Contents page
Table of Contents
Questions
SESSION 1 ......................................................................................................................................................................... 1
Solving Equations Inequalities and Simplifying Expressions Arithmetic Sequences and Series .................................. 1
SESSION 2 ......................................................................................................................................................................... 8
Geometric Sequences and Series Quadratic Sequences Financial Mathematics ........................................................ 8
SESSION 3 ....................................................................................................................................................................... 17
Functions Differential Calculus Probability ................................................................................................................ 17
SESSION 4 ....................................................................................................................................................................... 51
Trigonometry Statistical Reasoning ........................................................................................................................... 51
SESSION 5 ....................................................................................................................................................................... 85
Coordinate Geometry Euclidean Geometry .............................................................................................................. 85
Answers
SESSION 1 ..................................................................................................................................................................... 138
Solving Equations, Inequalities and Simplifying Expressions................................................................................... 138
SESSION 2 ..................................................................................................................................................................... 143
Geometric Sequences and Series ............................................................................................................................ 143
SESSION 3 ..................................................................................................................................................................... 149
Functions.................................................................................................................................................................. 149
SESSION 4 ..................................................................................................................................................................... 163
Trigonometry ........................................................................................................................................................... 163
SESSION 5 ..................................................................................................................................................................... 172
Analytical Geometry ................................................................................................................................................ 172
SESSION 1
Solving Equations Inequalities and Simplifying Expressions Arithmetic
Sequences and Series
Nov 2019
May-June 2019
1
November 2018
June 2018
2
March 2018
November 2017:
3
June 2017:
March 2017:
4
ARITHMETIC SEQUENCES AND SERIES
Nov 2019
5
May-June 2019
Nov 2018
June 2018
6
March 2018
November 2017:
June 2017:
7
SESSION 2
Geometric Sequences and Series Quadratic Sequences Financial Mathematics
Nov 2019
May-June 2019
8
Nov 2018
June 2018
March 2018
9
November 2017:
June 2017:
March 2017:
10
Quadratic Sequences:
November 2019:
May-June 2019
November 2017:
11
June 2017:
March 2017:
FINANCIAL MATHEMATICS
November 2019
12
May-June 2019
13
November 2018
June 2018
14
March 2018
November 2017:
June 2017:
15
March 2017:
16
SESSION 3
Functions Differential Calculus Probability
Functions
November 2019
17
May-June 2019
18
19
November 2018
20
21
June 2018
22
23
March 2018
24
25
26
November 2017:
27
June 2017:
28
29
30
March 2017:
31
32
33
Differential Calculus:
November 2019
34
May-June 2019
35
November 2018
36
37
June 2018
38
March 2018
39
November 2017:
40
41
June 2017:
42
March 2017:
43
Probability
November 2019
44
May-June 2019
45
November 2018
46
June 2018
47
March 2018
48
November 2017:
June 2017:
49
March 2017:
50
SESSION 4
Trigonometry Statistical Reasoning
TRIGONOMETRY:
November 2019
51
52
May-June 2019
53
November 2018
54
55
June 2018
56
57
March 2018
58
59
November 2017:
60
61
62
June 2017:
63
64
65
66
March 2017:
67
68
STATISTICAL REASONING:
November 2019
69
May-June 2019
70
71
November 2018
72
73
74
75
June 2018
76
March 2018
77
78
November 2017:
79
80
June 2017:
81
March 2017:
82
83
84
SESSION 5
Coordinate Geometry Euclidean Geometry
Coordinate (Analytical) Geometry
November 2019
85
May-June 2019
86
87
88
November 2018
89
June 2018
90
91
March 2018
92
93
November 2017:
94
95
96
June 2017:
97
98
March 2017:
99
100
Euclidean Geometry
November 2019
101
102
103
104
105
May-June 2019
106
107
108
109
November 2018
110
111
112
113
June 2018
114
115
116
March 2018
117
118
119
120
121
November 2017:
122
123
124
125
June 2017:
126
127
128
129
130
131
March 2017:
132
133
134
135
136
Answers to Questions
137
Q1.1.4
SESSION 1
Q1.1.2
Solving Equations,
Inequalities and
Simplifying Expressions
Nov 2019
Q1.1.1
Q1.2
Q1.3
Q1.1.3
Q1.1.2
Q1.1.4
Nov 2018
Q1.1.1
Q1.1.2
Q1.1.3
Q1.3
Q1.2
May-June 2019
Q1.1.1
138
Q1.1.2
Q1.3
