Gizmos for Alberta - Mathematics: Math 31 (Program of Studies adopted 1995)

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.

CGLE: : Course General Learner Expectations

CGLE.2: : Measurement and Geometry: Mastery of course expectations enables students to demonstrate the conceptual underpinnings of calculus to determine limits, derivatives, integrals, rates of change and averages, using geometrical representations.

CGLE.2.CUO: : Conceptual Understanding Outcomes - Students will demonstrate understanding of the concepts of Mathematics 31, by:

CGLE.2.CUO.1: : describing the relationships among functions after performing translations, reflections, stretches and compositions on a variety of functions

CGLE.2.CUO.2: : linking displacement, velocity and acceleration of an object moving in a straight line with nonuniform velocity.

CGLE.2.PKO: : Procedural Knowledge Outcomes - Students will demonstrate competence in the procedures of Mathematics 31, by:

CGLE.2.PKO.1: : drawing the graphs of functions by applying transformations to the graphs of known functions

CGLE.2.PKO.2: : calculating the displacement, velocity and acceleration of an object moving in a straight line with nonuniform velocity.

CGLE.4: : Calculus of Derivatives and Integrals: Mastery of course expectations enables students to determine limits, derivatives, integrals and rates of change.

CGLE.4.PKO: : Procedural Knowledge Outcomes - Students will demonstrate competence in the procedures of Mathematics 31, by:

CGLE.4.PKO.1: : computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods

CGLE.4.PSCO: : Problem-Solving Contexts Outcomes - Students will demonstrate problem-solving skills in Mathematics 31, by:

CGLE.4.PSCO.3: : connecting a derivative and the appropriate rate of change, and using this connection to relate complicated rates of change to simpler ones.

RC: : Required Components

RC.PCL: : Precalculus and Limits

RC.PCL.GLE: : General Learner Expectations

RC.PCL.GLE.1: : Students are expected to understand that functions, as well as variables, can be combined, using operations, such as addition and multiplication, and demonstrate this, by:

RC.PCL.GLE.1.3: : expressing final algebraic and trigonometric answers in a variety of equivalent forms, with the form chosen to be the most suitable form for the task at hand

RC.PCL.GLE.1.4: : constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable.

RC.PCL.GLE.2: : Students are expected to understand that functions can be transformed, and these transformations can be represented algebraically and geometrically, and demonstrate this, by:

RC.PCL.GLE.2.1: : describing the relationship among functions after performing translations, reflections, stretches and compositions on a variety of functions

RC.PCL.GLE.2.2: : drawing the graphs of functions by applying transformations to the graphs of known functions

RC.PCL.GLE.2.3: : expressing final algebraic and trigonometric answers in a variety of equivalent forms, with the form chosen to be the most suitable form for the task at hand

RC.PCL.GLE.2.4: : constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable.

RC.PCL.GLE.3: : Students are expected to understand that final answers may be expressed in different equivalent forms, and demonstrate this, by:

RC.PCL.GLE.3.2: : expressing final algebraic and trigonometric answers in a variety of equivalent forms, with the form chosen to be the most suitable form for the task at hand.

RC.PCL.CUO: : Conceptual Understanding Outcomes

RC.PCL.CUO.1: : Students will demonstrate conceptual understanding of the algebra of functions, by:

RC.PCL.CUO.1.3: : expressing the sum, product, difference and quotient, algebraically and graphically, given any two functions

RC.PCL.CUO.1.5: : illustrating the solution sets for linear, quadratic and absolute value inequalities

RC.PCL.CUO.1.5.a: : |P(x)| is greater than or equal to a

RC.PCL.CUO.1.5.b: : |P(x)| is less than or equal to a

RC.PCL.CUO.1.5.c: : ax² + bx + c is greater than or equal to d

RC.PCL.CUO.2: : Students will demonstrate conceptual understanding of the transformation of functions, by:

RC.PCL.CUO.2.1: : describing the similarities and differences between the graphs of y = f(x) and y = af[k(x + c)] + d, where a, k, c and d are real numbers

RC.PCL.CUO.2.2: : describing the effects of the reflection of the graphs of algebraic and trigonometric functions across any of the lines y = x, y = 0, or x = 0

RC.PCL.CUO.2.3: : describing the effects of the parameters a, b, c and d on the trigonometric function f(x) = a sin [b(x + c)] + d

RC.PCL.CUO.2.4: : describing the relationship between parallel and perpendicular lines

RC.PCL.CUO.2.6: : linking two problem conditions to a system of two equations for two unknowns.

