Integration

Integration

Simplifying Algebraic Fractions

  • Understand that an algebraic fraction is a fraction where the numerator and/or the denominator are algebraic expressions.
  • Identify and apply the rules of adding, subtracting, multiplying, and dividing algebraic fractions.
  • Factor algebraic expressions in the numerator and denominator.
  • Simplify algebraic fractions by canceling common factors in the numerator and denominator.

Solving Algebraic Equations

  • Practice solving both linear and quadratic equations.
  • Understand the importance of maintaining the balance of the equation throughout the solving process.
  • Pay attention to detail when checking solutions.
  • Get familiar with the quadratic formula and understand how to use it when you cannot factorize a quadratic equation.

Understanding Trigonometry

  • Understand the concept of sin, cos, and tan in relation to a right-angled triangle.
  • Know the unit circle fully and understand its significance in trigonometry.
  • Understand the differences between degrees and radians, and how to convert between the two.
  • Apply Pythagorean theorem in relation to the sine and cosine of an angle.
  • Appreciate the importance of SOHCAHTOA and know how to apply them.

Manipulating Trigonometric Equations

  • Become familiar with the trigonometric identities sin²(x) + cos²(x) = 1, tan(x) = sin(x)/cos(x), and the reciprocal identities.
  • Use these identities to simplify and solve trigonometric equations.
  • Understand the graphical representation of sin, cos, and tan functions, and how these can aid in solving trigonometric equations.

Applying Differentiation

  • Understand how to use power rule, product rule, quotient rule, and chain rule.
  • Understand the geometric interpretation of the derivative as a rate of change or slope of a curve.
  • Know how to find equations of tangents and normals to curves at given points.

Integrating Functions

  • Understand the concept of anti-differentiation.
  • Recognize when to use definite or indefinite integration.
  • Find the area under a curve using definite integration.
  • Understand and apply the method of integration by parts and substitution.

These key areas contain the foundational concepts in algebra, trigonometry, and calculus needed to ace the further mathematics GCSE.