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. Laws of Indices
Simple explanation: This section explains power rules and logarithms more gently so the patterns become easier to remember.
Indices (powers) are essential for simplifying complex algebraic expressions.
a^m Ć a^n = a^(m+n)
a^m / a^n = a^(m-n)
(a^m)^n = a^(mĆn)
a^0 = 1 | a^-n = 1/a^n | a^(1/n) = nāa
a^m / a^n = a^(m-n)
(a^m)^n = a^(mĆn)
a^0 = 1 | a^-n = 1/a^n | a^(1/n) = nāa
2. Logarithms
Simple explanation: This section explains power rules and logarithms more gently so the patterns become easier to remember.
A logarithm is just the inverse of an exponent. If b^x = y, then log_b(y) = x.
log_b(xy) = log_b(x) + log_b(y)
log_b(x/y) = log_b(x) - log_b(y)
log_b(x^k) = k Ć log_b(x)
log_b(x/y) = log_b(x) - log_b(y)
log_b(x^k) = k Ć log_b(x)
Examiner Tip
š” Examiner Tip: The "Change of Base" formula is your best friend when your calculator won't handle a specific base: log_b(a) = log_c(a) / log_c(b).Common Mistake
ā Common Mistake: Confusing log(x) + log(y) with log(x+y). They are NOT the same! Remember: Addition of logs corresponds to multiplication of their arguments.š 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.
Easy Q1: Simplify 2^3 Ć 2^4.
Medium Q2: Solve for x: 3^x = 27.
A1: 2^(3+4) = 2^7 = 128.
A2: 3^x = 3^3, therefore x = 3.