Gizmos for Nova Scotia - Mathematics: Pre-Calculus: Grade 12 (Mathematics Curriculum adopted 2022)

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

T: : Trigonometry

T03: : Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.

T03.01: : Determine, with technology, the approximate value of a trigonometric ratio for any angle with a measure expressed in either degrees or radians.

T03.02: : Determine, using a unit circle or reference triangle, the exact value of a trigonometric ratio for angles expressed in degrees that are multiples of 0°, 30°, 45°, 60°, or 90°, or for angles expressed in radians that are multiples of 0, pi/6, pi/4, pi/3, or pi/2, and explain the strategy.

T03.03: : Determine, with or without technology, the measures, in degrees or radians, of the angles in a specified domain, given the value of a trigonometric ratio.

T03.06: : Determine the exact values of the other trigonometric ratios, given the value of one trigonometric ratio in a specified domain.

T03.07: : Sketch a diagram to represent a problem that involves trigonometric ratios.

T03.08: : Solve a problem, using trigonometric ratios.

T04: : Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.

T04.01: : Sketch, with or without technology, the graph of y = sin x, y = cos x, or y = tan x.

T04.02: : Determine the characteristics (amplitude, asymptotes, domain, period, range, and zeros) of the graph of y = sin x, y = cos x, or y = tan x.

T04.03: : Determine how varying the value of a affects the graphs of y = a sin x and y = a cos x.

T04.04: : Determine how varying the value of d affects the graphs of y = sin x + d and y = cos x + d.

T04.05: : Determine how varying the value of c affects the graphs of y = sin (x + c) and y = cos (x + c).

T04.06: : Determine how varying the value of b affects the graphs of y = sin bx and y = cos bx.

T04.07: : Sketch, without technology, graphs of the form y = a sin b(x - c) + d or y = a cos b(x - c) + d, using transformations, and explain the strategies.

T04.08: : Determine the characteristics (amplitude, asymptotes, domain, period, phase shift, range and zeros) of the graph of a trigonometric function of the form y = a sin b(x - c) + d or y = a cos b(x - c) + d.

T04.09: : Determine the values of a, b, c, and d for functions of the form y = a sin b(x - c) + d or y = a cos b(x - c) + d that correspond to a given graph, and write the equation of the function.

T05: : Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.

T05.02: : Determine, algebraically, the solution of a trigonometric equation, stating the solution in exact form, when possible.

T06: : Prove trigonometric identities, using reciprocal identities, quotient identities, Pythagorean identities, sum or difference identities, or double-angle identities.

T06.06: : Prove, algebraically, that a trigonometric identity is valid.

T06.07: : Determine, using the sum, difference, and double-angle identities, the exact value of a trigonometric ratio.

RF: : Relations and Functions

RF01: : Demonstrate an understanding of operations on, and compositions of, functions.

RF01.02: : Write the equation of a function that is the sum, difference, product, or quotient of two or more functions, given their equations.

RF02: : Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.

RF02.01: : Compare the graphs of a set of functions of the form y - k = f(x) to the graph of y = f(x) and generalize, using inductive reasoning, a rule about the effect of k.

RF02.02: : Compare the graphs of a set of functions of the form y = f(x - h) to the graph of y = f(x) and generalize, using inductive reasoning, a rule about the effect of h.

RF02.03: : Compare the graphs of a set of functions of the form y - k = f(x - h) to the graph of y = f(x) and generalize, using inductive reasoning, a rule about the effects of h and k.

RF02.05: : Write the equation of a function whose graph is a vertical and/or horizontal translation of the graph of the function y = f(x).

RF03: : Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.

RF03.01: : Compare the graphs of a set of functions of the form y = af(x) to the graph of y = f(x) and generalize, using inductive reasoning, a rule about the effect of a.

RF03.02: : Compare the graphs of a set of functions of the form y = f(bx) to the graph of y = f(x) and generalize, using inductive reasoning, a rule about the effect of b.

RF03.03: : Compare the graphs of a set of functions of the form y = af(bx) to the graph of y = f(x) and generalize, using inductive reasoning, a rule about the effects of a and b.

RF03.05: : Write the equation of a function, given its graph which is a vertical and/or horizontal stretch of the graph of the function y = f(x).

RF04: : Apply translations and stretches to the graphs and equations of functions.

RF04.01: : Sketch the graph of the function y - k = af[b(x - h)] for given values of a, b, h, and k, given the graph of the function y = f(x), where the equation of y = f(x) is not given.