Q1.1.3
Q1.1.3
Q1.3
Q1.1.4
Q1.4
Q1.1.4
Q1.2
March 2018
Q1.1.1
June 2018
Q1.1.1
Q1.2
Q1.1.2
139
Q1.3.2
Q1.5.1
Q1.1.3
Q1.2
June 2017:
Q1.1.1
Q1.5.2
Q1.2
Q1.1.2
Q1.3
Nov 2017:
Q1.1.1
Q1.1.2
Q1.1.3
Q1.3.1
Q1.4
140
Q1.2
Q3.2
Q1.1.3
Q1.3.1
Q1.3
Q1.2.1
Q1.3.2
March 2017:
Q1.1.1
Q1.1.2
Q1.2.2
Arithmetic series and sequences
Nov 2019
Q3.1
May-June 2019
Q3.1.1
Q3.1.2
141
Q2.2
Q3.2
Q2.3
Q2.1.3
Q2.2
Sum of all multiples of 7 from 35 to 196:
Nov 2018
Q2.1.1
42
Q2.1.2
March 2018
Q3.1
Q3.2
Q3.3
June 2018
Q2.1.1
37 ; 50
Q2.1.2
Sum of all the natural numbers from 35 to 196:
Q3.4
Q2.1.3
142
Q2.2.2
November 2017:
Q2.2.1
Q2.2.2
Q2.2.3
SESSION 2
Q2.2.2
Geometric Sequences and
Series
Nov 2019
Q2.2.1
Q2.2.4
June 2017:
Q2.2.1
Q2.2.2
May-June 2019
Q2.2.1
143
He will pass halfway mark on the tenth day.
Q3.3
Nov 2018
Q3.1
Q3.4
Q2.2
March 2018
Q2.1.1
Q3.2
June 2018
Q3.1
Q3.3
November 2017:
Q3.1
Q3.2
Q3.2
Q2.1.2
144
Or you could write it as:
Q2.4
Q2.1.3
Q2.2
QUADRATIC PATTERNS:
Nov 2019
Q2.1.1
June 2017:
Q2.1.1
Q2.1.2
March 2017:
Q2.1
Q2.1.2
Q2.3
The series is:
The new positive series is:
Q2.1.3
145
November 2017:
Q2.1.1
Q3.1.2
Q2.1.4
Q2.1.2
Q3.2
May-June 2019
Q2.1.1
59
Q2.1.2
Q3.1.3
Q3.3
Q2.1.3
Q3.2
Q2.1.3
June 2017:
Q3.1
March 2017:
Q3.1.1
24
146
FINANCIAL MATHEMATICS
Q6.2.2
Nov 2019
Q6.1
Q6.2.1
Q7.1.2
Q6.2.2
Q7.2.1
Q6.2.1
May-June 2019
Q6.1.1
Q7.2.2
November 2018
Q7.1.1
Q6.1.2
June 2018
147
Q6.1
March 2018
Q7.1
Balance:
November 2017:
Q6.1
Q6.2
June 2017:
Q7.1
Q7.2.1
Q7.2.2
Q6.2.1
Q6.3
Q7.2
She pays 36 instalments of R3200 each
Q6.2.2
Amount pd for the year:
148
The machine will need to be replaced
at the beginning of 2020
Q6.1.3
OR
Q7.3
Q4.3
Q6.2
Q5.1
Q4.4
Q4.5
March 2017:
Q6.1.1
Q6.1.2
Q5.2
Lerato qualifies for a loan of
R 791 000 under the given conditions
SESSION 3
Functions
Nov 2019
Q4.1
Q5.3
Q4.6
OR
Q4.2
Q4.7
Q5.4.1
Q5.4.2
149
Q4.4.1
Q5.5
Q4.4.2
Q4.5
Q5.2.1
November 2018
Q4.1
Yes, it is a one-to-one mapping
Q4.2
R(-12;-6)
Q4.3
Qs.1.1
Q5.2.2
Q5.1.2
Q4.4
Q5.1.3
May-June 2019
Q4.1
Q5.2.3
Q4.2
Q5.1.4
Q5.1
Q5.2.4
Q5.2
Q5.2.5a
Q4.3
Q5.3
Q5.2.5b
150
Q6.4.2
Q5.4
Q4.3
Q6.1
Q6.5
Q5.3
Q6.2
Q4.4
Q4.5
Q6.3
Q6.6
Q5.1
Q5.2
June 2018
Q4.1
Q6.4.1
Q5.4
Q5.5
Q4.2
151
Q4.3
Q5.2
Q4.4
Q5.3
Q5.6
Q5.4
Q5.7
Q4.5
Q6.1
Q6.3
Q6.2
March 2018
Q4.1
Q4.2
Q4.6
November 2017:
Q4.1
Q5.1
152
Q5.4
Q4.4
Q5.5
Q4.5
Q4.4 and Q4.6
Q5.6
Q5.1
June 2017:
Q4.1
Q4.2
Q4.5
Q4.2
Q4.7
Q5.1
Q5.2
Q4.3
Q5.2
Q4.3
Q5.3
Q5.3
Q5.4
153
Q5.1.1
Q5.1.2
Q6.1
Q5.2
Q6.2
March 2017:
Q4.1
Q6.3
Q4.2
Q5.1.3
Q6.4
Q4.3
Q5.1.4
AV gradient =
Q6.5
DIFFERENTIAL CALCULUS
Q4.4
Nov 2019
Q7.1
Q5.1.5
Q4.5
y=0
Q4.6
Q5.1.6
Q5.1.7
Q4.7
154
Q9.1
May-June 2019
Q7.1
7.2
Q9.2.1
Q7.3.1
Q9.2.2
Q8.1
Q9.3
Q7.3.2
Q8.2
Q7.2.1
only once
Q8.3
Q7.4
Q7.2.2
Q9.4
155
Q9.1
Q7.3
Q9.2
Q9.3
Q8.1
Q8.2.1
Q9.1.3
Q8.2.2
Q8.2
Q9.2
Q9.1.1
Q8.3
Q8.4
November 2018
Q8.1
Q9.1.2
Q10.1
156
Q7.2.1
Q9.3
Q10.2
Q7.2.2
Q8.4
Q9.4
Q8.1
Q8.2
Q9.1.1
Q9.1.2
June 2018
Q7.1
Q8.3