RC.PCL.CUO.3: : Students will demonstrate conceptual understanding of equivalent forms, by:

RC.PCL.CUO.3.1: : describing what it means for two algebraic or trigonometric expressions to be equivalent.

RC.PCL.CUO.4: : Students will demonstrate conceptual understanding of limits and limit theorems, by:

RC.PCL.CUO.4.4: : explaining, and giving examples of, continuous and discontinuous functions

RC.PCL.PKO: : Procedural Knowledge Outcomes

RC.PCL.PKO.1: : Students will demonstrate competence in the procedures associated with the algebra of functions, by:

RC.PCL.PKO.1.2: : finding the sum, difference, product, quotient and composition of functions

RC.PCL.PKO.1.3: : solving inequalities of the types

RC.PCL.PKO.1.3.a: : |P(x)| is greater than or equal to a

RC.PCL.PKO.1.3.c: : |P(x)| is less than or equal to a

RC.PCL.PKO.1.3.e: : ax² + bx + c is greater than or equal to d

RC.PCL.PKO.1.4: : using the following trigonometric identities to simplify expressions and solve equations, express sums and differences as products, and rewrite expressions in a variety of equivalent forms.

RC.PCL.PKO.1.4.a: : primary and reciprocal ratio

RC.PCL.PKO.1.4.c: : sum and difference sin (A ± B) cos (A ± B)

RC.PCL.PKO.1.4.d: : Pythagorean

RC.PCL.PKO.2: : Students will demonstrate competence in the procedures associated with the transformation of functions, by:

RC.PCL.PKO.2.1: : sketching the graph of, and describing algebraically, the effects of any translation, reflection or dilatation on any of the following functions or their inverses:

RC.PCL.PKO.2.1.a: : linear, quadratic or cubic polynomial

RC.PCL.PKO.2.1.b: : absolute value

RC.PCL.PKO.2.1.c: : reciprocal

RC.PCL.PKO.2.1.d: : exponential

RC.PCL.PKO.2.2: : sketching and describing, algebraically, the effects of any combination of translation, reflection or dilatation on the following functions:

RC.PCL.PKO.2.2.a: : f(x) = a sin [b(x + c)] + d

RC.PCL.PKO.2.2.b: : f(x) = a cos [b(x + c)] + d

RC.PCL.PKO.2.3: : finding the equation of a line, given any two conditions that serve to define it

RC.PCL.PKO.2.4: : solving systems of linear–linear, linear–quadratic or quadratic–quadratic equations.

RC.PCL.PKO.3: : Students will demonstrate competence in the procedures associated with the construction of equivalent forms, by:

RC.PCL.PKO.3.1: : factoring expressions with integral and rational exponents, using a variety of techniques

RC.PCL.PKO.3.2: : rationalizing expressions containing a numerator or a denominator that contains a radical

RC.PCL.PSCO: : Problem-Solving Contexts Outcomes

RC.PCL.PSCO.1: : Students will demonstrate problem-solving skills, by:

RC.PCL.PSCO.1.1: : modelling problem situations, using sums, differences, products and quotients of functions

RC.PCL.PSCO.1.2: : investigating the connections between the algebraic form of a function f(x) and the symmetries of its graph.

RC.PCL.PSCO.1.3: : translating problem conditions into equation or inequality form.

RC.DT: : Derivatives and Derivative Theorems

RC.DT.GLE: : General Learner Expectations

RC.DT.GLE.1: : Students are expected to understand that the derivative of a function is a limit that can be found, using first principles, and demonstrate this, by:

RC.DT.GLE.1.2: : connecting the derivative with a particular limit, and expressing this limit in situations like secant and tangent lines to a curve

RC.DT.GLE.1.3: : computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods.

RC.DT.GLE.2: : Students are expected to understand that derivatives of more complicated functions can be found from the derivatives of simpler functions, using derivative theorems, and demonstrate this, by:

RC.DT.GLE.2.4: : computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods.

RC.DT.GLE.3: : Students are expected to understand that trigonometric functions have derivatives, and these derivatives obey the same derivative theorems as algebraic functions, and demonstrate this, by:

RC.DT.GLE.3.4: : computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods.

