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MATHEMATICS GRADE 12
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Course sections

Section 1
Relations and Functions
1
Equivalence Relation
2
Equivalence Relation – Problems
3
Types of Functions
4
Composite Functions, Exercise.1.3 [3(ii), 4]
5
Invertible Function, How to find the Value of Inverse, Exercise.1.3 [5]
6
Exercise.1.3 [8,11,13]
7
Exercise.1.3 [14], Binary Operations; Exercise.1.4 [1(i,iii),2,9(ii)]
8
Exercise.1.4 [9(i,v),11]; Identity Element
9
Exercise 1.1 (2, 3, 4 & 5)
10
Exercise 1.1 ( 6, 7, 9 i, 9 ii)
11
Exercise 1.1 [10( i, ii, iii, iv, v), 15, 16]
12
Exercise1.4 [6(i,ii,iii,iv,v),7,8,12(i,ii),13]
Section 2
Inverse Trigonometric Functions
1
Introduction, Properties; Exercise.2.1 [2, 3, 4]
2
Exercise.2.2 [1, 2, 3, 4, 5]
3
Exercise.2.2 [6, 7, 8, 9, 10]
4
Exercise.2.2 [11, 12, 13, 14, 15, 16]
5
Exercise.2.2 [17, 18, 19, 20, 21]
6
Miscellaneous Exercise. [3, 4, 5, 8]
7
Exercise 2.1 (1,5,6,7,8,9,10,11,12,13)
Section 3
Matrices - Part 1
1
Introduction, Types of Matrices, Operations on Matrices.
2
Transpose of a Matrix, Results of Transpose of a Matrix, Exercise. 3.1 [ 1, 2]
3
Exercise. 3.1 [ 4, 5]
4
Exercise 3.1 [6, 7, 9]
Section 4
Matrices - Part 2
1
Exercise 3.2 [1(i, ii, iii, iv, v), 2(i, ii, iii, iv), 3(i, ii, iii)
2
Exercise.3.2 [3 (iv, v, vi), 4, 5]
3
Exercise.3.2 [6, 7 (i, ii), 8, 9]
4
Exercise.3.2 [10, 11, 12 & 13]
5
Exercise.3.2 [14(i, ii)]
6
Exercise. 3.2 [15, 16]
7
Exercise. 3.2 [17, 18]
8
Exercise. 3.3 [ 1(i, ii, iii), 2(i, ii), 3(i, ii) , 4]
9
Exercise 3.3 [5(i, ii), 6(i, ii)]; Concept of Symmetric and Skew Symmetric Matrix
10
Exercise 3.3 [8(i, ii), 9, 12, 10(i)]
11
Exercise 3.3 [10 (iv)]; Ex 3.4 [1]
12
Exercise 3.4 [2, 3, 4, 5, 6]
13
Exercise 3.4 [7, 8, 9, 10, 11]
14
Exercise. 3.4 [12, 13, 14, 15]
Section 5
Determinants - Part 1
1
Introduction To Determinants; Exercise 4.1 [1, 2(i, ii), 3, 4]
2
Exercise 4.1 [5 (i,ii,iii,iv) , 6, 7 (i,ii), 8]
3
Properties of Determinants ; Exercise 4.2(1)
4
Exercise 4.2( 2 TO 5)
5
Exercise 4.2[ 6,7,8 (i,ii)]
6
Exercise 4.2[9,10(i,ii),11(i)]
7
Exercise 4.2[11(ii),12,13,14]
8
Area of triangle and Collinearity; Exercise 4.3 [ 1-(i,ii,iii),2,3(i,ii) ] ; Equation of line joining given two points
9
Exercise 4.3 [ 4(i,ii),5];Minors and Cofactors; Exercise 4.4 [1(i,ii),2(i),3,4]
10
Adjoint of Matrix; Exercise 4.5 (1,2,3,4)
11
Exercise 4.5 (5 to 10)
Section 6
Determinants - Part 2
1
Exercise 4.5 (11 to 14)
2
Exercise 4.5 (15,16)
3
Consistency of system of equations ; Exercise 4.6 (1,2,3,4,5,6)
4
Exercise 4.6 (7,8,9,10,11)
5
