Gizmos for Nova Scotia - Mathematics: Pre-Calculus: Grade 11 (Mathematics Curriculum adopted 2022)

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

AN: : Algebra and Number

AN01: : Demonstrate an understanding of the absolute value of real numbers.

AN01.01: : Determine the distance of two real numbers of the form plus or minus a, a is an element of R, from 0 on a number line, and relate this to the absolute value of a (|a|).

AN01.02: : Determine the absolute value of a positive or negative real number.

AN01.05: : Compare and order the absolute values of real numbers in a given set.

AN02: : Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.

AN02.02: : Express an entire radical with a numerical radicand as a mixed radical.

AN02.04: : Perform one or more operations to simplify radical expressions with numerical or variable radicands.

AN02.05: : Rationalize the denominator of a radical expression with monomial or binomial denominators.

AN03: : Solve problems that involve radical equations (limited to square roots).

AN.03.02: : Determine the roots of a radical equation algebraically, and explain the process used to solve the equation.

AN.04: : Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

AN.04.02: : Explain why a given value is non-permissible for a given rational expression.

AN.04.03: : Determine the non-permissible values for a rational expression.

T: : Trigonometry

T01: : Demonstrate an understanding of angles in standard position [0° to 360°].

T01.02: : Determine the reference angle for an angle in standard position.

T01.03: : Explain, using examples, how to determine the angles from 0° to 360° that have the same reference angle as a given angle.

T01.04: : Illustrate, using examples, that any angle from 90° to 360° is the reflection in the x-axis and/or the y-axis of its reference angle.

T01.05: : Determine the quadrant in which a given angle in standard position terminates.

T01.07: : Illustrate, using examples, that the points P(x, y), P(-x, y), P(-x, -y), and P(x, -y) are points on the terminal sides of angles in standard position that have the same reference angle.

T02: : Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position.

T02.02: : Determine the value of sin theta, cos theta, or tan theta, given any point P(x, y) on the terminal arm of angle theta.

T02.04: : Determine the sign of a given trigonometric ratio for a given angle, without the use of technology, and explain.

T02.06: : Determine the exact value of the sine, cosine, or tangent of a given angle with a reference angle of 30°, 45°, or 60°.

T02.07: : Describe patterns in and among the values of the sine, cosine, and tangent ratios for angles from 0° to 360°.

T02.08: : Sketch a diagram to represent a problem.

T02.09: : Solve a contextual problem, using trigonometric ratios.

T03: : Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

T03.02: : Describe the relationship among different systems of angle measurement, with emphasis on radians and degrees.

T03.05: : Express the measure of an angle in radians (exact value or decimal approximation), given its measure in degrees.

T03.06: : Express the measure of an angle in degrees, given its measure in radians (exact value or decimal approximation).

T03.09: : Explain the relationship between the radian measure of an angle in standard position and the length of the arc cut on a circle of radius r, and solve problems based upon that relationship.

T04: : Develop and apply the equation of the unit circle.

T04.01: : Derive the equation of the unit circle from the Pythagorean theorem.

T04.02: : Describe the six trigonometric ratios, using a point P(x, y) that is the intersection of the terminal arm of an angle and the unit circle.

T04.03: : Generalize the equation of a circle with centre (0, 0) and radius r.

RF: : Relations and Functions

RF01: : Factor polynomial expressions of the form ax^2 + bx + c, a not equal to 0; (a^2)(x^2) - (b^2)(y^2), a not equal to 0, b not equal to 0; a[f(x)]^2 + b[f(x)] + c, a not equal to 0; a^2[f(x)]^2 - b^2[g(y)]^2, a not equal to 0, b not equal to 0; where a, b, and c are rational numbers.

RF01.01: : Factor a given polynomial expression that requires the identification of common factors.

RF01.03: : Factor a given polynomial expression of the form ax^2 + bx + c, a not equal to 0, and (a^2)(x^2) - (b^2)(y^2), a not equal to 0.

RF02: : Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.

RF02.01: : Create a table of values for y = |f(x)|, given a table of values for y = f(x).

RF02.03: : Sketch the graph of y = |f(x)|; state the intercepts, domain, and range; and explain the strategy used.

RF02.04: : Solve an absolute value equation graphically, with or without technology.

RF02.05: : Solve, algebraically, an equation with a single absolute value, and verify the solution.

RF02.06: : Explain why the absolute value equation |f(x)| < 0 has no solution.

