4)

c) (-4, 0)

d) (0, –4)

35) The eccentricity of the conic $ 9x^2+5y^2-54x-40y+116=0 $ is ………..

a) $ \frac{1}{3} $

b) $ \frac{2}{3} $

c) $ \frac{4}{9} $

d) $ \frac{2}{\sqrt5} $

36) The distance between the foci of the ellipse $ 9x^2+5y^2=180 $ is ……….

a) 4

b) 6

c) 8

d) 2

37) The sum of the distances of any point on the ellipse $ 4x^2+9y^^2=36 $ from $ (\sqrt5, 0) $ and $ (-\sqrt5, 0) $ is …………….

a) 4

b) 8

c) 6

d) 18

38) The directions of the hyperbola $ x^2-4(y-3)^2=16 $ are:

a) $ y=\pm\frac{8}{\sqrt5} $

b) $ x=\pm\frac{8}{\sqrt5} $

c) $ y=\pm\frac{\sqrt5}{8} $

d) $ x=\pm\frac{\sqrt5}{8} $

39) The equation of the chord of contact of tangents from (2, 1) to the hyperbola $ \frac{x^2}{16}-\frac{y^2}[9}=1 $ is ………….

a) 9x-8y-72=0

b) 9x+8y+72=0

c) 8x-9y-72=0

d) 8x+9y+72=0

40) The eccentricity of the hyperbola with asymptotes x+2y-5=0, 2x-y+5=0 is ……….

a) 3

b) $ \sqrt2 $

c) $ \sqrt3 $

d) 2

41) One of the foci of the rectangular hyperbola xy=18 is …………….

a) (6, 6)

b) (3, 3)

c) (4, 4)

d) (5, 5)

42) The gradient of the curve $ y=-2x^3+3x+5 $ at x=2 is ………

a) –20

b) 27

c) –16

d) –21

43) The slope of the tangent to the curve $ y = 3x^2+3\; sin\;x $ at x=0 is …………….

a) 3

b) 2

c) 1

d) –1

44) If the normal to the curve $ x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}} $ makes an angle $ \Theta $ with the x-axis, then the slope of the normal is ……………..

a) $ –cot\;\Theta $

b) $ tan\;\Theta $

c) $ –tan\;\Theta $

d) $ cot\;\Theta $

45) If $ u=f(\frac{y}{x}) $ then $ x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y} $ is equal to ……..

a) 0

b) 1

c) 2u

d) u'