RF05: : Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections in the: x-axis, y-axis, and the line y = x.

RF05.01: : Generalize the relationship between the coordinates of an ordered pair and the coordinates of the corresponding ordered pair that results from a reflection in the x-axis, the y-axis, or the line y = x.

RF05.03: : Generalize, using inductive reasoning, and explain rules for the reflection of the graph of the function y = f(x) in the x-axis, the y-axis, or the line y = x.

RF06: : Demonstrate an understanding of inverses of relations.

RF06.03: : Sketch the graph of the inverse relation, given the graph of a relation.

RF06.07: : Explain the relationship between the domains and ranges of a relation and its inverse.

RF07: : Demonstrate an understanding of logarithms.

RF07.01: : Explain the relationship between logarithms and exponents.

RF07.02: : Express a logarithmic expression as an exponential expression and vice versa.

RF07.03: : Determine, without technology, the exact value of a logarithm, such as log base 2 of 8 and ln e.

RF09: : Graph and analyze exponential and logarithmic functions.

RF09.01: : Sketch, with or without technology, a graph of an exponential function of the form y = a^x , a > 0.

RF09.02: : Identify the characteristics of the graph of an exponential function of the form y = a^x , a > 0, including the domain, range, horizontal asymptote and intercepts, and explain the significance of the horizontal asymptote.

RF09.03: : Sketch the graph of an exponential function by applying a set of transformations to the graph of y = a^x , a > 0, and state the characteristics of the graph.

RF09.04: : Sketch, with or without technology, the graph of a logarithmic function of the form y = log base b of x, b > 1.

RF09.05: : Identify the characteristics of the graph of a logarithmic function of the form y = log base b of x, b > 1, including the domain, range, vertical asymptote and intercepts, and explain the significance of the vertical asymptote.

RF09.06: : Sketch the graph of a logarithmic function by applying a set of transformations to the graph of y = log base b of x, b > 1, and state the characteristics of the graph.

RF09.07: : Demonstrate, graphically, that a logarithmic function and an exponential function with the same base are inverses of each other.

RF10.05: : Solve a problem that involves exponential growth or decay.

RF10.06: : Solve a problem that involves the application of exponential equations to loans, mortgages, and investments.

RF10.08: : Solve a problem by modeling a situation with an exponential or a logarithmic equation.

RF11: : Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree less than or equal to 5 with integral coefficients).

RF11.1: : Explain how long division of a polynomial expression by a binomial expression of the form x - a , x is an element of Z is related to synthetic division.

RF11.2: : Divide a polynomial expression by a binomial expression of the form x - a, x is an element of Z using long division or synthetic division.

RF11.4: : Explain the relationship between the remainder when a polynomial expression is divided by x - a, x is an element of Z and the value of the polynomial expression at x = a (remainder theorem).

RF12: : Graph and analyze polynomial functions (limited to polynomial functions of degree less than or equal to 5).

RF12.02: : Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

RF12.03: : Generalize rules for graphing polynomial functions of odd or even degree.

RF12.04: : Explain the relationship among the zeros of a polynomial function, the roots of the corresponding polynomial equation, and the x-intercepts of the graph of the polynomial function.

RF12.05: : Explain how the multiplicity of a zero of a polynomial function affects the graph.

RF12.06: : Sketch, with or without technology, the graph of a polynomial function.

RF13: : Graph and analyze radical functions (limited to functions involving one radical).

RF13.01: : Sketch the graph of the function y = the square root of x using a table of values, and state the domain and range.

RF13.02: : Sketch the graph of the function y - k = a times the square root of [b(x - h)] by applying transformations to the graph of the function y = the square root of x and state the domain and range.

RF13.03: : Sketch the graph of the function y = the square root of f(x) given the graph of the function y = f(x) and explain the strategies used.

RF13.06: : Determine, graphically, an approximate solution of a radical equation.

RF14: : Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).

RF14.01: : Graph, with or without technology, a rational function.

RF14.03: : Explain the behaviour of the graph of a rational function for values of the variable near a non-permissible value.

RF14.04: : Determine if the graph of a rational function will have an asymptote or a hole for a non-permissible value.

RF14.06: : Describe the relationship between the roots of a rational equation and the x-intercepts of the graph of the corresponding rational function.

Correlation last revised: 3/27/2023

Nova Scotia - Mathematics: Pre-Calculus: Grade 12

Mathematics Curriculum | Adopted: 2022

T: : Trigonometry

RF: : Relations and Functions