All Lessons

(G) Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

(Y10A) Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)

HSF.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

(F) Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

(I) Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

(E) Determine or analyze an appropriate piecewise model for problem situations

(Y11-12) Interpret and use graphs in practical situations, including travel graphs and conversion graphs (ACMEM124)

HSF.IF.7.B Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

HSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

HSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

(D) Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

(B) Represent arithmetic sequences and geometric sequences using recursive formulas

HSF.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*

(C) Determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d

(A) Analyze the effect on the graphs of f(x) = x3 and f(x) = 3√x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d

HSF.IF.7.B Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

(B) Determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points

(B) Analyze numerical data using measures of central tendency (mean, median, and mode) and variability (range, interquartile range or IQR, and standard deviation) in order to make inferences with normal distributions

(Y10A) Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)

(Y11-12) Calculate and interpret statistical measures of spread, such as the range, interquartile range and standard deviation (ACMEM055)

HSS.IDA.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

(A) Represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

(Y11-12) Display numerical data as frequency distributions, dot plots, stem and leaf plots, and histograms (ACMEM046)

HSS.IDA.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

(D) Summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.

(Y9) Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226)

(Y11-12) Identify relative frequency as probability (ACMEM152)

HSS.IDA.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

(A) Compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads

(Y9) Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283)

(Y10) Construct and interpret box plots and use them to compare data sets (ACMSP249)

(Y10A) Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)

(Y11-12) Compare back-to-back stem plots for different datasets (ACMEM057)

HSS.IDA.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

(B) Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

(E) Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

(Y11-12) Find the line of best fit by eye (ACMEM141)

(Y11-12) Use the line of best fit to make predictions, both by interpolation and extrapolation (ACMEM145)

HSS.IDA.6.A Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

(C) Compare different linear models for the same set of data to determine best fit, including discussions about error

(Y11-12) Find the line of best fit by eye (ACMEM141)

(Y11-12) Use technology to find the line of best fit (ACMEM142)

HSS.IDA.6.B Informally assess the fit of a function by plotting and analyzing residuals.

(A) Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association

(Y11-12) Use technology to find the correlation coefficient (an indicator of the strength of linear association) (ACMEM144)

HSS.IDA.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.