Finance & Functions – The Maths That Builds Your Future

Dear Grade 12s

You’re deep in the final stretch, and now more than ever, your effort matters.

Let’s take a moment to explore two core topics that appear in nearly every exam and have real-life meaning too: Finance and Functions.

These aren’t just about marks.

They’re about thinking ahead, planning smartly, and solving problems in a way that prepares you for both university and life.

Let’s make sense of them — together.

💰 Part 1: Finance – Understanding Money Over Time

Maths Finance is all about how money grows or decreases over time, using either simple or compound interest.

🧮 1. Simple Interest

Formula:

A = P(1 + i × n)Where:

• A = final amount

• P = principal (initial amount)

• i = interest rate per annum (as a decimal)

• n = time in years

🧠 Simple interest grows in a linear pattern.

📈 2. Compound Interest

Formula:

A = P(1 + i)ⁿ

Here, interest is earned on interest already added, so it grows exponentially.

✅ Know how to:

• Compare compound and simple interest

• Use your calculator for exponentiation

• Interpret graphs of both types of growth

💸 3. Present Value

This is the reverse of compound interest — used when you want to know how much to invest now to reach a certain future amount.

Formula:

P = A / (1 + i)ⁿ

🧠 Use this for loan repayments and investments.

📉 4. Annuities & Future Value of Payments

Use this when making regular deposits or payments over time.

Formula:

FV = R[(1 + i)ⁿ – 1] / i

Where:

• R = recurring payment

• i = interest rate per period

• n = number of payments

  
  

📝 Finance Exam Tips:

✅ Always convert interest rate to decimal

✅ Double-check if it’s monthly or annual interest

✅ Use correct formula for the situation

✅ Show all steps clearly

✅ Know how to use your calculator efficiently

📘 Part 2: Functions – The Language of Mathematical Patterns

Functions are like machines — you input a value (x), and it gives you an output (y). They're the foundation of modern maths.

🔑 1. What Is a Function?

A function is a rule that assigns exactly one output for each input.

Function notation:

f(x) = ...e.g., f(x) = x² or f(x) = 2x + 3

📊 2. Types of Grade 12 Functions

✅ Linear Functions:

f(x) = mx + cStraight line, constant rate of change

✅ Quadratic Functions:

f(x) = ax² + bx + cParabola (U or ∩ shape)

✅ Hyperbolic Functions:

f(x) = a/xTwo separate curves (asymptotes)

✅ Exponential Functions:

f(x) = a·bˣCurve that increases/decreases quickly

✏️ 3. Key Concepts in Functions:

• Domain and range (input/output values)

• Intercepts (x- and y-axis crossings)

• Turning points (for parabolas)

• Asymptotes (lines a function approaches but never touches)

• Transformations – shifts, stretches, and reflections

🔄 4. Inverses and Sketching

• An inverse swaps x and y: f⁻¹(x)

• Reflected over the line y = x

You should be able to:

• Sketch all types

• Interpret features (growth, decay, turning points)

• Compare functions on the same set of axes

📘 Functions Exam Tips:

✅ Practise sketching neatly and labelling axes

✅ Memorise standard shapes and their properties

✅ Use your calculator for table values and checking points

✅ Read the question carefully — some ask for comparisons or interpretations

✅ Revise using past paper graphs and scenarios

🌱 Why These Topics Matter

Finance teaches you how to manage money and plan for the future.

Functions teach you how to recognise and predict patterns.

Together, they build the type of thinking you’ll use in business, science, economics, and your everyday life.

Mathematics-Functions and Finance.pdf

Download PDF • 27.05MB