Q9.2
March 2018
Q8.1
157
Q9.1
Q9.4
Q9.2
November 2017:
Q7.1
Q8.2.1
Q9.5
Q10
Q8.2.2
Q9.3
Q7.2.1
Q7.2.2
158
Q8.1
Q8.3
Q8.3
Q8.4.1
Q8.4.2
June 2017:
Q8.1
Q9:
Q8.2
Q9.1
Q8.2
Q9.2
159
Q10.2
Q9.3
Q8.1
Q7.2
Q7.3
Q9.4
March 2017:
Q7.1
or y = 1
Q8.2
Q9.5
Q10.1
160
Q11.1.1
OR
Q8.3
Q11.1.2
May-June 2019
Q10.1
OR
Q8.4
OR
PROBABILITY:
Q11.2
Nov 2019
Q10.1
Q10.2.1
OR
Q9
Q10.2
Q10.2.2
161
Q11.2
Q11.1
Q11.2.3
Q11.2.1
March 2018
Q11.1.1
Q11.2.2
Q11.1.2
November 2018
Q11.1.1
Q11.1.2
June 2018
Q10.1
November 2017:
Q10.1
Q11.1.3
Q10.2
Q11.2
Q12.1
Q10.3
Q11.2.1
Q11.2.2
Q10.2
Q12.2
Q11.1
162
Q10.3
Q10.2.1
Q11.1
Q10.2.2
Q11.2
SESSION 4
Q11.3.1
Q10.3
Q11.3.2
June 2017:
Q11.1
Trigonometry
Nov 2019
Q5.1
Q11.3.3
Q11
Q11.2
March 2017:
Q10.1.1
Q11.3
Q10.1.2
Q5.2
163
Q5.3
Q6.1
Q5.4.1
May-June 2019
Q5.1.1
Q7.1
Q6.2.1a
Q5.1.2
Q6.2.1b
Q5.2
Q5.4.2
Q7.2
Q6.1
Q6.2.2a
Q6.2.2b
Q7.3
Q6.2.3
Q6.2
Q6.3
Q5.3
Q7.1.1
Q7.1.2
164
Q6.2
AB = 2h
Q7.2
Q7.2
Q5.1.3
OR
Q6.3
Q7.3
June 2018
Q5.1.1
Q5.2
Q5.1.2
November 2018
Q5.1.1
Q6.4
Q6.5
Q5.1.2a
Q5.3
Q5.2
Q7.1
Q5.1.2b
Q5.1.2c
Q6.1
Q5.3.1
165
Q5.3.2
Q5.4.1
Q6.1
Q6.2
Q6.3
Q5.4.2
Q7.3
Q5.1.2
Q6.4.1
Q5.4.3
Q6.4.2
March 2018
Q5.1.1
Q5.5.1
Q7.1
Q7.2
Q5.2
Q5.5.2
=sinx.cosx + sinxcosx
=2sinxcosx
=sin2x
Q5.3
Q5.5.3
166
Q7.1
Q7.2
Q6.1
Q6.1.1
Q5.2.1
Q6.1.2
Q5.2.2
Q6.2
Q5.2.3
Q7.3
Q6.2
Q5.3.1
Q6.3
Q6.3
June 2017:
Q5.1.1
Q5.3.2
November 2017:
Q5.1
167
Q5.2
Q5.1.2
Q7.1
Q5.3
Q7.2
Q6.1.1
Q5.5.1
Q6.1.2
Q5.2
Q6.2
Q5.5.2
Q5.3.1
Q7.3
Q5.3.2
Q6.1
Q6.2
Q5.4
Q6.3
March 2017:
Q5.1
Q6.3
168
Q2.4
STATISTICAL REASONING:
Q6.4.1
Q6.4.2
Nov 2019
Q1.1
Q1.4
Q1.2
Q2.5
Q1.3
Q7.1
Q1.4
Not to spend R9 000 per month
because the point (18 000 ; 9 000) lies
very far from the least squares
regression line. OR D
Q2.1
Number people paid R200 or less = 19
Q2.2
Q7.2
May-June 2019
Q1.1
45 children
Q1.2
Q1.5
Q1.3
Q2.1
Q7.3
Q2.3
Modal Class:
Q2.2.1
169
Q2.2.2
Q1.2.2a
Q1.3
Q1.2.2b
Q2.3.1
standard deviation =13,88
Q2.3.2
Q1.4
Q2.1
November 2018
Q1.1.1
Q1.1.2
Q1.5.1
Q1.1.3
Q2.2.1
Q2.2.2
Q1.5.2
Sd from the mean.
Q1.1.2
Q2.3
Q1.1.3
Q1.1.4
March 2018
Q1.1.1
Q1.2.1
Q2.1
Q2.4
Q1.2.2
Q1.1.5
June 2018
Q1.1.1
Q1.3
Q1.1.6
Q1.1.2
Q2.2
Q2.1
Q2.3
Q2.2
Q1.2.1a
Q1.2
Q1.2.1b
Q2.3
Q2.4
170
Q1.2
Modal class
Q2.3
Q2.4
November 2017:
Q1.1
Q2.2
Q1.3
Q2.4.1
Girls
Q2.4.2
Q2.3
Q1.2
Q1.3
The gradient increases
The point (12,3 ; 7,6) lies some
distance above the current data
Q2.1.1
None of the boys
5 girls completed in less than 15
seconds which was the minimum time
taken by the boys.
June 2017:
Q1.1
Q1.2
Q2.1.2
Q2.4
Q1.3
Q2.2
Q2.5
Q1.4
No. of learners = 65 – 54 = 11
Q2.1.1
IQR of Class B
Q2.1.2
Although the boxes contain the same
number of data points, the marks for
Class A are more widely spread
Q2.1.3
Medians are the same
Ranges are the same OR Maximum
and minimum values are the same
75% of both classes obtained 51 and
above
Q2.2.1
Q1.4
Q2.2.2
Q2.1
March 2017:
Q1.1
65 learners
171
Q2.2.3
Yes
because r = 0,9.
