VCE General Mathematics
Financial Mathematics
We explore simple and compound interest, depreciation, and loan repayments. These skills help us understand financial decision-making in real-life situations.
Simple and Compound Interest
Simple interest is calculated using the formula I = P × r × t, while compound interest uses A = P(1 + r)^t. Here, P is the principal, r is the annual interest rate, and t is time in years.
Practice Questions
Find the simple interest on $2,000 at 5% per annum for 3 years.
I = 2000 × 0.05 × 3 = $300
Find the total amount after 4 years if $5,000 is invested at 4% p.a. compounded annually.
A = 5000(1.04)^4 = $5,832.48
Linear Relationships
Linear Models
Linear relationships can be represented by equations of the form y = mx + c, where m is the gradient and c is the y-intercept. We interpret and apply these models in financial and real-world contexts.
Practice Questions
A taxi company charges a $4 booking fee plus $2 per kilometre. Write the equation and find the cost for a 10 km trip.
y = 2x + 4 → y = 2(10) + 4 = $24
Find the gradient of the line passing through (2, 5) and (8, 17).
m = (17 - 5)/(8 - 2) = 12/6 = 2
Data Analysis
We collect, display, and analyse data using measures of central tendency (mean, median, mode) and spread (range, IQR, standard deviation).
Interpreting Data
We use statistical displays such as boxplots and histograms to describe data distributions and identify outliers.
Practice Questions
The data set {5, 7, 7, 10, 12, 13, 15} has what median and range?
Median = 10, Range = 15 - 5 = 10
If the mean of five numbers is 12, what is their total?
12 × 5 = 60
Measurement and Geometry
Surface Area and Volume
We calculate surface area and volume of 3D shapes such as prisms, cylinders, and spheres, and apply them to real-world problems involving capacity and materials.
Practice Questions
Find the volume of a cylinder with radius 4 cm and height 10 cm.
V = πr²h = 3.14 × 16 × 10 = 502.4 cm³
Calculate the surface area of a cube with side length 6 cm.
A = 6 × 6² = 216 cm²
Networks and Matrices
Understanding Networks
We use networks to represent connections between locations or events. Concepts include vertices, edges, paths, and minimum spanning trees.
Practice Questions
In a network of four towns (A, B, C, D), the distances are AB = 5 km, AC = 7 km, AD = 9 km, BC = 4 km. What is the shortest route from A to C?
A → B → C = 5 + 4 = 9 km
Write the adjacency matrix for a network where A is connected to B and C, and C is connected to D.