RC.DT.CUO: : Conceptual Understanding Outcomes

RC.DT.CUO.1: : Students will demonstrate conceptual understanding of derivatives, by:

RC.DT.CUO.1.3: : explaining how the derivative is connected to the slope of the tangent line

RC.DT.CUO.2: : Students will demonstrate conceptual understanding of derivative theorems, by:

RC.DT.CUO.2.7: : illustrating second, third and higher derivatives of algebraic functions

RC.DT.CUO.2.8: : describing the second derivative geometrically.

RC.DT.CUO.3: : Students will demonstrate conceptual understanding of the derivatives of trigonometric functions, by:

RC.DT.CUO.3.1: : demonstrating that the three primary trigonometric functions have derivatives at all points where the functions are defined

RC.DT.PKO: : Procedural Knowledge Outcomes

RC.DT.PKO.1: : Students will demonstrate competence in the procedures associated with derivatives, by:

RC.DT.PKO.1.1: : finding the slopes and equations of tangent lines at given points on a curve, using the definition of the derivative

RC.DT.PKO.1.3: : using the definition of the derivative to determine the derivative of f(x) = x^n where n is a positive integer

RC.DT.PKO.2: : Students will demonstrate competence in the procedures associated with derivative theorems, by:

RC.DT.PKO.2.1: : finding the derivative of a polynomial, power, product or quotient function

RC.DT.PKO.2.5: : finding the slope and equations of tangent lines at given points on a curve

RC.DT.PKO.2.6: : finding the second and third derivatives of functions.

RC.DT.PKO.3: : Students will demonstrate competence in the procedures associated with derivatives of trigonometric functions, by:

RC.DT.PKO.3.1: : calculating the derivatives of the three primary and three reciprocal trigonometric functions

RC.DT.PKO.3.4: : using the derivative of a trigonometric function to calculate its slope at a point, and the equation of the tangent at that point.

RC.DT.PSCO: : Problem-Solving Contexts Outcomes

RC.DT.PSCO.1: : Students will demonstrate problem-solving skills, by:

RC.DT.PSCO.1.1: : deriving f’(x) for polynomial functions up to the third degree, using the definition of the derivative

RC.DT.PSCO.1.9: : using the definition of the derivative to find the derivative for the sine and cosine functions

RC.AD: : Applications of Derivatives

RC.AD.GLE: : General Learner Expectations

RC.AD.GLE.1: : Students are expected to understand that calculus is a powerful tool in determining maximum and minimum points and in sketching of curves, and demonstrate this, by:

RC.AD.GLE.1.1: : relating the zeros of the derivative function to the critical points on the original curve

RC.AD.GLE.2: : Students are expected to understand that complicated rates of change can be related to simpler rates, using the chain rule, and demonstrate this, by:

RC.AD.GLE.2.5: : expressing the connection between a derivative and the appropriate rate of change, and using this connection to relate complicated rates of change to simpler ones.

RC.AD.CUO: : Conceptual Understanding Outcomes

RC.AD.CUO.1: : Students will demonstrate conceptual understanding of maxima and minima, by:

RC.AD.CUO.1.1: : identifying, from a graph sketch, locations at which the first and second derivative are zero

RC.AD.CUO.1.3: : explaining how the sign of the first derivative indicates whether or not a curve is rising or falling; and by explaining how the sign of the second derivative indicates the concavity of the graph

RC.AD.CUO.1.4: : illustrating, by examples, that a first derivative of zero is one possible condition for a maximum or a minimum to occur

RC.AD.PKO: : Procedural Knowledge Outcomes

RC.AD.PKO.1: : Students will demonstrate competence in the procedures associated with maxima and minima, by:

RC.AD.PKO.1.4: : determining vertical, horizontal and oblique asymptotes, and domains and ranges of a function

RC.AD.PSCO: : Problem-Solving Contexts Outcomes

RC.AD.PSCO.1: : Students will demonstrate problem-solving skills, by:

RC.AD.PSCO.1.3: : calculating maxima and minima for such quantities as volumes, areas, perimeters and costs

RC.AD.PSCO.1.6: : constructing a mathematical model to represent a problem in economics, and using the model to find maximum profits or minimum cost