Exercise 4.6 (12,13,14)
6
Exercise 4.6 (15);Miscellaneous Exercise (16)
Section 7
Continuity and Differentiability
1
Introduction; Properties of Continuity
2
Exercise 5.1 (3-d,4,5,6,7)
3
Exercise 5.1 (8 to 13)
4
Exercise 5.1 (14 to 18, 20)
5
Exercise 5.1 (21 a,b,c)
6
Exercise 5.1 (22,23,24)
7
Differentiability; Exercise 5.3 (1 to 10)
8
Exercise 5.3 (11,13,14,15);Exercise 5.4 (1 to 10)
9
Exercise 5.5 (1 to 4)
10
Exercise 5.5 (5 to 8)
11
Exercise 5.5 (9 to 13)
12
Exercise 5.5 (14,15,16,17a)
13
Exercise 5.6 (1 to 7)
14
Exercise 5.6 (8 to 11); Exercise 5.7 (1 to 5)
15
Exercise 5.7 (6 to 11)
16
Exercise 5.7 (13 to 17)
17
Rolle’s theorem; Exercise 5.8 (1 to 4)
18
Exercise 5.1 (26 to 30)
19
Exercise 5.2 (1 to 9)
Section 8
Application of Derivatives - Part 1
1
Application of Derivatives; Rate of Change of Quatities ;Exercise 6.1 (1 to 4)
2
Exercise 6.1 (5 to 9)
3
Exercise 6.1 (10 to 18)
4
Increasing and Decreasing Functions; Theorem 1; Exercise 6.2 (1 to 5)
5
Exercise 6.2 (7,6)
6
Exercise 6.2 (9,10 ,13 to 16)(17 to 19)
7
Tangents
8
Exercise 6.3 (7 to 11)
9
Exercise 6.3 (13,14)
10
Exercise 6.3 (15 to 17)
Section 9
Application of Derivatives - Part 2
1
Exercise 6.3 (18 to 21)
2
Exercise 6.3 (22 to 26)
3
Exercise 6.4 [1 – (i to v)]
4
Exercise 6.4 [1 – (vi to xii)]
5
Exercise 6.4 [1 – (vi to xii),2,3]
6
Exercise 6.4 (4,5,6,7,8)
7
Exercise 6.4 (9) ;Exercise 6.5 [1-(a,b,c,d)]
8
Exercise 6.5 [2 – (i to v)]
9
Exercise 6.5 [3 – (i to iv)]
10
Exercise 6.5 [3 – (v to viii)]
11
Exercise 6.5 [4- (a,b,c),5-(a,b,c)]
12
Exercise 6.5 (5,6,7)
13
Exercise 6.5 (8,9,11)
14
Exercise 6.5 (12 to 14)
15
Exercise 6.5 (15 to 17)
16
Exercise 6.5 (19 to 20)
17
Exercise 6.5 (21,22)
18
Exercise 6.5 (23)
19
Exercise 6.5 (24,25)
20
Exercise 6.5 (27,28,29)
Section 10
Integrals - Part 1
1
Integrals ; Exercise 7.1 (1 to 7)
2
Exercise 7.1 (8,9,12,13,14,15)
3
Exercise 7.1 (16 to 21)
4
Exercise 7.1 (22) ;Exercise 7.2 (1 to 5)
5
Exercise 7.2 (6 to 10)
6
Exercise 7.2 (11 to 17)
7
Exercise 7.2 (18,21 to 26)
8
Exercise 7.2 (27 to 33)
9
Exercise 7.2 (34 to 39); Exercise 7.3 (1,2)
10
Exercise 7.3 (3,5,6)
11
Exercise 7.3 (7 to 10)
12
Exercise 7.3 (11 to 13)
13
Exercise 7.3 (14 to 18)
14
Exercise 7.3 (20,21)
15
Exercise 7.3 (22 to 24); Exercise 7.4(1)
16
Exercise 7.4 (2,4,5,6)
17
Exercise 7.4 (7 to 11)
18
Exercise 7.4 (12 to 14)
19
Exercise 7.4 (15 to 17)
20
Exercise 7.4 (18)
21
Exercise 7.4 (19,20)
22
Exercise 7.4 (21,22)
23
Exercise 7.4(23 to 25)
24
Exercise 7.5 (1 to 3)
25
Exercise 7.5 (4,5)
Section 11
Integrals - Part 2
1
Exercise 7.5 (9,10)
2
Exercise 7.5 (11,12)
3
Exercise 7.5 (13 to 15)
4
