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  • IB Mathematics
    • SL Applications and Interpretation
    • HL Applications and Interpretation
    • SL Analysis and Approaches
    • HL Analysis and Approaches
  • Cambridge Mathematics
    • Lower Secondary
    • IGCSE Core
    • IGCSE Extended
    • IGCSE Additional
    • IGCSE International Core
    • IGCSE International Extended
    • IGCSE (US) Core
    • IGCSE (US) Extended
    • IGCSE (US) Additional
    • O Level
    • O Level Additional
    • International AS and A Level
    • International AS and A Level Further
  • HSC Mathematics
    • Year 11 Standard
    • Year 11 Advanced
    • Year 11 Extension 1
    • Year 12 Standard 1
    • Year 12 Standard 2
    • Year 12 Advanced
    • Year 12 Extension 1
    • Year 12 Extension 2
  • VCE Mathematics
    • Foundation Units 1 and 2
    • General Units 1 and 2
    • Maths Methods Units 1 and 2
    • Specialist Units 1 and 2
    • Further Units 3 and 4
    • Maths Methods Units 3 and 4
    • Specialist Units 3 and 4
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Lesson

RATES OF CHANGE

Home > My Courses > IB Mathematics Applications and Interpretation SL – Calculus > RATES OF CHANGE
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IB Mathematics Applications and Interpretation SL – Calculus