RF02.08: : Solve a problem that involves an absolute value function.

RF03: : Analyze quadratic functions of the form and determine the vertex, domain and range, direction of opening, axis of symmetry, and x- and y-intercepts.

RF03.01: : Explain why a function given in the form y = a(x - p)^2 + q is a quadratic function.

RF03.02: : Compare the graphs of a set of functions of the form y = ax^2 to the graph of y = x^2, and generalize, using inductive reasoning, a rule about the effect of a.

RF03.03: : Compare the graphs of a set of functions of the form y = x^2 + q to the graph of y = x^2, and generalize, using inductive reasoning, a rule about the effect of q.

RF03.04: : Compare the graphs of a set of functions of the form y = (x – p)^2 to the graph of y = x^2 , and generalize, using inductive reasoning, a rule about the effect of p.

RF03.05: : Determine the coordinates of the vertex for a quadratic function of the form y = a(x - p)^2 + q, and verify with or without technology.

RF03.06: : Generalize, using inductive reasoning, a rule for determining the coordinates of the vertex for quadratic functions of the form y = a(x - p)^2 + q.

RF03.07: : Sketch the graph of y = a(x - p)^2, using transformations, and identify the vertex, domain and range, direction of opening, axis of symmetry, and x-intercepts and y-intercepts.

RF04: : Analyze quadratic functions of the form y = ax^2 + bx + c to identify characteristics of the corresponding graph, including vertex, domain and range, direction of opening, axis of symmetry, x-intercept and y-intercept, and to solve problems.

RF04.02: : Write a quadratic function given in the form y = ax^2 + bx + c as a quadratic function in the form y = a(x – p)^2 + q by completing the square.

RF04.04: : Determine the characteristics of a quadratic function given in the form y = ax^2 + bx + c, and explain the strategy used.

RF04.05: : Sketch the graph of a quadratic function given in the form y = ax^2 + bx + c.

RF04.06: : Verify, with or without technology, that a quadratic function in the form y = ax^2 + bx + c represents the same function as a given quadratic function in the form y = a(x – p)^2 + q.

RF04.07: : Write a quadratic function that models a given situation, and explain any assumptions made.

RF04.08: : Solve a problem, with or without technology, by analyzing a quadratic function.

RF05: : Solve problems that involve quadratic equations.

RF05.01: : Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function, and the x-intercepts of the graph of the quadratic function.

RF05.02: : Derive the quadratic formula, using deductive reasoning.

RF05.03: : Solve a quadratic equation of the form ax^2 + bx + c = 0 by using strategies such as determining square roots, factoring, completing the square, applying the quadratic formula, or graphing its corresponding function.

RF05.04: : Select a method for solving a quadratic equation, justify the choice, and verify the solution.

RF05.05: : Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots, and relate the number of zeros to the graph of the corresponding quadratic function.

RF05.07: : Solve a problem by analyzing a quadratic equation or determining and analyzing a quadratic equation.

RF07: : Solve problems that involve linear and quadratic inequalities in two variables.

RF07.01: : Explain, using examples, how test points can be used to determine the solution region that satisfies an inequality.

RF07.02: : Explain, using examples, when a solid or broken line should be used in the solution for an inequality.

RF07.03: : Sketch, with or without technology, the graph of a linear or quadratic inequality.

RF07.04: : Solve a problem that involves a linear or quadratic inequality.

RF09: : Analyze arithmetic sequences and series to solve problems.

RF09.03: : Derive a rule for determining the general term of an arithmetic sequence.

RF09.04: : Describe the relationship between arithmetic sequences and linear functions.

RF09.05: : Determine t sub 1, d, n, or t sub n in a problem that involves an arithmetic sequence.

RF09.08: : Solve a problem that involves an arithmetic sequence or series.

RF10: : Analyze geometric sequences and series to solve problems.

RF10.03: : Derive a rule for determining the general term of a geometric sequence.

RF10.04: : Determine t sub 1, r, n, or t sub n in a problem that involves a geometric sequence.

RF10.09: : Solve a problem that involves a geometric sequence or series.

RF11.01: : Compare the graph of y = 1/f(x) to the graph of y = f(x).

Correlation last revised: 3/28/2023

Nova Scotia - Mathematics: Pre-Calculus: Grade 11

Mathematics Curriculum | Adopted: 2022

AN: : Algebra and Number

T: : Trigonometry

RF: : Relations and Functions