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    is ………..

a)   

b)   

c)   

d)   

32) If    is the cube root of unity, then the value of    is ………….

a) 9

b) –9

c) 16

d) 32

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

a) –1

b) –2

c) 4

d) –4

34) The focus of the parabola    is ………

a) (4, 0)

b) (0, 4)

c) (-4, 0)

d) (0, –4)

35) The eccentricity of the conic    is ………..

a)   

b)   

c)   

d)   

36) The distance between the foci of the ellipse    is ……….

a) 4

b) 6

c) 8

d) 2

37) The sum of the distances of any point on the ellipse    from    and    is …………….

a) 4

b) 8

c) 6

d) 18

38) The directions of the hyperbola    are:

a)   

b)   

c)   

d)   

39) The equation of the chord of contact of tangents from (2, 1) to the hyperbola    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)   

c)   

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    at x=2 is ………

a) –20

b) 27

c) –16

d) –21

43) The slope of the tangent to the curve    at x=0 is …………….

a) 3

b) 2

c) 1

d) –1

44) If the normal to the curve    makes an angle    with the x-axis, then the slope of the normal is ……………..

a)   

b)   

c)   

d)   

45) If    then    is equal to ……..

a) 0

b) 1

c) 2u

d) u'