1 of 123

91578 – Worked Solutions - 2025

2 of 123

QUESTION ONE

3 of 123

3.6 (AS 91578) – 2025 Answers

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

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

​

Question 1(a)

​

Question 1(b)

​

Question 1(c)

​

Question 1(d)

​

Question 1(e)

4 of 123

Question 1(a)

  •  

5 of 123

Question 1(a)

  •  

6 of 123

Question 1(a)

  •  

 

7 of 123

Question 1(a)

  •  

 

 

8 of 123

Question 1(a)

  •  

 

 

9 of 123

Question 1(a)

  •  

 

 

10 of 123

Question 1(a)

  •  

 

 

11 of 123

Question 1(a)

  •  

 

 

12 of 123

Question 1(a)

  •  

 

 

13 of 123

Question 1(a)

  •  

 

 

14 of 123

Question 1(a)

  •  

 

 

15 of 123

Question 1(a)

  •  

 

 

You do not need to simplify this, but if you did, you could do the following:

16 of 123

Question 1(b)

  •  

17 of 123

Question 1(b)

  •  

18 of 123

Question 1(b)

  •  

 

19 of 123

Question 1(b)

  •  

 

 

20 of 123

Question 1(b)

  •  

 

 

21 of 123

Question 1(b)

  •  

 

 

22 of 123

Question 1(b)

  •  

 

23 of 123

Question 1(b)

  •  

 

24 of 123

Question 1(b)

  •  

 

 

25 of 123

Question 1(b)

  •  

 

 

 

26 of 123

Question 1(b)

  •  

 

 

 

27 of 123

Question 1(c)

  •  

28 of 123

Question 1(c)

  •  

29 of 123

Question 1(c)

  •  

 

30 of 123

Question 1(c)

  •  

 

 

31 of 123

Question 1(c)

  •  

 

We need to differentiate this function using the Product Rule

32 of 123

Question 1(c)

  •  

 

We need to differentiate this function using the Product Rule

 

 

33 of 123

Question 1(c)

  •  

 

 

 

34 of 123

Question 1(c)

  •  

 

 

 

 

35 of 123

Question 1(c)

  •  

 

 

 

36 of 123

Question 1(c)

  •  

 

 

 

 

 

37 of 123

Question 1(c)

  •  

 

 

 

38 of 123

Question 1(c)

  •  

 

 

 

39 of 123

Question 1(c)

  •  

 

 

 

40 of 123

Question 1(c)

  •  

 

 

 

41 of 123

Question 1(c)

  •  

 

 

 

42 of 123

Question 1(c)

  •  

 

 

 

43 of 123

Question 1(c)

  •  

 

 

 

44 of 123

Question 1(c)

  •  

 

 

 

45 of 123

Question 1(c)

  •  

 

 

 

46 of 123

Question 1(c)

  •  

 

 

 

47 of 123

Question 1(c)

  •  

 

 

 

48 of 123

Question 1(c)

  •  

 

 

 

Make sure your calculator is set up in radians

49 of 123

Question 1(c)

  •  

 

 

50 of 123

Question 1(c)

  •  

 

 

51 of 123

Question 1(c)

  •  

 

 

52 of 123

Question 1(c)

  •  

 

 

53 of 123

Question 1(d)

  •  

54 of 123

Question 1(d)

  •  

55 of 123

Question 1(d)

  •  

56 of 123

Question 1(d)

  •  

57 of 123

Question 1(d)

  •  

 

58 of 123

Question 1(d)

  •  

 

59 of 123

Question 1(d)

  •  

 

60 of 123

Question 1(d)

  •  

 

61 of 123

Question 1(d)

  •  

 

 

62 of 123

Question 1(d)

  •  

 

 

63 of 123

Question 1(d)

  •  

 

 

 

64 of 123

Question 1(d)

  •  

 

 

 

 

65 of 123

Question 1(d)

  •  

 

 

 

66 of 123

Question 1(d)

  •  

 

 

67 of 123

Question 1(d)

  •  

 

 

68 of 123

Question 1(d)

  •  

 

 

 

69 of 123

Question 1(d)

  •  

 

 

 

70 of 123

Question 1(d)

  •  

 

 

 

71 of 123

Question 1(d)

  •  

 

 

 

72 of 123

Question 1(d)

  •  

 

 

 

 

73 of 123

Question 1(d)

  •  

 

 

 

 

74 of 123

Question 1(d)

  •  

 

 

 

75 of 123

Question 1(d)

  •  

 

 

 

 

76 of 123

Question 1(d)

  •  

 

 

 

 

77 of 123

Question 1(e)

  •  

78 of 123

Question 1(e)

  •  

79 of 123

Question 1(e)

  •  

 

80 of 123

Question 1(e)

  •  

 

81 of 123

Question 1(e)

  •  

 

 

82 of 123

Question 1(e)

  •  

 

 

83 of 123

Question 1(e)

  •  

 

 

84 of 123

Question 1(e)

  •  

 

 

85 of 123

Question 1(e)

  •  

 

 

86 of 123

Question 1(e)

  •  

 

 

 

87 of 123

Question 1(e)

  •  

 

 

88 of 123

Question 1(e)

  •  

 

 

89 of 123

Question 1(e)

  •  

 

 

 

90 of 123

Question 1(e)

  •  

 

 

 

91 of 123

Question 1(e)

  •  

 

 

 

 

92 of 123

Question 1(e)

  •  

 

 

 

93 of 123

Question 1(e)

  •  

 

 

 

 

94 of 123

Question 1(e)

  •  

 

 

 

 

95 of 123

Question 1(e)

  •  

 

 

 

 

96 of 123

Question 1(e)

  •  

 

 

 

 

97 of 123

Question 1(e)

  •  

 

 

 

 

 

98 of 123

Question 1(e)

  •  

 

 

 

 

 

99 of 123

Question 1(e)

  •  

 

 

 

 

 

100 of 123

Question 1(e)

  •  

 

 

 

 

 

101 of 123

Question 1(e)

  •  

 

 

 

 

 

102 of 123

Question 1(e)

  •  

 

 

 

 

 

103 of 123

Question 1(e)

  •  

 

 

 

 

 

104 of 123

Question 1(e)

  •  

 

 

 

 

105 of 123

Question 1(e)

  •  

 

 

 

 

106 of 123

Question 1(e)

  •  

 

 

 

 

107 of 123

Question 1(e)

  •  

 

 

 

 

108 of 123

Question 1(e)

  •  

 

 

 

 

109 of 123

Question 1(e)

  •  

 

 

 

 

110 of 123

Question 1(e)

  •  

 

 

 

 

111 of 123

Question 1(e)

  •  

 

 

 

112 of 123

Question 1(e)

  •  

 

 

 

113 of 123

Question 1(e)

  •  

 

 

 

114 of 123

Question 1(e)

 

 

 

 

115 of 123

Question 1(e)

  •  

 

 

 

Factorise

116 of 123

Question 1(e)

  •  

 

 

 

117 of 123

Question 1(e)

  •  

 

 

 

118 of 123

Question 1(e)

  •  

 

 

119 of 123

Question 1(e)

  •  

 

 

 

120 of 123

Question 1(e)

  •  

 

 

121 of 123

Question 1(e)

  •  

 

 

122 of 123

Question 1(e)

  •  

 

 

123 of 123

Question 1(e)

  •