RATES OF CHANGE
Average Rates of Change
  • Video – Average Rates of Change (2:56)
  • Topic – Words in Average Rate of Change
  • Topic – Basic Average Rate of Change
  • Topic – Average Rate of Change through Tables
  • Topic – Average Rate of Change through Functions
Gradient using Rates of Change
  • Video – Instantaneous Rates of Change (6:49)
  • Topic – Gradient using Rate of Change in Quadratic Expressions
  • Topic – Gradient using Rate of Change in Cubic Expressions
  • Topic – Gradient of Tangent using Rate of Change
Limits at Constants
  • Video – Understanding Limits at Constant Values (6:58)
  • Topic – Limits at Constant Values
  • Topic – Limits at Constant Values involving Common Factors
  • Topic – Limits at Constant Values involving Differences of Squares
  • Topic – Limits at Constant Values involving Factorise
  • Topic – Limits at Constant Values involving Quadratic Factorise
Limits at Infinity
  • Video – Understanding Limits at Infinity (6:20)
  • Video – Calculating Limits at Infinity (7:51)
  • Topic – Limits at Infinity
  • Topic – Limits at Infinity involving Linear Fractions
  • Topic – Limits at Infinity involving Quadratic Fractions
  • Topic – Limits at Infinity involving Fractions Higher Degree Numerators
DIFFERENTIATION
Basic Differentiation Rules
  • Video – Differentiation of Constant Terms (2:14)
  • Video – Differentiation of Linear Functions (3:16)
  • Video – Methods of Differentiation (5:01)
  • Video – Differentiation of Negative Exponents (5:12)
  • Video – Differentiation of Non-Monic Negative Exponents (8:13)
  • Video – Simplifying Expressions before Differentiation (6:37)
  • Video – Differentiation of Polynomial Functions (3:48)
  • Video – Differentiation of Functions in Terms of Specific Letters (2:43)
  • Video – Differentiation of Functions in Terms of Specific Letters involving Additions (4:37)
  • Video – Differentiation of Functions in Terms of Specific Letters involving Multiplications (6:20)
  • Video – Equations involving Differentiation (1:51)
Differentiation of Surds
  • Video – Principle of Differentiation of Surds (5:02)
  • Video – Principle of Differentiation of Surds: Square Roots (4:58)
  • Video – Principle of Differentiation of Surds: Quad Roots (2:24)
  • Video – Principle of Differentiation of Surds involving Fractions (6:35)
Tangents
  • Video – Gradient of Tangents (4:46)
  • Video – Application of Gradient of Tangents (7:49)
  • Video – Equation of Tangents (6:15)
  • Video – Angle and Gradient of Tangents (3:39)
  • Video – Gradient of Parallel and perpendicular Tangents (8:38)
  • Video – Horizontal Tangents (2:39)
  • Video – Tangents and Corresponding y-intercepts (2:07)
  • Video – Tangents and Corresponding x-intercepts (4:33)
Normals
  • Video – Equation of Normals (7:13)
  • Video – Equation of Normals at Hyperbola (5:42)
  • Video – Applications of Tangents and Normals of Cubic Polynomials (4:29)
  • Video – Equation of Normals involving Surd Functions (3:33)
  • Video – Normal of Parabola Cuts Parabola Again (4:52)
  • Video – Equation of Tangents and Normals at Hyperbola (7:18)
Increasing and Decreasing Functions
  • Video – Theory of Increasing Functions (4:02)
  • Video – Increasing Functions (6:39)
  • Video – Always Increasing Functions (2:57)
  • Video – Decreasing Functions (8:06)
  • Video – Always Decreasing Functions (2:22)
  • Video – Determining Increasing Decreasing or Stationary at Certain Points (3:07)
Basic Integration Rules
  • Video – Principles of Antidifferentiation (7:29)
  • Video – Antidifferentiation and Differentiation (6:10)
  • Video – Antidifferentiation of Polynomial Functions (3:51)
  • Video – Basic Integration Rules (7:18)
  • Video – Integration of Multi Term Expressions (2:25)
Basic Integration Rules involving Algebra
  • Video – Integration of Fractions (7:09)
  • Video – Integration for Surds (7:34)
  • Video – Integration of Rational Exponents (9:38)
  • Video – Simplifying before Integration (9:37)
  • Video – Expanding before Integration (7:27)
  • Video – Binomial Expansion before Integration (6:34)
APPLICATION OF DIFFERENTIATION
Turning Points
  • Video – Coordinates of Turning Points (7:30)
  • Video – Identifying Nature of Turning Points from Derivative Curves (5:25)
  • Video – Identifying Nature of Turning Points using Tables (5:08)
  • Video – Identifying Stationary Points (8:17)
  • Video – Understanding Nature of Stationary Points (5:31)
  • Video – No Stationary Points (1:50)
  • Video – Condition of Being Stationary Points (2:51)
  • Video – Maximum and Minimum Turning Points (6:49)
  • Video – Stationary Points by their Shapes (7:34)
  • Video – Maximum and Minimum Turning Points of Quartic Functions (7:54)
Optimisation
  • Video – Maxima and Minima of Quadratic Functions (4:16)
  • Video – Maxima and Minima of Cubic Functions 1 (8:47)
  • Video – Maxima and Minima of Cubic Functions 2 (4:02)
  • Video – Maxima and Minima in 2D Applications (4:23)
  • Video – Maxima and Minima in 3D Applications 1 (6:09)
  • Video – Maxima and Minima in 3D Applications 2 (3:53)
  • Video – Absolute Maximum and Minimum (8:59)
  • Video – Minimum Speed of the Motion (1:43)
  • Video – Maximum Velocity Given Displacement (1:35)
Application of Derivatives of Trigonometric Functions
  • Video – Speed and Velocity using Trigonometric Functions (0:59)
  • Video – Motion At Rest in Trigonometric Functions (2:57)
Maxima and Minima with Trigonometry
  • Video – Maximum Speed involving Trigonometric Functions (3:34)
  • Video – Maxima and Minima for Trigonometric Functions (5:30)
  • Video – Maximum and Minimum Velocity using Trigonometric Displacement (1:10)
INTEGRATION
Integration of Power Functions
  • Video – Principle of Integration of Power Function (2:49)
  • Video – Integration of Power Functions (1:56)
  • Video – Integration of Power Functions involving Fractions (2:23)
  • Video – Integration of Power Functions Surds (1:06)
  • Video – Integration of Power Functions (5:32)
  • Video – Integration of Reciprocal Functions (1:35)
  • Video – Integration of Irrational Functions (4:32)
  • Video – Integration of Reciprocal Irrational Functions (4:41)
Particular Values
  • Video – Finding Integral Constants (7:27)
  • Video – Finding Integral Constants involving Point of Inflections (4:45)
  • Video – Finding Integral Constants involving Second Derivatives (2:33)
  • Topic – Finding Integral Constants from Linear Expressions
  • Topic – Integral Constants by Non-Monic Expressions from Linearity
  • Topic – Finding Integral Constants from Quadratics
  • Topic – Integral Constants using Non-Monic Expressions from Quadratics
  • Topic – Finding Two Integral Constants from Linear Expressions
Upper and Lower Rectangles
  • Topic – Calculating Upper Rectangles using Diagrams
  • Topic – Calculating Lower Rectangles using Diagrams
  • Topic – Calculating Upper Rectangles using Tables
  • Topic – Calculating Lower Rectangles using Tables
Definite Integrals
  • Video – Theory of Definite Integrals (5:46)
  • Video – Evaluating Plain Definite Integrals (4:56)
  • Video – Evaluating Definite Integrals of Higher Orders (8:05)
  • Video – Differentiating Definite Integrals (4:38)
  • Video – Finding Unknown Limits of Definite Integrals (5:00)
  • Video – Finding Unknowns of Expressions involving Definite Integrals (4:54)
  • Video – Definite Integrals involving Simplifications (3:47)
  • Video – Definite Integrals Backwards (1:58)
Calculating Integrals using Trapezoidal Rule
  • Video – Trapezoidal Rule & Definite Integrals (7:54)
  • Topic – Trapezoidal Rule 1
  • Topic – Trapezoidal Rule 2
  • Topic – Trapezoidal Rule 3
  • Topic – Trapezoidal Rule 4
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