§-Maths Standard 2 syllabus

NSW · NESA← Maths Standard 2

Maths Standard 2 syllabus, dot point by dot point

Every dot point in the NSW Maths Standard 2 syllabus, in syllabus order, with a focused answer for each. Open any dot point for the answer, exam-style questions and links to related points.

Year 11: Algebra

Module overview →

What does it mean for one quantity to vary directly with another, how do you find the constant of variation k from a single data pair and write the equation y = kx, why is the graph always a straight line through the origin, and how is direct variation different from inverse variation y = k/x?

Recognise and model direct variation y = kx, where one quantity is a constant multiple of another, find the constant of variation k from a data pair, write and use the equation, identify direct variation from a constant ratio in a table or a straight-line graph through the origin, and contrast it with simple inverse variation y = k/x

18 min read →

How do you turn a real situation with a fixed cost plus a steady rate into the equation y = mx + b, what do the gradient and y-intercept mean in that context, and how do you use the model to predict a value and read it backwards?

Construct a linear model y = mx + b for a practical situation made of a fixed amount plus a constant rate, interpret the gradient as the rate and the y-intercept as the fixed starting amount in context, and use the model to predict an output and to find the input that gives a required output

18 min read →

How do you turn a linear relationship into a straight-line graph, plotting points from a table of values, recognising the line, sketching horizontal and vertical lines, and finding the intercepts?

Graph linear functions by constructing a table of values and plotting the points, recognise a linear relationship, sketch horizontal and vertical lines, and graph a line using its x- and y-intercepts

17 min read →

How do you solve a linear equation by keeping it balanced and undoing the operations in reverse order?

Solve linear equations using inverse operations, including one-step, two-step and multi-step equations, equations with brackets and fractions, and equations with the variable on both sides

14 min read →

How do you estimate blood alcohol content from a formula or a table, and work out how long until it is safe and legal to drive?

Use the blood alcohol content formulae for males and females to estimate BAC by substitution, read BAC from a body-weight table, and use the time formula BAC divided by 0.015 to estimate the hours until BAC reaches zero or a legal limit

16 min read →

What do m and b mean in the equation y = mx + b, how do you read them straight off an equation or a graph, and how do you sketch a line quickly from its gradient and y-intercept?

Use the gradient-intercept form y = mx + b: read the gradient m and the y-intercept b directly from the equation (rearranging first if needed), write the equation of a line from its graph, and sketch a line from m and b

17 min read →

What is the gradient of a straight line, what do its sign and size tell you, and how do you find the gradient from a graph or from two points and read the y-intercept?

Find the gradient of a straight line as rise over run, interpret the sign of the gradient and what steepness means, read the y-intercept from a graph, and calculate the gradient between two points

16 min read →

How do you rearrange a formula to make a different variable the subject by undoing the operations around it?

Change the subject of a formula by rearranging it to isolate any chosen variable, including a subject that appears in a power, a root or a fraction, and check the rearrangement by substitution

15 min read →

How are distance, speed and time linked by one formula, and how do you rearrange it and keep the units consistent?

Use the relationship between distance, speed and time to solve problems, rearranging the formula to find any of the three quantities and converting between km/h and m/s

13 min read →

How do you work out the right dose of medicine for a child or infant, and the drip rate for an IV infusion, by substituting into a given formula?

Use the paediatric dosage formulae (Fried's rule for infants, Young's rule by age and Clark's rule by weight) and the IV flow-rate formula to calculate doses and drip rates by substitution

16 min read →

How do you find an unknown that is not the subject of a formula by substituting the known values first and then solving the equation that is left?

Substitute known values into a formula and then solve the resulting equation to find an unknown quantity that is not the subject of the formula

15 min read →

How do you evaluate a formula correctly once you replace its pronumerals with numbers?

Substitute numerical values into a formula or algebraic expression and evaluate it, including expressions with powers, fractions and negative numbers

12 min read →

Year 11: Data Analysis

Module overview →

How do you classify data as categorical or numerical, and how does the type of data decide which display is appropriate?

Classify data relating to a single random variable as categorical (nominal or ordinal) or numerical (discrete or continuous), and select and use an appropriate graphical display for the data type

13 min read →

How is a five-number summary turned into a box plot, and how do parallel box plots let you compare two groups by centre, spread, skew and outliers?

