Math 111 Past Paper 2021 PDF

# Math 111 - **Year:** 2021 - **Work Completion:** 90/150 ≈ 60% ## Course Work Breakdown - **Quizzes:** ~36% - **Midterm:** 40% - **Final:** 24% ### Course Content - **Part 1:** Mathematical Concepts and Functions - **Part 2:** Partial Fractions - **Part 3:** Matrices and Vector Geometry - **Pa...

# Math 111 - **Year:** 2021 - **Work Completion:** 90/150 ≈ 60% ## Course Work Breakdown - **Quizzes:** ~36% - **Midterm:** 40% - **Final:** 24% ### Course Content - **Part 1:** Mathematical Concepts and Functions - **Part 2:** Partial Fractions - **Part 3:** Matrices and Vector Geometry - **Part 4:** Some Equations and Draw the Result - **Part 5:** Principles of Analytical Engineering and Comic Sector ### Mathematical Concepts and Functions - **y = f(x)** #### Types of Functions 1. **Linear Functions:** - **y = x** - **y = mx** - **y = mx + b** - **y = 3x +5** - **y = 3x - 5** 2. **Power Functions** - **y = x^n, n ∈ I** - **y = x^1** - **y = -x** - **y = x^2** - **y = x^3** - **y = x^4** - **y = x^n** 3. **Polynomial Functions:** - **y = a_0 + a_1x + a_2x^2 + a_3x^3 + ... + a_nx^n** - **Ex:** - **y = 1 + 2x - 3x^2 + x^4** - **y = 5 + 3x^2** 4. **Rational Functions** - **y = p(x)/q(x)** - **y = 3x^2+2x-1/x+1** - **y = x^3-3x/2x** - **y = 5-x/x** 5. **Algebraic Functions:** - **y = 3 + 2x + √x^3 + 5x + 5x+1/x^2** #### Example 1: Find *f+g*, *f-g*, *fog*, *gof*? **Given:** - **f(x) = 3x + 1** - **g(x) = 5x - 1** **Solution** - **f+g = 3x + 1 + (5x -1)** - **f-g = 3x + 1 - (5x-1)** - **f*g = (3x+1)(5x-1) = ** [(5x+1)(5x-1)/2x^3] **= 15x^2 + 5x - 1/2x^3** - **g*f = (5x-1)(3x+1) = (5x-1)(3x+1)/2x^3 = (15x^2 + 2x -1)/2x^3** - **log = f(g(x)) = f(5x-1) = 3(5x-1) + 1 = 15x-3x+1** - **gof = g(f(x)) = g(3x+1) = 5(3x+1)-1 = 15x +4** #### Example 2: - **If f(x) = x+1, g(x)=1/x-1, then find f*o*g** #### Even and Odd Functions | Even Function | Odd Function | |---|---| | **y=x^2** | **y = x^3** | | **y = f(-x) = f(x)** | **y = f(-x) = -f(x)** |