MYP 4 Mathematics Final Exam Study Guide

Quadratics

• Surds are irrational roots that cannot be simplified. (e.g., $(\sqrt{2})$, $(\sqrt{3})$)
• Quadratic equations take the form: $ax^2 + bx + c = 0$
• Key Skills:
  • Factor quadratic expressions.
  • Solve quadratics using factoring or identities.

Trigonometry

• Key Ratios:
  • $sin(θ) = \frac{opposite}{hypotenuse}$
  • $cos(θ) = \frac{adjacent}{hypotenuse}$
  • $tan(θ) = \frac{opposite}{adjacent}$
• Key Skills:
  • Identify sides in a right triangle (O, A, H).
  • Use SOH-CAH-TOA to find missing sides or angles.
  • Use a calculator for inverse trig functions (e.g., $sin^{-1}$).
• Tips:
  • Ensure your calculator is in degree mode.
  • Draw diagrams and label the sides.

Sets and Venn Diagrams

• Key Vocabulary:
  • Set: Collection of elements
  • Union ($A \cup B$): All elements in A or B
  • Intersection ($A \cap B$): Elements common to both sets
  • Complement ($A'$): Elements not in A
  • Universal set U: All elements in the context
• Key Skills:
  • Interpret and draw Venn diagrams.
  • Find number of elements using the formula: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$
• Tips:
  • Read questions carefully.
  • Use shading in Venn diagrams.

Probability

• Key Concepts:
  • Probability of an event: $P(E) = \frac{favorable \space outcomes}{total \space outcomes}$
  • $0 ≤ P(E) ≤ 1$
  • Complement rule: $P(E') = 1 - P(E)$
• Key Skills:
  • Work with simple experiments (dice, coins, cards).
  • Use tree diagrams and tables when needed.
  • Solve compound events (AND = multiply, OR = add, for independent events).
• Tips:
  • Break down multiple-step problems.
  • Be careful with replacement vs. no replacement.

Final Exam Preparation Tips

• Practice past papers and textbook questions.
• Use Toddle resources.
• Time yourself when doing mock questions.
• Check your answers.
• Ask questions in class if you’re unsure!
• Rest and manage your time before the exam.