Learning Objectives
What You Should Be Able To Do
Interactive Study Tools
These tools are here to help students slow down and think about the method before rushing to an answer.
Tool 1
Study Planner
Use this to break a topic into small study sessions.
Plan: A clear breakdown will appear here.
Tool 2
Method Reminder
This quick guide reminds students what to do when they feel stuck.
- Read the story: what is the question really asking?
- Choose the method: identify the correct idea before calculating.
- Show the reason: do not skip the logic.
- Check the answer: make sure it fits the situation.
1. The Factor & Remainder Theorems (Higher Level)
Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.
These theorems are powerful tools for breaking down high-degree polynomials.
- Remainder Theorem: When a polynomial f(x) is divided by (x - c), the remainder is f(c).
- Factor Theorem: If f(c) = 0, then (x - c) is a factor of f(x).
2. Quadratic Inequalities
Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.
To solve x² - 5x + 6 < 0:
- Find the roots (where the graph hits zero): x=2, x=3.
- Sketch the parabola.
- Identify the region where the graph is below the axis (between the roots).
- Answer: 2 < x < 3.
Examiner Tip
💡 Examiner Tip: Always sketch a quick graph for inequalities! It prevents the most common mistake of just guessing the inequality direction.📝 Exam Style Questions
Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.
Medium Q1: Use the Factor Theorem to show (x-2) is a factor of x³ - 8.
Hard Q2: Solve the inequality x² - 4 ≥ 0.
A1: f(2) = 2³ - 8 = 8 - 8 = 0. Since f(2)=0, (x-2) is a factor.
A2: Roots are x=2, x=-2. Parabola opens up. We want the region ABOVE the axis. Answer: x ≤ -2 or x ≥ 2.