Mathematics

• What is set notation used for?

  Representing solutions to inequalities
• What does the notation $x > 2$ represent in set notation?

  $x \in (2, \infty)$
• What does the notation $x \geq 2$ represent in set notation?

  $x \in [2, \infty)$
• What does the notation $x < 2$ represent in set notation?

  $x \in (-\infty, 2)$
• What does the notation $x \leq 2$ represent in set notation?

  $x \in (-\infty, 2]$
• How can the inequality $x^2 - 16 < 0$ be expressed in set notation?

  $x \in (-4, 4)$
• How can the inequality $x^2 + 5x - 14 > 0$ be expressed in set notation?

  $x \in (-\infty, -7) \cup (2, \infty)$
• What is factoring in mathematics?

  Turning an expression into products of factors
• How do you factor the equation $x^2 - 25 = 0$?

  $(x-5)(x+5) = 0$
• What are the roots of the equation $x^2 - 25 = 0$?

  $x=5$ or $x=-5$
• How do you factor the equation $x^2 + 14x + 49 = 0$?

  $(x+7)^2 = 0$
• What are the roots of the equation $x^2 + 14x + 49 = 0$?

  $x=-7$
• What are the roots of a quadratic function?

  Its x-intercepts when equated to zero
• What are the roots of the equation $x^2 - 14x + 49 = 0$?

  $x=7$
• How is the equation $5x^2 + 2 = 0$ solved?

  $5x^2 = -2$
• What is the solution for $x^2 = -\frac{2}{5}$?


  $x=\pm \sqrt{-\frac{2}{5}}$
• What is a quadratic expression?

  Any expression of the form $ax^2 + bx + c$
• Give an example of a quadratic expression.

  $2x^2 - 5x + 7$
• What is the quadratic formula used for?

  Solving any quadratic equation
• What is the quadratic formula for $ax^2 + bx + c = 0$?

  $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• Solve $3x^2 + 4x - 6 = 0$ using the quadratic formula.

  $x = \frac{-4 \pm \sqrt{88}}{6}$
• Simplify $x = \frac{-4 \pm 2\sqrt{22}}{6}$.

  $x = \frac{-2 \pm \sqrt{22}}{3}$
• What are perfect squares in mathematics?

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

  $x^2 - 6x + 9 = (x-3)^2$
• How can $x^2 + 6x + 9$ be expressed?

  $(x+3)^2$
• What is the process of completing the square?

  Expressing $x^2 + bx + c$ in two terms
• How do you complete the square for $y = x^2 + 8x - 1$?

  $y = (x+4)^2 - 17$
• Solve $x^2 + 6x + 5 = 0$ by completing the square.

  $x = -1$ or $x = -5$
• What are simultaneous equations?

  A pair of equations involving two variables
• How can simultaneous equations be solved?

  By elimination or substitution
• Solve the simultaneous equations $3x + 2y = 9$ and $x - y = 2$ by elimination.

  $x = \frac{13}{5}$
• Solve the simultaneous equations $3x + 2y = 9$ and $x - y = 2$ by substitution.

  $y = \frac{3}{5}$
• What is a crucial difference when solving inequalities compared to equations?

  Change the inequality symbol when dividing by negative
• How many solutions can a pair of quadratic and linear simultaneous equations have?

  Up to two solutions where graphs intersect
• What is probability defined as?

  Number of favourable outcomes over total outcomes
• What is the probability of getting heads when flipping a coin?

  P(Head) = 1/2
• What does a sample space diagram show?

  All possible outcomes of two events
• What are mutually exclusive events?

  Events that cannot happen at the same time
• How do you calculate the probability of mutually exclusive events?

  P(A or B) = P(A) + P(B)
• What is a Venn diagram used for?

  To show all possible outcomes for events