RC.ITA: : Integrals, Integral Theorems and Integral Applications

RC.ITA.CUO: : Conceptual Understanding Outcomes

RC.ITA.CUO.2: : Students will demonstrate conceptual understanding of area limits, by:

RC.ITA.CUO.2.1: : defining the area under a curve as a limit of the sums of the areas of rectangles

RC.ITA.CUO.2.2: : establishing the existence of upper and lower bounds for the area under a curve

RC.ITA.PKO: : Procedural Knowledge Outcomes

RC.ITA.PKO.2: : Students will demonstrate competence in the procedures associated with area limits, by:

RC.ITA.PKO.2.1: : sketching the area under a curve (polynomials, rational, trigonometric) over a given interval, and approximating the area as the sum of individual rectangles.

EC: : Elective Components

EC.A: : Calculus of Exponential and Logarithmic Functions

EC.A.CUO: : Conceptual Understanding Outcomes

EC.A.CUO.1: : Students will demonstrate conceptual understanding of the calculus of exponential and logarithmic functions, by:

EC.A.CUO.1.1: : defining exponential and logarithmic functions as inverse functions

EC.B: : Numerical Methods

EC.B.GLE: : General Learner Expectations

EC.B.GLE.1: : Students are expected to understand that many limits, derivatives, equation roots and definite integrals can be found numerically, and demonstrate this, by:

EC.B.GLE.1.3: : computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods

EC.B.CUO: : Conceptual Understanding Outcomes

EC.B.CUO.1: : Students will demonstrate conceptual understanding of the principles of numerical analysis, by:

EC.B.CUO.1.5: : describing the basis of a limit, derivative, equation root or integral procedure in geometric terms

EC.B.PKO: : Procedural Knowledge Outcomes

EC.B.PKO.1: : Students will demonstrate competence in the procedures associated with numerical methods, by:

EC.B.PKO.1.2: : calculating the numerical value of the derivative at a point on a curve, whether or not there is a defining formula for the curve

EC.B.PKO.1.4: : calculating the upper and lower Riemann sums for a definite integral

EC.C: : Volumes of Revolution

EC.C.PSCO: : Problem-Solving Contexts Outcomes

EC.C.PSCO.1: : Students will demonstrate problem-solving skills, in one of the following, by:

EC.C.PSCO.1.1: : deriving formulas for the volume of a cylinder, cone and sphere

EC.D: : Applications of Calculus to Physical Sciences and Engineering

EC.D.PSCO: : Problem-Solving Contexts Outcomes

EC.D.PSCO.1: : Students will demonstrate problem-solving skills, in one of the following, by:

EC.D.PSCO.1.1: : determining the half-life, the decay rate, and the activity as a function of time for a radioisotope

EC.D.PSCO.1.2: : analyzing the motion and energy in an oscillating spring system (Hooke’s law)

EC.D.PSCO.1.4: : determining the moment of inertia for rigid bodies

EC.D.PSCO.1.5: : determining the centre of mass for individual bodies and for systems of bodies

EC.E: : Applications of Calculus to Biological Sciences

EC.E.CUO: : Conceptual Understanding Outcomes

EC.E.CUO.1: : Students will demonstrate conceptual understanding of the links between calculus and the biological sciences, by:

EC.E.CUO.1.1: : defining exponential and logarithmic functions as inverse functions

EC.F: : Applications of Calculus to Business and Economics

EC.F.PKO: : Procedural Knowledge Outcomes

EC.F.PKO.1: : Students will demonstrate competence in the procedures associated with the application of calculus to business and economics, by:

EC.F.PKO.1.1: : sketching polynomial, exponential and trigonometric functions of one variable

EC.F.PKO.1.2: : using a given revenue, profit or cost function to calculate and justify optimum values

EC.F.PKO.1.3: : finding the maximum of a revenue or profit function that is expressed as a function of price or number sold

EC.F.PSCO: : Problem-Solving Contexts Outcomes

EC.F.PSCO.1: : Students will demonstrate problem-solving skills, in one or both of the following, by:

EC.F.PSCO.1.1: : determining a revenue, profit or cost function from a problem situation that can be modeled, using polynomial functions

Correlation last revised: 11/11/2022

Alberta - Mathematics: Math 31

Program of Studies | Adopted: 1995

CGLE: : Course General Learner Expectations

RC: : Required Components

EC: : Elective Components