Maths Standard 2 Q&A by dot point

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Model practical problems with linear cost and revenue functions and find the break-even point

Compare linear and non-linear models of real-world data and select the most appropriate model

Model practical problems with exponential functions of the form $y = a b^x$ and interpret growth, decay and asymptotes

Model practical situations with quadratic functions and find maximum or minimum values, intercepts and zeros

Model practical problems involving reciprocal functions and inverse variation of the form $y = \frac{k}{x}$

Solve a pair of simultaneous linear equations graphically and algebraically, and use simultaneous equations to model practical situations

Use the future value formula for an annuity to find the accumulated value of regular contributions to superannuation or a savings plan

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

Use the compound interest formula to find future values, present values, interest rates and time periods for investments

Calculate credit card interest using daily compounding, identify the interest-free period and the minimum monthly repayment

Use the Consumer Price Index to calculate inflation rates and compare real and nominal values over time

Use recurrence relations and amortisation tables to calculate loan repayments, outstanding balances and the total interest paid on a reducing-balance loan

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

Use the straight-line and declining-balance methods to calculate the value of a depreciating asset over time

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

Use the cosine rule to find a side given two sides and the included angle, or an angle given three sides

Use compass and true bearings, and radial surveys, to solve practical navigation and surveying problems

Use rates and unit conversions to solve practical problems including fuel consumption, dosage, power consumption and energy efficiency

Use ratios and scale drawings to interpret maps and plans, and use the trapezoidal rule to estimate the area of an irregular region

Use the sine rule to find unknown sides and angles in non-right-angled triangles, including the ambiguous case

Construct an activity network from a precedence table, identify the critical path and find the minimum project duration

Perform forward and backward scanning to find earliest start, latest start, earliest finish, latest finish times and float for each activity

Find a minimum spanning tree for a weighted graph using Prim's or Kruskal's algorithm

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

Use network terminology including vertex, edge, weight, degree, path, cycle and directed graph to describe and analyse networks

Find the shortest path between two vertices in a weighted network by inspection or by systematic labelling

Calculate and interpret Pearson's correlation coefficient using statistical technology, including the sign and magnitude

Distinguish between interpolation and extrapolation when using a regression line, and assess the reliability of predictions

Find and use the equation of the least-squares regression line to model a linear relationship between two variables

Recognise the features of the normal distribution and apply the empirical $68$-$95$-$99.7$ rule

Construct and interpret scatterplots to describe the relationship between two variables in bivariate data

Calculate z-scores and use them to compare values from different normal distributions and find probabilities