Construct and interpret box-and-whisker plots and use them, including parallel (side-by-side) box plots, to compare data sets in terms of centre, spread, skewness and outliers

15 min read →

How do you display grouped data as a frequency histogram and polygon, and read the median and quartiles off a cumulative frequency graph (ogive)?

Construct and interpret frequency histograms and polygons, and cumulative frequency graphs (ogives), including using an ogive to estimate the median and quartiles of a data set

15 min read →

How are the mean, median and mode used to summarise the centre of a data set, and which is the most appropriate measure?

Calculate measures of central tendency, including the mean, median and mode, for both raw data and data presented in a frequency table

14 min read →

How are measures of spread used to describe how widely data is spread out, and how do they let you compare two data sets?

Calculate measures of spread, including the range, quartiles and interquartile range, and the population standard deviation using technology

14 min read →

How do you test whether a value is an outlier, name the shape of a data set, and write a full description of a distribution?

Determine outliers using the interquartile range, describe and interpret the shape and features of a distribution (symmetry, skewness, modality, centre, spread and outliers) and compare data displays using these features

14 min read →

How are dot plots and stem-and-leaf plots used to display a data set and reveal its clusters, gaps, outliers and shape?

Display and interpret numerical data using dot plots and stem-and-leaf plots, including back-to-back stem-and-leaf plots, and describe the clusters, gaps, outliers and shape of the data

14 min read →

Which statistical chart best displays a set of data, and how do you construct and read column, sector, line and Pareto charts correctly?

Display categorical and numerical data using a range of statistical graphs, including column graphs, sector graphs, line graphs, divided bar graphs and Pareto charts, and interpret the displays

14 min read →

How do you organise raw data into a frequency table, group it into class intervals with class centres, and build a cumulative frequency column?

Organise, interpret and display data into appropriate tabular and graphical representations including frequency distribution tables, both ungrouped and grouped using class intervals and class centres, and cumulative frequency

14 min read →

How are data collected and sampled so that the results fairly represent the whole population?

Investigate sampling techniques, including census, simple random, systematic and stratified sampling, and identify the target population and sources of bias in data collection

14 min read →

Year 11: Financial Mathematics

Module overview →

Why does straight-line depreciation plot as a falling straight line, how do you find the value after n years or the annual depreciation amount, and how is it different from declining-balance depreciation?

Model the value of a depreciating asset with straight-line (prime-cost) depreciation S = V0 - Dn, find the salvage value after n years, the annual depreciation D and the time to reach a given value, work with a rate given as a percentage of the original cost, and contrast it with declining-balance depreciation

15 min read →

Why does simple interest plot as a straight line, what does the gradient of that line mean, and how do you compare two interest rates and read values straight off the graph?

Graph simple interest as a straight line of interest I (or amount A) against time n, interpret the gradient as the interest earned each period, compare two rates on the same axes by their gradients, and read interest, amount or time off the line

15 min read →

How does the simple interest formula I = Prn work, why does the amount grow as a straight line, and how do you rearrange it to find the principal, the rate or the time, including over part of a year?

Apply the simple interest formula I = Prn and the amount A = P + I, rearrange it to solve for the principal, the rate or the time, and calculate interest over part-years measured in months or days

16 min read →

How is the 10% GST added to a price and then pulled back out of a GST-inclusive total, and why do percentage changes only behave predictably when you treat them as multipliers?

Add the 10% GST to a pre-GST price, find the GST contained in a GST-inclusive total and the pre-GST price, calculate percentage increases and decreases, and combine successive percentage changes using multipliers

15 min read →

How is income calculated when pay depends on sales, output or intellectual property rather than fixed hours, and how do leave loading, bonuses and government payments add to it?

Calculate earnings from commission (flat and sliding scale), piecework, royalties, annual leave loading and bonuses, and government allowances

14 min read →

How is pay calculated from a salary or an hourly wage, and how do overtime rates and allowances change a worker's earnings?

Calculate earnings from wages, salaries and overtime, including conversion between pay periods, hourly rates, penalty rates and allowances

13 min read →

How does the Australian Taxation Office turn a person's gross income into the tax they actually owe, and how does the PAYG system settle that bill across a financial year?