Exercise 7.5 (16 to 18)
5
Exercise 7.5 (20 to 23)
6
Exercise 7.6 (1 to 5)
7
Exercise 7.6 (6 to 9)
8
Exercise 7.6 (10 to 14)
9
Exercise 7.6 (15 to 21)
10
Exercise 7.6 (22 to 24); Exercise 7.7 (1,2)
11
Exercise 7.7 (3,4,5,6)
12
Exercise 7.7 (7 to 11)
13
Definite Integrals ; Exercise 7.8(1,2)
14
Exercise 7.8(4)
15
Exercise 7.8(5.6)
16
Exercise 7.9(1 to 8)
17
Exercise 7.9(15 to 18)
18
Exercise 7.9(19,21,22); Exercise 7.10(1)
19
Exercise 7.10(2,3)
20
Exercise 7.10(4,5,7,8)
21
Exercise 7.11(2,3,4,5)
22
Exercise 7.11(7,8,9,10)
23
Exercise 7.11(15,17,18,19,20,21)
Section 12
Applications of Integrals
1
Introduction
2
Exercise 8.1(1,2,3)
3
Exercise 8.1(8,9,10)
4
Exercise 8.1(11,12,13); Exercise 8.2(1)
5
Exercise 8.2(2,3)
6
Exercise 8.2(4,6,7)
Section 13
Differential Equations
1
Introduction
2
Exercise 9.4(11)
3
Exercise 9.4(12,13,14,16)
4
Exercise 9.2(1,2,3,4,5,6)
5
Exercise 9.2(7,8,9,10,11,12)
6
Exercise 9.3(1,2,5,10,11,12)
7
Exercise 9.4(1,2,3,4,5,6,7,9)
8
Exercise 9.4(17,18,19)
9
Exercise 9.4(22,23);Exercise 9.5(1)
10
Exercise 9.5(2,3,4)
11
Exercise 9.5(5,6,7)
12
Exercise 9.5(8,9,10)
13
Exercise 9.5(12,17)
14
Exercise 9.6(1,2,3,5)
15
Exercise 9.6(6,7,8,10)
16
Exercise 9.6(11,12,13,14,15)
17
Exercise 9.6(16,17,18,19)
Section 14
Vector Algebra
1
Introduction
2
Exercise 10.2 (2,3,4,6,7,9,10)
3
Exercise 10.2 (12 to 18)
4
Exercise 10.3 (1 to 7)
5
Exercise 10.3 (8 to 15)
6
Exercise 10.3 (18); Exercise 10.4 (1,2,3,5)
7
Exercise 10.4 (6,7,9,10,11,12)
Section 15
Three Dimensional Geometry
1
Introduction
2
Exercise 11.1(1,2,3,4)
3
Exercise 11.1(5);Exercises 11.2(1,2,3,4)
4
Exercise 11.2(6,7,12)
5
Exercise 11.2(13,14,15)
6
Exercise 11.2(16,17);Exercise 11.3(1)
7
Exercise 11.3(3,4,7)
8
Exercise 11.3(8,9,10)
9
Exercise 11.3(11,12,13)
10
Exercise 11.3 [14(a,b,c,d)]
Section 16
Linear Programming
1
Introduction
2
Exercise 12.1(4,5)
3
Exercise 12.1(6,7)
4
Exercise 12.2(1,2)
5
Exercise 12.2(3,4)
6
Exercise 12.2(5)
7
Exercise 12.2(6,7)
8
Exercise 12.2(8)
9
Exercise 12.2(9,11)
Section 17
Probability
1
Introduction
2
Exercise 13.1(1 to 5)
3
Exercise 13.1[6(i,ii)]
4
Exercise 13.1[6(iii),8,9]
5
Exercise 13.1(10,11)
6
Exercise 13.1(12,14,15); Exercise 13.2(1,2)
7
Exercise 13.2(3,5,8,11)
8
Exercise 13.2(10,16)
9
Exercise 13.2(6,7,9,12,15)
10
Exercise 13.3(1,3,4)
11
Exercise 13.3(5,6,7)
12
Exercise 13.3(8,9,10,11)
13
Exercise 13.3(12,13); Exercise 13.4(1,2,3)
14
Exercise 13.4(4,6)
15
Exercise 13.4(9,11,14)
16
Exercise 13.5(1,9,12,13)

Relations and Functions

Equivalence Relation

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Relations and Functions Equivalence Relation – Problems