1st Year Mathematics Notes

Practice110 MCQs & 90 exam questions with answers & mark schemes →

Every chapter of the mathematics syllabus for 1st Year under the Punjab Board, in the order the book takes them. 15 lessons are published so far — each with notes, worked examples, a graph you can move, flashcards and a quiz — and more are being written.

Also called 11th Class, FSc Part 1, ICS Part 1, HSSC Part 1.

01

Complex Numbers

▸Complex NumbersWhat happens when you stop refusing to take the square root of −1 · 20 min · 8 questions→▸Complex Numbers in Polar FormModulus and argument, and why multiplying becomes rotating · 20 min · 8 questions→

02

Functions and Graphs

▸Functions and GraphsDomain, range, and the shapes you should recognise before plotting a point · 20 min · 8 questions→

03

Theory of Quadratic Functions

▸Quadratic EquationsStandard form, the three methods of solution, and the discriminant · 20 min · 6 questions→

04

Matrices and Determinants

▸Algebra & MatricesQuadratics, and the grid that moves space · 20 min · 6 questions→

05

Partial Fractions

▸Partial FractionsTaking a single fraction apart again, because the pieces are easier to work with · 18 min · 8 questions→

06

Sequences and Series

▸Sequences and SeriesPatterns with a rule, and what happens when you add them all up · 22 min · 8 questions→

07

Permutations and Combinations

▸Permutations and CombinationsCounting arrangements and selections without listing them · 20 min · 8 questions→

08

Mathematical Induction and Binomial Theorem

▸Mathematical Induction and the Binomial TheoremProving infinitely many statements at once, and expanding a bracket without multiplying it out · 22 min · 8 questions→

09

Division of Polynomials

▸Division of PolynomialsLong division, and the two theorems that make most of it unnecessary · 18 min · 8 questions→

10

Trigonometric Identities

▸TrigonometryOne circle explains every wave you will ever meet · 18 min · 6 questions→

11

Trigonometric Functions and their Graphs

▸Trigonometric Functions and their GraphsAmplitude, period and phase — three letters, three separate jobs · 20 min · 8 questions→

12

Limit and Continuity

▸Functions & LimitsWhat a function approaches, whether or not it arrives · 18 min · 6 questions→

13

Differentiation

▸CalculusRates of change, and areas under curves · 22 min · 6 questions→

14

Vectors in Space

▸Vectors in SpaceThree dimensions, and the two ways of multiplying vectors · 22 min · 8 questions→

Frequently asked questions

What does 1st Year Mathematics cover?

All 14 chapters — Complex Numbers, Functions and Graphs, Theory of Quadratic Functions, and more. The finished lessons carry notes, worked examples, an interactive diagram and a quiz; the remaining topics are mapped and being written.

Do these notes follow the Punjab Board syllabus?

Yes. They follow the 1st Year Mathematics syllabus (1st Year, 11th Class, FSc Part 1) under the Punjab Board, chapter by chapter, in the order the textbook takes them.

Are there practice questions or past-paper-style questions?

Yes — 110 multiple-choice questions and 90 exam-style questions with mark schemes, all with answers, on the 1st Year Mathematics practice page.

Are the 1st Year Mathematics notes free?

Yes — completely free, with no sign-up or login. Every topic has notes, worked examples, an interactive diagram you can change, flashcards and a quiz that explains each answer.