Calculate gross and net pay, identify allowable deductions and taxable income, compute the tax payable from a tax-bracket table, add the Medicare levy, and reconcile PAYG withheld against the tax assessed

16 min read →

How do you work out a household bill from a tiered tariff with a supply charge and stepped usage rates, cost the purchase and running of a car including stamp duty from a scale, and balance a personal budget to find the surplus or shortfall?

Prepare and interpret a budget. Calculate household bills such as electricity and water from a tariff with a fixed supply charge plus stepped (tiered) usage rates. Calculate the costs of purchasing and running a motor vehicle, including stamp duty from a published scale, registration, insurance and running costs. Balance a personal budget of income against expenses and find the surplus, shortfall or the saving required

17 min read →

Year 11: Measurement

Module overview →

How accurate is a measurement, and how do you state its error and the range the true value must lie in?

Describe the limit of reading of an instrument, calculate the absolute error and percentage error of a measurement, and find the greatest possible error and the upper and lower bounds

13 min read →

How do you choose the right metric unit and convert correctly between units of length, area, volume, mass and speed?

Use units of measurement and convert between them, including length, area, volume, capacity, mass and compound units such as speed, multiplying or dividing by the correct power of 10

14 min read →

How do you calculate the area of a circle, a sector and shapes built from circular and straight-sided parts?

Calculate the area of circles, sectors and composite figures, including the annulus, by adding and subtracting the areas of simpler shapes

15 min read →

How do you find the surface area of a prism, cylinder, sphere, pyramid or cone, and when must you first find a slant height?

Calculate the surface area of right prisms, cylinders, spheres and pyramids, and of right cones using the slant height, including solids formed as a combination of these

15 min read →

How do you calculate the volume of prisms, cylinders, pyramids, cones, spheres and composite solids, and convert that volume into a capacity?

Calculate the volume of right prisms, cylinders, pyramids, cones, spheres and composite solids, and convert between units of volume and capacity

15 min read →

How do you use rates and ratios to compare value, measure how fast something happens, share a quantity fairly, and read distances off a scale map or plan?

Review and use rates and ratios, including identifying rates from a context (such as best buys, fuel consumption, heart rate and pay rates), working with unit rates, simplifying ratios, dividing a quantity in a given ratio, and using scale factors on maps and plans

15 min read →

How do you measure energy in joules and kilowatt-hours, work out what an appliance costs to run, and balance the kilojoules you eat against the energy your body needs each day?

Solve problems involving energy and mass, including the joule and the watt, energy consumption measured in kilowatt-hours, the energy content of food measured in kilojoules, and daily energy requirements based on basal metabolic rate and level of activity

15 min read →

How do you estimate the area of a block of land or a body of water with one irregular boundary, using the trapezoidal rule with a single strip and with several strips?

Calculate the approximate area of an irregularly shaped region using the trapezoidal rule, A = h/2 (d_f + d_l), and apply the rule repeatedly to find the approximate area between an irregular boundary and a straight line, where d_f and d_l are the first and last measurements and h is the strip width

14 min read →

How do you write very large and very small numbers in standard form, and round a measurement to a stated number of significant figures?

Write numbers in scientific (standard) form as a number between 1 and 10 times a power of 10, convert back to a numeral, round to a given number of significant figures, and operate with numbers in standard form

14 min read →

Year 11: Relative Frequency and Probability

Module overview →

Why does every probability lie between 0 and 1, and how do complementary events help you find a chance the short way?

Recognise that probabilities of events range from 0 to 1, identify the complement of an event and use the relationship that the probability of an event and its complement sum to 1, so the probability of 'not E' equals 1 minus the probability of E

13 min read →

How do we calculate the theoretical probability of an event from its sample space?

List the sample space of equally likely outcomes and calculate the theoretical probability of an event using

P(E)=\dfrac{n(E)}{n(S)}

, the number of favourable outcomes divided by the total number of outcomes

14 min read →

How do we describe and measure the chance of an event in words and as a number between 0 and 1?

Describe the likelihood of an event using the language of chance and the probability scale from 0 to 1, distinguishing fair from biased and equally likely outcomes

13 min read →

How do we estimate a probability from experimental data using relative frequency, and why does the estimate settle toward the theoretical probability as more trials are run?

