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Questions and Answers

What is the degree of the polynomial equation x^3 + 2x^2 - 7x - 12 = 0?

  • 5
  • 3 (correct)
  • 4
  • 2

What is the derivative of the function f(x) = 3x^2 sin(x)?

  • 6x cos(x) - 3x^2 sin(x)
  • 6x^2 cos(x) - 3x sin(x)
  • 6x sin(x) + 3x^2 cos(x) (correct)
  • 6x cos(x) + 3x^2 sin(x)

What is the magnitude of the vector a = 3i + 4j?

  • 3
  • 4
  • 5 (correct)
  • 7

What is the equation of the circle with center (2, 3) and radius 4?

<p>(x - 2)^2 + (y - 3)^2 = 16 (A)</p> Signup and view all the answers

What is the value of sin(30°)?

<p>1/2 (A)</p> Signup and view all the answers

What is the integral of the function f(x) = x^2 + 3x - 4?

<p>(1/3)x^3 + (3/2)x^2 - 4x + C (B)</p> Signup and view all the answers

What is the vector equation of the line passing through the points (2, 3) and (4, 5)?

<p>r = &lt;2, 3&gt; + t&lt;2, 2&gt; (B)</p> Signup and view all the answers

What is the area of the triangle with vertices (0, 0), (3, 0), and (0, 4)?

<p>6 (D)</p> Signup and view all the answers

What is the equation of the parabola with vertex (1, 2) and axis parallel to the x-axis?

<p>y - 2 = (x - 1)^2 (B)</p> Signup and view all the answers

What is the limit of the function f(x) = (sin(x)) / x as x approaches 0?

<p>1 (C)</p> Signup and view all the answers

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Study Notes

Algebra

  • Equations and Inequalities:
    • Linear equations: ax + by = c, where a, b, and c are constants
    • Quadratic equations: ax^2 + bx + c = 0, where a, b, and c are constants
    • Inequalities: linear and quadratic inequalities, graphical representation
  • Functions:
    • Domain and range of a function
    • Types of functions: polynomial, rational, trigonometric, exponential, and logarithmic
    • Composite functions and inverse functions
  • Graphs:
    • Graphical representation of linear and quadratic equations
    • Graphical representation of functions: domain and range
  • Matrices:
    • Order and types of matrices: square, diagonal, and scalar matrices
    • Operations on matrices: addition, subtraction, and multiplication
    • Inverse of a matrix

Calculus

  • Limits:
    • Concept of limits
    • Properties of limits: sum, difference, product, and chain rule
    • Standard limits: trigonometric, exponential, and logarithmic
  • Derivatives:
    • Geometric interpretation of derivatives
    • Rules of differentiation: power rule, product rule, and quotient rule
    • Derivatives of trigonometric, exponential, and logarithmic functions
  • Applications of Derivatives:
    • Finding the maximum and minimum values of a function
    • Increasing and decreasing functions
    • Tangents and normals
  • Integration:
    • Basic integration formulas: power, exponential, and logarithmic functions
    • Integration by substitution and integration by parts

Vector Algebra

  • Vectors:
    • Types of vectors: free vectors, bound vectors, and unit vectors
    • Operations on vectors: addition, subtraction, and scalar multiplication
    • Magnitude and direction of a vector
  • Vector Operations:
    • Dot product (scalar product) and cross product (vector product)
    • Applications of dot product: projection of a vector, work done, and energy
    • Applications of cross product: area of a parallelogram, torque, and moment
  • Vector Equations:
    • Vector equation of a line and a plane
    • Vector equation of a sphere and a circle

Coordinate Geometry

  • Rectangular Coordinates:
    • Coordinates of a point in a plane
    • Distance formula and section formula
    • Centroid, incenter, and circumcenter of a triangle
  • Circle:
    • Equation of a circle: general form and standard form
    • Properties of a circle: center, radius, and circumference
    • Tangent and normal to a circle
  • Parabola:
    • Equation of a parabola: vertex form and standard form
    • Properties of a parabola: vertex, axis, and focus
    • Applications of parabola: projectile motion and optics

Trigonometry

  • Angles and Triangles:
    • Measurement of angles: degree, radian, and grades
    • Trigonometric ratios: sine, cosine, and tangent
    • Trigonometric identities: Pythagorean identity and sum and difference formulas
  • Trigonometric Functions:
    • Graphs of trigonometric functions: sine, cosine, and tangent
    • Properties of trigonometric functions: periodicity, amplitude, and phase shift
    • Inverse trigonometric functions: arcsine, arccosine, and arctangent
  • Applications of Trigonometry:
    • Heights and distances: problems involving right triangles
    • Waves and periodic motion: simple harmonic motion and circular motion

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