A: Mathematical Models

A.1: evaluate powers with rational exponents, simplify algebraic expressions involving exponents, and solve problems involving exponential equations graphically and using common bases;

A.1.2: simplify algebraic expressions containing integer exponents using the laws of exponents

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

A.1.7: solve exponential equations in one variable by determining a common base (e.g., 2 to the x power = 32, 4 to the (5x - 1) power = 2 to the (2(x + 11)) power, 3 to the (5x + 8) power = 27 to the x power)

Exponential Functions

A.2: describe trends based on the interpretation of graphs, compare graphs using initial conditions and rates of change, and solve problems by modelling relationships graphically and algebraically;

A.2.2: describe trends based on given graphs, and use the trends to make predictions or justify decisions (e.g., given a graph of the men’s 100-m world record versus the year, predict the world record in the year 2050 and state your assumptions; given a graph showing the rising trend in graduation rates among Aboriginal youth, make predictions about future rates)

Trends in Scatter Plots

A.2.3: recognize that graphs and tables of values communicate information about rate of change, and use a given graph or table of values for a relation to identify the units used to measure rate of change (e.g., for a distance–time graph, the units of rate of change are kilometres per hour; for a table showing earnings over time, the units of rate of change are dollars per hour)

Compound Interest

A.2.4: identify when the rate of change is zero, constant, or changing, given a table of values or a graph of a relation, and compare two graphs by describing rate of change (e.g., compare distance–time graphs for a car that is moving at constant speed and a car that is accelerating)

Direct and Inverse Variation

A.2.5: compare, through investigation with technology, the graphs of pairs of relations (i.e., linear, quadratic, exponential) by describing the initial conditions and the behaviour of the rates of change (e.g., compare the graphs of amount versus time for equal initial deposits in simple interest and compound interest accounts)

Exponential Functions

C: Geometry and Trigonometry

C.1: solve problems involving measurement and geometry and arising from real-world applications;

C.1.2: solve problems involving the areas of rectangles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

C.1.3: solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite figures, in situations arising from real-world applications

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

C.3: solve problems using primary trigonometric ratios of acute and obtuse angles, the sine law, and the cosine law, including problems arising from real-world applications, and describe applications of trigonometry in various occupations.

C.3.1: solve problems in two dimensions using metric or imperial measurements, including problems that arise from real-world applications (e.g., surveying, navigation, building construction), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios, and of acute triangles using the sine law and the cosine law

Sine, Cosine, and Tangent Ratios

C.3.5: gather, interpret, and describe information about applications of trigonometry in occupations, and about college programs that explore these applications

Sine, Cosine, and Tangent Ratios

D: Data Management

D.1: collect, analyse, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data;

D.1.1: distinguish situations requiring one-variable and two-variable data analysis, describe the associated numerical summaries (e.g., tally charts, summary tables) and graphical summaries (e.g., bar graphs, scatter plots), and recognize questions that each type of analysis addresses (e.g., What is the frequency of a particular trait in a population? What is the mathematical relationship between two variables?)

Box-and-Whisker Plots
Least-Squares Best Fit Lines
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

D.1.4: create a graphical summary of two-variable data using a scatter plot (e.g., by identifying and justifying the dependent and independent variables; by drawing the line of best fit, when appropriate), with and without technology

Graphing Skills
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

D.1.6: describe possible interpretations of the line of best fit of a scatter plot (e.g., the variables are linearly related) and reasons for misinterpretations (e.g., using too small a sample; failing to consider the effect of outliers; interpolating from a weak correlation; extrapolating nonlinearly related data)

Solving Using Trend Lines

D.1.7: determine whether a linear model (i.e., a line of best fit) is appropriate given a set of two-variable data, by assessing the correlation between the two variables (i.e., by describing the type of correlation as positive, negative, or none; by describing the strength as strong or weak; by examining the context to determine whether a linear relationship is reasonable)

Least-Squares Best Fit Lines

D.2: demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

D.2.3: interpret statistics presented in the media (e.g., the UN’s finding that 2% of the world’s population has more than half the world’s wealth, whereas half the world’s population has only 1% of the world’s wealth), and explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view (e.g., by making a general statement based on a weak correlation or an assumed cause-and- effect relationship; by starting the vertical scale on a graph at a value other than zero; by making statements using general population statistics without reference to data specific to minority groups)

Polling: City

D.2.4: assess the validity of conclusions presented in the media by examining sources of data, including Internet sources (i.e., to determine whether they are authoritative, reliable, unbiased, and current), methods of data collection, and possible sources of bias (e.g., sampling bias, non-response bias, a bias in a survey question), and by questioning the analysis of the data (e.g., whether there is any indication of the sample size in the analysis) and conclusions drawn from the data (e.g., whether any assumptions are made about cause and effect)

Polling: City

Correlation last revised: 1/22/2020

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