Mathematics Class Section A & B

Section A - MCQ

• Multiple Choice Questions (MCQ) were presented
• Correct answers and corresponding letters were provided for each MCQ
• Answers ranged from letters 1 to 8

Section A - Problem Solving

• Find the cartesian coordinates of (2, π/4) in polar form.

  • The cartesian coordinates (x, y) are derived using the formulas: x = r cos θ and y = r sin θ where r = 2 and θ = π/4
  • Calculations reveal that the cartesian coordinates are (√2, √2).

• Find the joint equation of two lines passing through (2, 3) parallel to the coordinate axes.

  • The equations of the lines parallel to the x-axis have the format y = 3.
  • The equations of the lines parallel to the y-axis have the format x = 2.
  • Combination of the equations produce the joint equation: (x-2)(y-3) = 0.

Section B - Mathematical Problems

• Write negations of the statements:

  • √2 is a rational number
  • All natural numbers are whole numbers

• Find the matrix x such that AX = B where A is the matrix [1 3; -1 2] and B is the matrix [2; 4].

  • Solving for X, the resultant matrix is [( 8/-1 ); ( 10/-1 )].

Section C - Mathematical Problems

• Prove trigonometric identities using relevant identities - Demonstrates the proof process for the given trigonometric equation

Section - Problem Solving

• Calculate the volume of a tetrahedron Given the position vectors of the points forming the tetrahedron (A, B, C, and D), the volume is computed using the formula.

Question 9.18

• Find shortest distance

Question 9.19

• Calculate cosine of an angle given vectors.
• Find the unit vector.

Question 9.20

• Differentiate y = emtanx with respect to x.

Question 9.21

• Vector equation of a plane passing through A(a) and perpendicular to BC

Question 9.22

• Find the values of x where function f(x) is increasing.

Question 9.23

• Evaluating the integral of function x² + 8x + 12.

Question 9.24

• Find x by solving the equations involving matrices.

Question 9.25

• Calculate angles and values using given information in a triangle.

Question 9.26

• Prove the equality of Boolean algebra expression without truth tables.

Question 9.27

• Find the value of x using equations.

Question 9.28

• Given information in equation form is given
• Find 'x' by determining the inverse of 'A' (matrix).

Question 9.29

• Given information in equation form and calculate the cofactor of the given matrices
• Calculate the adjoint and the solution for X

Question 9.30

• Graphing and finding the feasible region of a given system of inequalities.

Question 9.31

• Solve for y using information provided (including differential equation).

Question 9.32

• Finding the vector equation of a line (based on given vectors).

Question 9.33

• Given information in equation form involving two variables
• Solving differential equation and find solution.

Question 9.34

• Given information in equation form
• Solving differential equation and find particular solution with specific values.

Section - Problem Solving

• Solving a problem relating to the rate of change, including specific formulas.

This quiz covers various mathematical concepts, including multiple choice questions, polar to Cartesian coordinate conversions, and problem-solving involving equations of lines and matrix calculations. It also explores the negation of statements related to numbers. Test your mathematical understanding across these topics!