1st Year Mathematics Notes

Every chapter of the mathematics syllabus for 1st Year under the Punjab Board, in the order the book takes them. 15 chapters have a finished lesson — notes, worked examples, a graph you can move, flashcards and a quiz. The rest are mapped and 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→