NSW · NESASyllabus
Maths Standard 2 syllabus, dot point by dot point
Every dot point in the NSW Maths Standard 2 syllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Generated by Claude Opus and reviewed by Better Tuition Academy tutors.
Year 12: Algebra
Module overview →- How are linear cost and revenue functions used to model break-even points and profit?Model practical problems with linear cost and revenue functions and find the break-even point8 min answer →
- How do we decide whether a real situation is best modelled by a linear, quadratic, exponential or reciprocal function?Compare linear and non-linear models of real-world data and select the most appropriate model7 min answer →
- How are exponential functions used to model growth, decay and compound processes in the real world?Model practical problems with exponential functions of the form and interpret growth, decay and asymptotes8 min answer →
- How are quadratic functions used to model real-world situations such as projectile motion and maximum revenue?Model practical situations with quadratic functions and find maximum or minimum values, intercepts and zeros8 min answer →
- How are reciprocal functions used to model inverse variation, and what does the graph look like?Model practical problems involving reciprocal functions and inverse variation of the form7 min answer →
- How are simultaneous linear equations solved algebraically and graphically, and how are they used to model practical situations?Solve a pair of simultaneous linear equations graphically and algebraically, and use simultaneous equations to model practical situations8 min answer →
Year 12: Financial Mathematics
Module overview →- How does an annuity work, and how is superannuation modelled as a regular contribution growing at compound interest?Use the future value formula for an annuity to find the accumulated value of regular contributions to superannuation or a savings plan8 min answer →
- How is compound interest calculated, and how do compounding frequency and time affect investment growth?Use the compound interest formula to find future values, present values, interest rates and time periods for investments8 min answer →
- How is credit card interest calculated, and how do the interest-free period and daily compounding affect the cost of using a credit card?Calculate credit card interest using daily compounding, identify the interest-free period and the minimum monthly repayment7 min answer →
- How is inflation measured by the Consumer Price Index, and how does it affect the real value of money and investments?Use the Consumer Price Index to calculate inflation rates and compare real and nominal values over time7 min answer →
- How are reducing-balance loan repayments calculated, and how does each repayment split between interest and principal?Use recurrence relations and amortisation tables to calculate loan repayments, outstanding balances and the total interest paid on a reducing-balance loan9 min answer →
- How are share investments analysed using dividends, yields and price-earnings ratios?Calculate dividend yield, dividend payout, capital gain and total return on share investments7 min answer →
- How is depreciation calculated using the straight-line and declining-balance methods?Use the straight-line and declining-balance methods to calculate the value of a depreciating asset over time7 min answer →
Year 12: Measurement
Module overview →- How is the area of a non-right-angled triangle calculated using two sides and the included angle?Use the formula to find the area of any triangle given two sides and the included angle6 min answer →
- How is the cosine rule used to find missing sides and angles in non-right-angled triangles?Use the cosine rule to find a side given two sides and the included angle, or an angle given three sides7 min answer →
- How are bearings and radial surveys used to find distances and directions in navigation and surveying?Use compass and true bearings, and radial surveys, to solve practical navigation and surveying problems8 min answer →
- How are rates used to solve practical problems involving fuel consumption, energy use and dosage, and how do we convert between units?Use rates and unit conversions to solve practical problems including fuel consumption, dosage, power consumption and energy efficiency8 min answer →
- How are ratios and scale drawings used to read maps and plans, and how does the trapezoidal rule estimate irregular areas?Use ratios and scale drawings to interpret maps and plans, and use the trapezoidal rule to estimate the area of an irregular region9 min answer →
- How is the sine rule used to find missing sides and angles in non-right-angled triangles, and when does the ambiguous case arise?Use the sine rule to find unknown sides and angles in non-right-angled triangles, including the ambiguous case7 min answer →
Year 12: Networks
Module overview →- What is the critical path in a project network, and how does it determine the minimum project duration?Construct an activity network from a precedence table, identify the critical path and find the minimum project duration8 min answer →
- How do forward and backward scanning give the earliest and latest start times of each activity, and how is float calculated?Perform forward and backward scanning to find earliest start, latest start, earliest finish, latest finish times and float for each activity9 min answer →
- What is a minimum spanning tree, and how is it found using Prim's or Kruskal's algorithm?Find a minimum spanning tree for a weighted graph using Prim's or Kruskal's algorithm8 min answer →
- What are the basic terms and components of a network, and how are real-world systems represented as graphs?Use network terminology including vertex, edge, weight, degree, path, cycle and directed graph to describe and analyse networks7 min answer →
- How is the shortest path between two vertices in a weighted network found?Find the shortest path between two vertices in a weighted network by inspection or by systematic labelling7 min answer →
Year 12: Statistical Analysis
Module overview →- What does Pearson's correlation coefficient measure, and how is it interpreted?Calculate and interpret Pearson's correlation coefficient using statistical technology, including the sign and magnitude7 min answer →
- What is the difference between interpolation and extrapolation, and why is extrapolation less reliable?Distinguish between interpolation and extrapolation when using a regression line, and assess the reliability of predictions6 min answer →
- How is the least-squares regression line calculated, and how is it used to model a linear relationship between two variables?Find and use the equation of the least-squares regression line to model a linear relationship between two variables7 min answer →
- What is the normal distribution, and how does the empirical rule give the percentage of data within , and standard deviations?Recognise the features of the normal distribution and apply the empirical -- rule7 min answer →
- How do scatterplots reveal the form, direction and strength of the relationship between two variables?Construct and interpret scatterplots to describe the relationship between two variables in bivariate data7 min answer →
- What is a z-score, and how is it used to compare observations from different normal distributions?Calculate z-scores and use them to compare values from different normal distributions and find probabilities7 min answer →