TASC General Mathematics Level 3 study guide
TASC General Mathematics Level 3 · Work through your exam, one topic at a time.
General Mathematics (Level 3) is a Tasmanian senior secondary mathematics course, administered within the Tasmanian Assessment, Standards and Certification (TASC) system. It is designed for students who want practical, applied mathematics rather than a heavily theoretical pathway, and it suits learners heading toward careers or further study in business, health, social science, education, trades, and other fields where quantitative reasoning matters more than abstract proof. The course typically develops four connected strands: algebra and linear relationships, functions, graphs and modelling, statistics and probability, and financial and discrete mathematics. Students learn to interpret real situations, choose appropriate mathematical tools, carry out multi-step calculations, and communicate conclusions clearly. Topics on this exam: Algebra and Linear Relationships, Functions, Graphs and Modelling, Statistics and Probability, and Financial and Discrete Mathematics. The TASC General Mathematics Level 3 study guide has 4 sections and about 1,593 words.
01Algebra and Linear Relationships
A linear relationship has a constant rate of change. The slope-intercept form y = mx + b tells you the slope m (change in y per unit change in x) and the y-intercept b. The point-slope form y − y₁ = m(x − x₁) is useful when you know a point and the slope. To find a line through two points, compute m = (y₂ − y₁)/(x₂ − x₁), then substitute one point to solve for b.
358 words, about 2 min02Functions, Graphs and Modelling
A function assigns exactly one output to each input; the vertical line test confirms this on a graph. Function notation f(x) means the output when the input is x, so f(3) requires substituting 3 everywhere x appears. Understand domain (allowed inputs) and range (possible outputs), and recognise common families: linear (constant rate), quadratic (parabola, symmetric, vertex), exponential (repeated multiplication, rapid growth or decay), and absolute value (V-shape). Transformations follow patterns: f(x) + k shifts up k units, f(x − h) shifts right h units, and a·f(x) stretches vertically when a 1.
334 words, about 2 min03Graphs and Modelling
Graphs display relationships visually so patterns and comparisons become clear. Know how to read and construct: coordinate-plane plots, bar graphs, line graphs, scatterplots, and histograms. For scatterplots, describe the association (positive, negative, or none), its strength, and whether it is linear. A line of best fit summarises the trend and supports prediction; interpolation (predicting inside the data range) is more reliable than extrapolation (predicting beyond it).
318 words, about 2 min04Statistics and Probability
Statistics summarise data: mean (average), median (middle value), mode (most frequent), and range (max − min). The mean is sensitive to outliers; the median is resistant. For probability, P(event) = favourable outcomes / total equally likely outcomes, always between 0 and 1. Complementary events satisfy P(not A) = 1 − P(A).
583 words, about 3 min