3 of 90

3.5 (AS 91577) – 2025 Answers

Quite often, there are different ways to solve a Mathematics problem.

These solutions/strategies show one possible way to solve them.

Question 2 (a)

4 of 90

Question 2(a)

5 of 90

Question 2(a)

6 of 90

Question 2(a)

7 of 90

Question 2(a)

8 of 90

Question 2(a)

9 of 90

Question 2(a)

10 of 90

Question 2(a)

11 of 90

Question 2(a)

12 of 90

Question 2(a)

13 of 90

Question 2(a)

Expand brackets

14 of 90

Question 2(a)

Simplify by adding real parts together and imaginary parts together

15 of 90

Question 2(a)

16 of 90

Question 2(b)

17 of 90

Question 2(b)

18 of 90

Question 2(b)

19 of 90

Question 2(b)

20 of 90

Question 2(b)

21 of 90

Question 2(b)

22 of 90

Question 2(b)

23 of 90

Question 2(b)

24 of 90

Question 2(b)

25 of 90

Question 2(b)

26 of 90

Question 2(b)

27 of 90

Question 2(b)

28 of 90

Question 2(c)

29 of 90

Question 2(c)

30 of 90

Question 2(c)

31 of 90

Question 2(c)

So, we can use Pythagoras to determine this distance

32 of 90

Question 2(c)

33 of 90

Question 2(c)

Square both sides

34 of 90

Question 2(c)

35 of 90

Question 2(c)

Divide both sides by 4

36 of 90

Question 2(c)

Square root both sides;

Don’t forget the positive and negative solutions.

37 of 90

Question 2(c)

38 of 90

Question 2(d)

39 of 90

Question 2(d)

40 of 90

Question 2(d)

41 of 90

Question 2(d)

Expand quadratic

42 of 90

Question 2(d)

43 of 90

Question 2(d)

Gather real parts and imaginary parts together

44 of 90

Question 2(d)

Factorise the imaginary part

45 of 90

Question 2(d)

46 of 90

Question 2(d)

Expand quadratic

47 of 90

Question 2(d)

48 of 90

Question 2(d)

Simplify

49 of 90

Question 2(d)

50 of 90

Question 2(d)

51 of 90

Question 2(d)

52 of 90

Question 2(d)

53 of 90

Question 2(d)

54 of 90

Question 2(d)

Divide everything by 3

55 of 90

Question 2(d)

Substitute into equation 2

56 of 90

Question 2(d)

Expand the brackets

57 of 90

Question 2(d)

Add 22 to both sides

58 of 90

Question 2(d)

Multiply everything by 3

59 of 90

Question 2(d)

60 of 90

Question 2(d)

Simplify by dividing everything by 2

61 of 90

Question 2(d)

Solve the quadratic

62 of 90

Question 2(d)

63 of 90

Question 2(d)

64 of 90

Question 2(e)

65 of 90

Question 2(e)

66 of 90

Question 2(e)

67 of 90

Question 2(e)

68 of 90

Question 2(e)

69 of 90

Question 2(e)

70 of 90

Question 2(e)

71 of 90

Question 2(e)

72 of 90

Question 2(e)

73 of 90

Question 2(e)

74 of 90

Question 2(e)

75 of 90

Question 2(e)

76 of 90

Question 2(e)

77 of 90

Question 2(e)

78 of 90

Question 2(e)

Simplify

79 of 90

Question 2(e)

Separate out the real parts and the imaginary parts

80 of 90

Question 2(e)

Separate out the real parts and the imaginary parts

81 of 90

Question 2(e)

82 of 90

Question 2(e)

83 of 90

Question 2(e)

Converting radians to degrees

84 of 90

Question 2(e)

Real

Imaginary

85 of 90

Question 2(e)

Real

Imaginary

86 of 90

Question 2(e)

Real

Imaginary

They have a common denominator

87 of 90

Question 2(e)

Real

Imaginary

88 of 90

Question 2(e)

Real

Imaginary

Solve the quadratic

89 of 90

Question 2(e)

Real

Imaginary

90 of 90

Question 2(e)

Real

Imaginary