SESSION 5
Q4.3
Q3.4
Analytical Geometry
Nov 2019
Q3.1
Equation of PR: y = 5
Q3.2.1
Q3.5
Q3.2.2
Q4.4
Tangents to circle:
Q4.5
May-June 2019
Q3.1.1
Q3.1.2
Q3.2.3
Q3.1.3
Q4.1
Q3.3
Q4.6
Q4.2
172
Q3.5.1
Q3.1.4
Q4.2.2
Q3.2
Q3.1.1
Q3.3.1
Q4.2.3
Q3.3.2
Q3.5.2
Q3.1.2
Q3.6
Q3.2
Q4.3
Q3.3
Q4.1
Q4.1
November 2018
Q3.4
Q4.2
Q4.2.1
173
Q4.3
Q3.4.2
Q4.4
Q4.2.2
Q3.2.1
Q4.5.1
Q4.2.3
Q3.4.3
Q4.5.2
Q4.5.3
Q3.2.2
Q3.4.4
Q4.3
Q3.3
Q4.1
June 2018
Q3.1
Q3.4.1
Q4.2.1
174
Q4.5
Q3.4
Q3.5
Q4.3.1
November 2017:
Q3.1.1
Q4.4
Q3.6
Q4.3.2
Q4.3.3
March 2018
Q3.1
x=3
Q3.2
Q3.1.2
Q4.1
Q3.3
Q4. 4
Q4.2
175
Q4.2
Q3.3
Q4.1.2
Q4.3
Q3.2
Q3.3
The coordinates of the midpt of AB:
Q3.4
Q4.1.3
June 2017:
Q3.1
Q3.4
Q4.1.1
Q4.1.4
Q4.1.5
Q3.2
Q3.5
Q3.6
176
Q4.1
Q3.3
Q3.6.2
Q4.2
Q3.4
Q4.3
Q4.6
Q3.5
Q4.1
line from centre to midpt of chord
Q4.2
March 2017:
Q3.1
Q3.6.1
Q4.4
Q4.5
Q3.2
Q4.3
P(0 ; 11) [y-intercept of chord NP]
 radius is 6 units
R(0 ; –1)
Equations of the tangents to the circle
parallel to the x-axis
177
Q4.4
Q4.5
May-June 2019
Q8.1.1a
Q8.2.2
Q8.1.1b
Q10.2.1
Q8.1.2
Equation of circle through S, T and M:
Q9
Q10.2.2a
Q8.2.1
EUCLIDEAN GEOMETRY
Q10.2.2b
Nov 2019
Q8.1.1
Q10.1
Q8.1.2
Q8.2.2
Q8.1.3
Q10.2.2c
Q8.1.4
Q10.2.2d
Q9.1
Q8.2.1
178
November 2018
Q8.1.1
Q9.2
Q10.2.1b
[tan chord theorem/raaklyn koordst]
Q8.1.2
Q9.1
[∠ in semi circle/∠ in halfsirkel]
Q10.2.2a
Q8.1.3
Q10.1
Q10.2.2b
[sum of ∠s of /som van ∠e MNP] Δ
Q8.1.4
Q9.2.1a
Q9.2.1b
[corres. ∠s;/ooreenk ∠e, PM || OR]
Q8.1.5
Q9.2.2
Q9.2.3
Q10.2.1a
Q10.2.2c
Q8.2.1
Q8.2.2
Q10.1.1
179
Q8.2.1
Q10.1.2
Q8.2.2a
Q10.2.1
Q9.2.2
Q8.2.2b
Q10.2
Q9.1
Q10.1.1
Q10.2.2
Q10.1.2
June 2018
Q8.1.1
Q9.2.1
Q10.1.3
March 2018
Q7.1.1
Q7.1.2
Q7.2.1
Q8.1.2
Q7.2.2
180
Q8.1.1
Q8.1.2
Q8
Q10.2.2
Q8.2
Q10.2.1a
Q9.1
Q10.2.1b
Q9.2
Thus CF is a tangent to the circle
[converse tan chord theorem
Q9.1.1
Q10.2.2
Q10.2.3
Q9.3
Q9.1.2
Q10.2.3
Q9.4
Q9.2
Q11.1
Q10.2.4
Q10.1
November 2017:
Q10.1
Line from centre to midpoint of chord
Q10.2.1
Q11.2.1(a)
Angle in a semi circle
Q11.2.1(b)
181
Q8.1
Q11.2.1(c)
Q8.2
Q11.2.2(a)
Q10.2.2
Q11.2.1(b)
Q8.3
Q11.2.2(b)
Q9.1.1
Q10.2.3
Q11.2.2(a)
Q9.1.2
Q9.2.1
Q11.2.3(a)
Q11.2.2(b)
Q9.2.2
Q11.1
Q11.2.3(b)
March 2017:
Q8.1
Q9.3
Q8.2
Q10.1
Tangent-chord theorem
Q10.2.1
June 2017:
Q8.3
Q11.2.1(a)
Q8.4
182
Q9.1.1
Q11.2
Q9.1.2
Q10.2.1
Q11.3.1
Q10.2.2
Q9.2
Q11.3.2
Q10.2.3
Q9.3
Q10.2.4
Q10.2.5
Q9.4
Q10.1
Q11.1
183