AP EAMCET / TS EAMCET Mathematics - Calculus, Geometry and Probability Syllabus

Mathematics - Calculus, Geometry and Probability 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, Geometry and Probability in AP EAMCET / TS EAMCET, not a summary of it.

1. 1

   Coordinate Geometry (2D)

   4 topics

   • Straight Lines
     • Forms of a line and distance formulae
     • Angle between lines and concurrency
   • Pair of Straight Lines
     • Homogeneous second degree equations
     • Angle and bisectors
   • Circle and System of Circles
     • Equation, tangent and normal
     • Radical axis and orthogonality
   • Conic Sections
     • Parabola: focus and directrix
     • Ellipse: eccentricity and properties
     • Hyperbola: asymptotes and properties
2. 2

   Three Dimensional Geometry and Vectors

   4 topics

   • 3D Coordinates
     • Distance, section formula and direction cosines
     • Equation of a plane
   • Addition of Vectors
     • Position vectors and collinearity
   • Scalar and Vector Products
     • Dot product and projections
     • Cross product, area and moment
   • Product of Three Vectors
     • Scalar triple product and volume
     • Vector triple product
3. 3

   Limits, Continuity and Differentiation

   3 topics

   • Limits and Continuity
     • Standard limits
     • Continuity at a point and on an interval
   • Differentiation
     • Derivatives of standard functions and chain rule
     • Implicit, parametric and logarithmic differentiation
   • Applications of Derivatives
     • Tangents, normals and rate of change
     • Maxima, minima and monotonicity
     • Errors, approximations and mean value theorems
4. 4

   Integration and Differential Equations

   3 topics

   • Indefinite Integration
     • Substitution and by parts
     • Partial fractions
   • Definite Integration
     • Properties of definite integrals
     • Areas under curves and reduction formulae
   • Differential Equations
     • Order, degree and formation
     • Variable separable and homogeneous
     • Linear differential equations of first order
5. 5

   Probability and Statistics

   3 topics

   • Measures of Dispersion
     • Variance and standard deviation
     • Coefficient of variation
   • Probability
     • Addition and multiplication theorems
     • Conditional probability and Bayes' theorem
   • Random Variables and Distributions
     • Probability distributions
     • Binomial and Poisson distributions

Mathematics - Calculus, Geometry and Probability flashcards for AP EAMCET / TS EAMCET

25 of 55 cards from the Mathematics - Calculus, Geometry and Probability deck — real questions with worked answers.

1. What is the slope of a straight line passing through points (x1, y1) and (x2, y2)?

   m = (y2 - y1)/(x2 - x1)

2. State the formula for the perpendicular distance from point (x1, y1) to the line ax + by + c = 0.

   d = |ax1 + by1 + c| / sqrt(a^2 + b^2)

3. What is the condition for two lines with slopes m1 and m2 to be (a) parallel and (b) perpendicular?

   Parallel: m1 = m2. Perpendicular: m1 * m2 = -1.

4. Give the formula for the angle theta between two lines with slopes m1 and m2.

   tan theta = |(m1 - m2)/(1 + m1*m2)|

5. When does the second-degree equation ax^2 + 2hxy + by^2 = 0 represent a pair of straight lines through the origin?

   It always represents a pair of lines through the origin; they are real and distinct if h^2 > ab, coincident if h^2 = ab, imaginary if h^2 < ab.

6. For the pair of lines ax^2 + 2hxy + by^2 = 0, what is the angle between them?

   tan theta = |2*sqrt(h^2 - ab) / (a + b)|. They are perpendicular when a + b = 0.

7. What is the condition that ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pair of straight lines?

   abc + 2fgh - af^2 - bg^2 - ch^2 = 0 (the determinant Delta = 0).

8. Write the standard equation of a circle with centre (h, k) and radius r.

   (x - h)^2 + (y - k)^2 = r^2

9. For the general circle x^2 + y^2 + 2gx + 2fy + c = 0, give its centre and radius.

   Centre = (-g, -f); radius = sqrt(g^2 + f^2 - c).

10. What is the equation of the tangent to the circle x^2 + y^2 = a^2 at the point (x1, y1)?

    x*x1 + y*y1 = a^2

11. Define the radical axis of two circles and state its key property.

    The radical axis is the locus of points having equal lengths of tangents to both circles. It is obtained by S1 - S2 = 0 and is perpendicular to the line joining the centres.

12. What is the condition for two circles to intersect orthogonally?

    2*g1*g2 + 2*f1*f2 = c1 + c2

13. Give the standard equation of a parabola with vertex at origin opening rightward, and its focus and directrix.

    y^2 = 4ax; focus = (a, 0); directrix: x = -a; latus rectum length = 4a.

14. For the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b), state its eccentricity and the relation among a, b, e.

    b^2 = a^2(1 - e^2), so e = sqrt(1 - b^2/a^2), with 0 < e < 1. Foci at (+/-ae, 0).

15. For the hyperbola x^2/a^2 - y^2/b^2 = 1, state its eccentricity relation and equations of asymptotes.

    b^2 = a^2(e^2 - 1), e > 1. Asymptotes: y = +/-(b/a)x.

16. Define eccentricity for each conic: circle, parabola, ellipse, hyperbola.

    Circle: e = 0; Parabola: e = 1; Ellipse: 0 < e < 1; Hyperbola: e > 1.

17. What is the distance formula between two points (x1, y1, z1) and (x2, y2, z2) in 3D?

    d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

18. State the section formula (internal division) for a point dividing the segment joining (x1,y1,z1) and (x2,y2,z2) in ratio m:n.

    ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n), (m*z2 + n*z1)/(m+n))

19. What are direction cosines of a line and what relation do they satisfy?

    Direction cosines l, m, n are cosines of angles the line makes with x, y, z axes; they satisfy l^2 + m^2 + n^2 = 1.

20. State the triangle law and parallelogram law of vector addition.

    Triangle law: if two vectors are represented by two sides of a triangle taken in order, their sum is the third side taken in reverse order. Parallelogram law: the sum of two vectors from a point is the diagonal of the parallelogram with them as adjacent sides.

21. How do you find a unit vector in the direction of vector a?

    a_hat = a / |a|, where |a| is the magnitude of a.

22. Give the position vector of the point dividing the line joining vectors a and b in ratio m:n internally.

    r = (m*b + n*a)/(m + n)

23. Define the scalar (dot) product of two vectors and give its formula.

    a . b = |a||b| cos theta, where theta is the angle between them. In components: a.b = a1*b1 + a2*b2 + a3*b3.

24. What is the dot-product condition for two non-zero vectors to be perpendicular?

    a . b = 0

25. Define the vector (cross) product and give its magnitude.

    a x b is a vector perpendicular to both a and b with magnitude |a||b| sin theta, directed by the right-hand rule. |a x b| equals the area of the parallelogram with sides a and b.

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