GCSE Mathematics — Equations, Inequalities and Sequences

Led by Leonhard Euler Simulacrum

The fourth module of the OCR GCSE Mathematics course — linear, quadratic and simultaneous equations, inequalities, iteration, functions and sequences. Hosted by Leonhard Euler Simulacrum.

1. Module 1

   Linear and Quadratic Equations

   Led by Leonhard Euler Simulacrum

   The question

   Solving linear equations (including with unknowns on both sides and set up from context) and quadratic equations by factorising, completing the square, or the quadratic formula. Emphasis on choosing the appropriate method and interpreting solutions.

   Outcome

   The student can solve linear and quadratic equations by appropriate methods and set up equations from context. (Equation solving)

   Sub-units

   1. ○ 1.1 Linear and Quadratic Equations Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   Simultaneous Equations and Approximate Solutions

   Led by Leonhard Euler Simulacrum

   The question

   Two linear simultaneous equations solved algebraically; one linear and one quadratic at Higher tier; graphical solutions by reading intersection points; and approximate solutions by iterative methods (decimal search, interval bisection) at Higher tier.

   Outcome

   The student can solve simultaneous equations algebraically, find graphical solutions, and use iteration to approximate roots. (Systems and numerical methods)

   Sub-units

   1. ○ 2.2 Simultaneous Equations and Approximate Solutions Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   Inequalities

   Led by Leonhard Euler Simulacrum

   The question

   Solving linear inequalities and representing solutions on number lines, solving quadratic inequalities and expressing solutions in set notation at Higher tier, and solving and graphing linear inequalities in two variables with dashed/solid line conventions.

   Outcome

   The student can solve linear and quadratic inequalities and represent solutions on number lines and graphs. (Inequality solving)

   Sub-units

   1. ○ 3.3 Inequalities Open this unit → ✓ ↻
   Open this module → Print certificate of completion
4. Module 4

   Functions and Sequences

   Led by Leonhard Euler Simulacrum

   The question

   Functions as input-output relationships (inverse and composite at Higher), generating sequences from rules, finding the nth term of arithmetic and quadratic sequences, subscript notation, and recognising special sequences — triangular, square, cube, Fibonacci, and geometric progressions.

   Outcome

   The student can find nth term formulae for arithmetic and quadratic sequences and recognise special sequence types. (Sequence analysis)

   Sub-units

   1. ○ 4.4 Functions and Sequences Open this unit → ✓ ↻
   Open this module → Print certificate of completion