Mathematics

• What is set notation used for?


  It is a formal way of representing a solution to an inequality
• What does the inequality $x +$$3 \geq 2$ represent in set notation?


  $x \geq -1$
• What does the inequality $x +$$3 < 2$ represent in set notation?


  $x < -1$
• What does the inequality <latex{x^2 + x - 6 \leq 0}</latex> represent in set notation?


  <latex{-3 \leq x \leq 2}</latex>
• What does the inequality <latex{x^2 - 4x + 3 > 0}</latex> represent in set notation?


  <latex{x < 1 \cup x > 3}</latex>
• What is factorising?


  A methodical way to turn an expression into the product of two or more basic expressions
• What is an example of factorising?


  $x^2 +$$x - 6 =$$(x + 3)(x - 2)$
• What is the difference of two squares formula?


  <latex{a^2 - b^2 = (a - b)(a + b)}</latex>
• How would you factorise <latex{x^2 - 121}</latex>?


  <latex{(x - 11)(x + 11)}</latex>
• What are the roots of a quadratic function?


  The solutions where it is equated to zero
• What are the roots of the equation <latex{x^2 - 14x + 48 = 0}</latex>?


  <latex{x = 6 \text{ and } x = 8}</latex>
• What are the roots of the equation <latex{x^2 + 2x - 15 = 0}</latex>?


  <latex{x = -5 \text{ and } x = 3}</latex>
• What are the roots of the equation <latex{x^2 + 5x + 6 = 0}</latex>?


  <latex{x = -2 \text{ and } x = -3}</latex>
• What is a quadratic equation?


  Any expression of the form <latex{ax^2 + bx + c}</latex>, where a, b, c are numbers
• What is the quadratic formula used for?


  To solve quadratic equations when factorising doesn't work
• How would you solve the equation <latex{x^2 + 4x - 8 = 0}</latex> using the quadratic formula?


  <latex{x = \frac{-4 \pm \sqrt{16 - 4(1)(-8)}}{2}}</latex>
• What is the simplified result of <latex{x = \frac{-4 \pm \sqrt{16 - 4(1)(-8)}}{2}}</latex>?


  <latex{x = -2 \pm 2\sqrt{3}}</latex>
• What are perfect squares?


  Linear equations raised to a power of 2
• Give an example of a perfect square.


  <latex{(3x)^2 = 9x^2}</latex>
• What is the process of completing the square?


  Expressing <latex{a^2 + bx + c}</latex> in a specific form
• How would you complete the square for <latex{x^2 + 8x + 1}</latex>?


  <latex{x^2 + 8x + 16 - 15 = (x + 4)^2 - 15}</latex>
• What are simultaneous equations?


  A pair of equations involving two variables requiring a common solution
• How can you find simultaneous equations?


  By elimination or substitution methods
• What is the elimination method in solving simultaneous equations?


  Making the coefficients of one variable the same in both equations
• How do you use substitution in simultaneous equations?


  Substituting an expression for a variable from one equation into the other
• What must you remember when solving inequalities?


  If you multiply or divide by a negative number, change the inequality symbol
• How many solutions can a pair of quadratic and linear simultaneous equations have?


  Up to two solutions
• How do you find the coordinates where two graphs intersect?


  By solving their equations simultaneously
• What are the key components of a probability tree diagram?


  • Represents all possible outcomes
  • Shows the probabilities of each outcome
  • Useful for calculating probabilities of combined events
• What is a sample space diagram?


  • A visual representation of all possible outcomes
  • Used in probability to show outcomes of experiments
  • Helps in understanding the likelihood of events
• What is the significance of rolling a dice and flipping a coin in probability?


  • Demonstrates independent events
  • Each outcome has a specific probability
  • Useful for teaching basic probability concepts