Calculate relative frequencies to estimate probabilities of events, where relative frequency = frequency of the event divided by the total number of trials, recognising that as the number of trials increases the relative frequency approaches the theoretical probability

13 min read →

How do we predict how many times an event will happen over many trials?

Calculate the expected frequency of an event from the probability of the event and the number of trials, using expected frequency = P(E) x number of trials

13 min read →

How do tree diagrams and two-way tables find probabilities for multi-stage events?

Use arrays and tree diagrams to determine the outcomes and probabilities for multi-stage experiments, including two-way tables, multiplying probabilities along the branches of a tree diagram and adding the probabilities of mutually exclusive outcomes, with and without replacement

15 min read →

Year 11: Working with Time

Module overview →

How do world time zones work as offsets from Coordinated Universal Time, and how do you find the local time in another city by adding to the east, subtracting to the west and allowing for daylight saving?

Understand and use Coordinated Universal Time (UTC) and the relationship between time zones around the world expressed as offsets from UTC, including the link between longitude and time, to calculate the local time in different locations

14 min read →

How are points located on Earth by latitude and longitude, and how is the angular distance between two points turned into a distance in kilometres and nautical miles?

Understand the relationship between distance, angular distance (degrees and minutes) and time, using latitude and longitude to locate points on Earth's surface, and the definition of a nautical mile as one minute of arc along a great circle

14 min read →

How do you convert between units of time, read 12-hour and 24-hour time, and work out how long something lasts when it crosses noon or midnight?

Use units of time, convert between 12-hour and 24-hour time, and solve problems involving elapsed time and the addition and subtraction of time

14 min read →

How do you read a transport timetable to find a journey's duration, plan a connection and its waiting time, and work out the average speed of the trip?

Interpret timetables for buses, trains and ferries, including calculating the duration of a journey and the average speed of a trip

14 min read →

How do you find the time difference between two places from their UTC offsets, and find the local time you arrive after a long flight that crosses the International Date Line?

Determine the time difference between two places given their time zones or UTC offsets, and solve problems involving the International Date Line and the local time of arrival after a journey, allowing for the change of date when crossing the line

14 min read →

Year 12: Algebra

Module overview →

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 model

12 min read →

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

y = a b^x

and interpret growth, decay and asymptotes

13 min read →

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 zeros

14 min read →

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 form

y = \frac{k}{x}

12 min read →

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 point

13 min read →

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 situations

13 min read →

Year 12: Financial Mathematics

Module overview →

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 investments

13 min read →

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 time

11 min read →

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 repayment

12 min read →

What is the present value of an annuity, and how do future value and present value annuity tables let you find or back-solve a contribution?

Use future value and present value annuity tables, and calculate the present value of an annuity

14 min read →

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 time

10 min read →

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 plan

12 min read →

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 loan

14 min read →

How are share investments analysed using dividends, yields and price-earnings ratios?

Calculate dividend yield, dividend payout, capital gain and total return on share investments

10 min read →

Year 12: Measurement

Module overview →

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 efficiency

12 min read →

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 region

13 min read →

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 sides

12 min read →

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 case

12 min read →

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 problems

13 min read →

How is the area of a non-right-angled triangle calculated using two sides and the included angle?

Use the formula

A = \frac{1}{2} a b \sin C

to find the area of any triangle given two sides and the included angle

11 min read →

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 duration

15 min read →

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 networks

15 min read →

How is the greatest possible flow through a directed network found, and why does the smallest cut decide it?

Solve network flow problems, including finding the maximum flow using the maximum-flow minimum-cut theorem

16 min read →

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 algorithm

12 min read →

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 activity

16 min read →

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 labelling

14 min read →

Year 12: Relative Frequency and Probability (2024 syllabus)

Module overview →

How do Venn diagrams and two-way tables organise information about two attributes, and how do we use them to find probabilities and proportions?

Construct and interpret Venn diagrams and two-way tables from given information, limited to combinations of two attributes, and use them to solve problems in a variety of contexts

11 min read →

Year 12: Statistical Analysis

Module overview →

What is the normal distribution, and how does the empirical rule give the percentage of data within $1$ , $2$ and $3$ standard deviations?

Recognise the features of the normal distribution and apply the empirical

68

95

99.7

12 min read →

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 predictions

10 min read →

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 data

12 min read →

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 probabilities

12 min read →

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 variables

13 min read →

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 magnitude

11 min read →