WBJEE Mathematics - Calculus and Trigonometry Syllabus

Mathematics - Calculus and Trigonometry syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics - Calculus and Trigonometry in WBJEE, not a summary of it.

1. 1

   Trigonometry

   4 topics

   • Trigonometric Functions and Identities
     • Trigonometric ratios and signs in quadrants
     • Compound, multiple and submultiple angles
     • Transformation of products and sums
   • Trigonometric Equations
     • General solutions of trigonometric equations
     • Principal solutions and periodicity
   • Inverse Trigonometric Functions
     • Domains, ranges and principal values
     • Properties and identities of inverse functions
   • Properties of Triangles
     • Sine rule, cosine rule and projection formulae
     • Area of a triangle and half-angle formulae
2. 2

   Limits, Continuity and Differentiation

   3 topics

   • Functions, Limits and Continuity
     • Types of functions, domain and range
     • Limits, standard limits and L'Hospital's rule
     • Continuity and differentiability of functions
   • Differentiation
     • Derivatives of standard functions
     • Product, quotient and chain rules
     • Implicit, parametric and logarithmic differentiation
     • Successive differentiation and nth derivatives
   • Applications of Derivatives
     • Tangents, normals and rate of change
     • Maxima, minima and monotonicity
     • Rolle's and Lagrange's mean value theorems
3. 3

   Integral Calculus and Differential Equations

   3 topics

   • Indefinite Integration
     • Integration by substitution and parts
     • Integration by partial fractions
     • Standard integral forms
   • Definite Integration
     • Properties of definite integrals
     • Definite integral as limit of a sum
     • Area under curves and between curves
   • Differential Equations
     • Order, degree and formation
     • Variable separable and homogeneous equations
     • Linear differential equations of first order
4. 4

   Coordinate Geometry and Vectors

   4 topics

   • Straight Lines and Pair of Lines
     • Distance, section formula and locus
     • Various forms of equation of a line
     • Angle between lines and distance of point from line
     • Pair of straight lines and homogeneous equations
   • Circles
     • General and standard equation of a circle
     • Tangents, normals and length of tangent
     • Intersection of circles and radical axis
   • Conic Sections
     • Parabola - equation, focus, directrix, latus rectum
     • Ellipse - eccentricity, foci and properties
     • Hyperbola - asymptotes and conjugate axis
   • Vectors and 3D Geometry
     • Dot and cross product of vectors
     • Scalar triple product and coplanarity
     • Direction cosines and equation of a line in space
     • Equation of a plane and distance formulae

Mathematics - Calculus and Trigonometry flashcards for WBJEE

18 of 51 cards from the Mathematics - Calculus and Trigonometry deck — real questions with worked answers.

1. What are the signs of the six trigonometric functions in each of the four quadrants (the "ASTC" / All-Silver-Tea-Cups rule)?

   Quadrant I: all positive. Quadrant II: only $\sin$ and $\csc$ positive. Quadrant III: only $\tan$ and $\cot$ positive. Quadrant IV: only $\cos$ and $\sec$ positive.

2. State the three fundamental Pythagorean trigonometric identities.

   $\sin^{2}\theta + \cos^{2}\theta = 1$, $\quad 1 + \tan^{2}\theta = \sec^{2}\theta$, $\quad 1 + \cot^{2}\theta = \csc^{2}\theta$.

3. What are the periods of $\sin x$, $\cos x$, $\tan x$, and $\sec x$?

   $\sin x$ and $\cos x$ have period $2\pi$; $\tan x$ and $\cot x$ have period $\pi$; $\sec x$ and $\csc x$ have period $2\pi$.

4. State the sine and cosine compound-angle (addition) formulas for $A+B$ and $A-B$.

   $\sin(A\pm B) = \sin A\cos B \pm \cos A\sin B$; $\quad \cos(A\pm B) = \cos A\cos B \mp \sin A\sin B$.

5. State the tangent compound-angle formula for $\tan(A\pm B)$.

   $\tan(A\pm B) = \dfrac{\tan A \pm \tan B}{1 \mp \tan A\tan B}$.

6. Give the three standard forms of the double-angle formula for $\cos 2A$.

   $\cos 2A = \cos^{2}A - \sin^{2}A = 2\cos^{2}A - 1 = 1 - 2\sin^{2}A$.

7. Express $\sin 2A$ and $\tan 2A$ in terms of $A$.

   $\sin 2A = 2\sin A\cos A = \dfrac{2\tan A}{1+\tan^{2}A}$; $\quad \tan 2A = \dfrac{2\tan A}{1-\tan^{2}A}$.

8. State the triple-angle formulas for $\sin 3A$ and $\cos 3A$.

   $\sin 3A = 3\sin A - 4\sin^{3}A$; $\quad \cos 3A = 4\cos^{3}A - 3\cos A$.

9. State the triple-angle formula for $\tan 3A$.

   $\tan 3A = \dfrac{3\tan A - \tan^{3}A}{1 - 3\tan^{2}A}$.

10. Write the Weierstrass (half-angle / submultiple) substitutions for $\sin A$, $\cos A$, $\tan A$ in terms of $t = \tan\frac{A}{2}$.

    $\sin A = \dfrac{2t}{1+t^{2}}$, $\quad \cos A = \dfrac{1-t^{2}}{1+t^{2}}$, $\quad \tan A = \dfrac{2t}{1-t^{2}}$, where $t=\tan\frac{A}{2}$.

11. State the product-to-sum formula for $2\sin A\cos B$ and $2\cos A\sin B$.

    $2\sin A\cos B = \sin(A+B) + \sin(A-B)$; $\quad 2\cos A\sin B = \sin(A+B) - \sin(A-B)$.

12. State the product-to-sum formulas for $2\cos A\cos B$ and $2\sin A\sin B$.

    $2\cos A\cos B = \cos(A+B) + \cos(A-B)$; $\quad 2\sin A\sin B = \cos(A-B) - \cos(A+B)$.

13. State the sum-to-product formulas for $\sin C + \sin D$ and $\sin C - \sin D$.

    $\sin C + \sin D = 2\sin\dfrac{C+D}{2}\cos\dfrac{C-D}{2}$; $\quad \sin C - \sin D = 2\cos\dfrac{C+D}{2}\sin\dfrac{C-D}{2}$.

14. State the sum-to-product formulas for $\cos C + \cos D$ and $\cos C - \cos D$.

    $\cos C + \cos D = 2\cos\dfrac{C+D}{2}\cos\dfrac{C-D}{2}$; $\quad \cos C - \cos D = -2\sin\dfrac{C+D}{2}\sin\dfrac{C-D}{2}$.

15. What is the general solution of $\sin\theta = \sin\alpha$?

    $\theta = n\pi + (-1)^{n}\alpha$, where $n \in \mathbb{Z}$.

16. What is the general solution of $\cos\theta = \cos\alpha$?

    $\theta = 2n\pi \pm \alpha$, where $n \in \mathbb{Z}$.

17. What is the general solution of $\tan\theta = \tan\alpha$?

    $\theta = n\pi + \alpha$, where $n \in \mathbb{Z}$.

18. What is the general solution of $\sin\theta = 0$, $\cos\theta = 0$, and $\tan\theta = 0$?

    $\sin\theta = 0 \Rightarrow \theta = n\pi$; $\quad \cos\theta = 0 \Rightarrow \theta = (2n+1)\frac{\pi}{2}$; $\quad \tan\theta = 0 \Rightarrow \theta = n\pi$, for $n \in \mathbb{Z}$.

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