12Th Class Smart Syllabus Maths 2026-2027

The Punjab Education, Curriculum, Training and Assessment Authority (PECTAA) has released the 12th Class Smart Syllabus Maths / Accelerated Learning Programme (ALP) for Mathematics-12. It lists the exercises, examples, and questions excluded for the BISE Annual Examination-2027. Find your unit below and skip what is deleted—study smart, not hard!

What Is the Smart Syllabus (ALP) for Math-12?

To facilitate students, the content of Mathematics-12 has been rationalized and reduced from the compulsory textbook. The aim is to help students focus on the key Student Learning Outcomes (SLOs) that are essential for conceptual understanding and exam preparation, rather than covering the entire textbook. Teachers and students are advised to follow this Smart Syllabus (ALP) for effective teaching, learning, and exam preparation.

Math-12 Deleted Topics & Exercise Questions – Unit Wise

Unit 1: Graphical Representation of Functions

Exercise # 1.2: Q # 4 & 6; Pages # 14 to 15
Example # 13 (1.9 Transformation of Graphs of Functions); Page # 22
Exercise # 1.3: Q # 5, 7, 8 & 10; Pages # 23 to 24
Example # 20 (1.10 Exponential and Logarithmic Equations and Inequalities); Page # 27
Exercise # 1.4: Q # 2 (iv & vi); Page # 28
1.11 Applications of Exponential and Logarithmic Functions, Examples 21 to 27; Pages # 29 to 32
Exercise # 1.5 (Complete); Page # 33

Unit 2: Further Differentiation

Example # 6 (2.4 Derivatives of Inverse Trigonometric Functions); Page # 40
Exercise # 2.1: Q # 9, 10, 11, 12 & Q # 16 (ii & iv); Page # 41
Exercise # 2.4: Q # 1 (iv), Q # 2 (iv & v); Pages # 55 to 56
2.11 Local Linear Approximation (Linearization), Examples 22 & 23; Pages # 56 to 59
Exercise # 2.5 (Complete); Page # 59
Examples # 31 & 32 (2.14 Applying Extrema to Real-World Problems); Pages # 65 to 66
Exercise # 2.7: Q # 1, 5 & 7; Page # 70

Unit 3: Integration

Examples # 11 & 12 (3.1 Antiderivatives and the Indefinite Integral); Pages # 75 to 76
Exercise # 3.1: Q # 3 (x & xii), Q # 4 (v & ix); Pages # 76 to 77
Examples # 14, 18 & 21 (3.2 Method of Substitution); Pages # 78 to 79
Examples # 22, 24, 25 & 28 (3.3 Trigonometric Substitution); Pages # 81 to 83
Exercise # 3.2: Q # 1 (v & viii), Q # 2 (vi, ix, xi & xiv); Page # 84
Examples # 35, 38 & 39 (3.4 Integration by Parts); Pages # 86 to 89
Exercise # 3.3: Q # 17, 18, 20 & 23; Page # 90
Exercise # 3.4: Q # 12, 13 & 15; Page # 94
Examples # 49 to 56 (3.6 The Definite Integral and its Properties); Pages # 98 to 101
Exercise # 3.5: Q # 1 (vii & ix), Q # 2, 4, 8, 9, 11, 13, 15 & 16; Pages # 101 to 103
3.7 Application of Definite Integrals (Area, Consumer and Producer Surplus, Solids of Revolution), Examples 57 to 65; Pages # 103 to 114
Exercise # 3.6 (Complete); Pages # 114 to 115
3.8 Applying Concepts of Integration to Real-Life Problems, Examples 66 to 72; Pages # 115 to 121
Exercise # 3.7 (Complete); Pages # 121 to 123

Unit 4: Differential Equations

Exercise # 4.1: Q # 5 & 6 (4.2.4 Flow of Electricity in Series Circuits); Pages # 128 to 129
4.5 Applications of First-Order Differential Equations, Examples 8 to 12; Pages # 138 to 142
Exercise # 4.3 (Complete); Page # 143

Unit 5: Analytical Geometry

Exercise # 5.1: Q # 6 (medians, altitudes and right bisectors of a triangle together) & Q # 7 (c & d); Page # 158
Exercise # 5.3: Q # 4, 6, 7, 8, 10, 11 & 12; Page # 166

Unit 6: Conics

Examples # 8 & 9 (6.1 Circle); Pages # 175 to 176
Exercise # 6.1: Q # 4, 8, 9 & 11; Page # 177
Example # 14 (6.2 Tangent and Normal to a Circle); Page # 183
Exercise # 6.2: Q # 4 & 6; Page # 187
Exercise # 6.3: Q # 4, 6, 7, 8 & 10; Pages # 192 to 193
Exercise # 6.4: Q # 3, 5, 6, 7, 10, 12 & 13; Pages # 202 to 203
Examples # 25, 26 & 27 (6.5 Hyperbola); Pages # 208 to 210
Exercise # 6.5: Q # 3, 4, 6, 7, 8 & Q # 13 to 20; Pages # 215 to 216
6.6 Applying Concepts of Conics to Real-Life Problems, Examples 31 to 37; Pages # 216 to 221
Exercise # 6.6 (Complete); Pages # 221 to 222

Unit 7: Kinematics

Example # 4 (7.1.4 Displacement-Time Graph); Page # 227
Example # 6 (7.1.5 Velocity-Time Graph); Page # 230
Exercise # 7: Q # 2 (c & d) & Q # 5; Page # 235

Unit 8: Numerical Solutions of Nonlinear Equations

Exercise # 8.1 (Complete); Page # 241
Exercise # 8.3: Q # 7 & 8; Page # 253
Exercise # 8.4 (Complete); Page # 258

Unit 9: Inverse Trigonometric Functions and Their Graphs

Exercise # 9.1: Q # 2 (vii & viii) & Q # 4; Page # 274
Exercise # 9.2: Q # 6, 7, 17, 18, 19, 20 & 21; Pages # 277 to 278

Unit 10: Solution of Trigonometric Equations

Exercise # 10.1: Q # 19 to 24; Page # 283
Exercise # 10.2: Q # 1 to 4; Page # 288

Unit 11: Vector Valued Functions and Their Derivatives

Exercise # 11.3 (Complete); Pages # 297 to 298

How to Use the Smart Syllabus for Better Marks

Mark your textbook: Cross out every deleted example and question using the page numbers above.
Prioritize what remains: Spend your time on the undeleted exercises—that is where your exam questions will come from.
Practice past papers: Solve BISE past papers, skipping any question from deleted portions.
Confirm with your teacher: Always cross-check with the official notification from your board or school.

Frequently Asked Questions (FAQs)

What is the Smart Syllabus (ALP) for Math-12?

It is a reduced version of the Mathematics-12 textbook released by PECTAA that lists the exercises, examples, and questions excluded from the BISE Annual Examination-2027.