Algebra II (PAP) Standards
*some units may not be included based prior knowledge of the students
Unit 5: Matrices
5.1 I can add and subtract matrices.
5.2 I can multiply matrices
5.3 I can use addition, subtraction, and multiplication of matrices to solve real-world problems.
5.4 I can calculate the determinant of 2x2 and 3x3 matrices
5.5 I can find the inverse of a 2x2 matrix.
5.6 I can solve systems of equations with 2 and 3 variables by using inverses of matrices or determinants.
5.7 I can use technology to perform operations on matrices, find determinants, and find inverses.
Unit 6: Graphing Systems of Linear Inequalities& Linear Programming
6.1 I can graph a system of linear inequalities in two variables with and without technology to find the solution set for the system.
6.2 I can solve linear programming problems by finding maximum and minimum values of a function over a region defined by linear inequalities.
Unit 7: Quadratics Analytical
7.1 I can multiply monomials.
7.2 I can multiply binomials
7.3 I can factor trinomials of the form ax2 + bx + c, including special forms.
7.4 I can solve quadratic equations by factoring.
7.5 I can solve quadratic equations using the quadratic formula
7.6 I can solve application problems involving quadratics.
7.7 I can use the discriminant to determine the number and type of roots for a given quadratic function.
7.8 I can solve quadratic equations with complex number systems.
7.9 I can identify complex numbers and write their conjugates.
7.10 I can add and subtract complex numbers.
7.11 I can multiply complex numbers.
7.12 I can simplify quotients of complex numbers.
Unit 8: Graphing Quadratic Functions.
8.1 I can identify quadratic functions and graphs.
8.2 I can graph quadratic functions in vertex form.
8.3 I can graph quadratic functions in standard form.
8.4 I can graph quadratic functions in intercept form.
8.5 I can determine the domain and range of quadratic functions.
8.6 I can solve quadratic systems graphically with and without technology.
8.7 I can solve quadratic systems algebraically with and without technology.
8.8 I can use transformations to draw the graph of quadratic functions.
8.9 I can explain the transformations of quadratic functions.
8.10 I can determine a quadratic function that fits a graph.
8.11 I can graph and analyze real-world problems involving quadratics.
8.12 I can graph a system of quadratic inequalities with and without technology to find the solution set to the system.
Unit 9: Polynomial Functions
9.1 I can classify polynomial expressions and equations.
9.2 I can evaluate and simplify polynomial expressions and equations.
9.3 I can factor polynomials using a variety of methods (factor theorems, synthetic division, long division, sums and differences of cubes, grouping.)
9.4 I can determine the number and type of rational zeroes for a polynomial function.
9.5 I can find all rational zeroes of a polynomial function.
9.6 I can recognize the connection among zeroes of a polynomial function, x-intercepts, factors of polynomials, and solutions of polynomial equations.
9.7 I can use technology to graph a polynomial function and approximate the zeroes, minimum, and maximum.
9.8 I can determine the domain and range of a polynomial function.
Unit10: Sequences and Series
10.1 I can differentiate between a sequence and a series.
10.2 I can find the nth term of an arithmetic sequence.
10.3 I can find the nth term of a geometric sequence.
10.4 I can find the sum of a finite arithmetic series.
10.5 I can find the sum of a finite geometric series.
10.6 I can write a rule for a sequence.
10.7 I can find the position of a given term of an arithmetic sequence.
10.8 I can find the position of a given term of a geometric sequence.
10.9 I can use sigma notation to express sums of sequences.
10.10 I can use sequences and series to solve real-world problems.
Unit 11: Radical Expressions and Equations
11.1 I can simplify radicals that have various indices.
11.2 I can add and subtract expressions containing radicals.
11.3 I can multiply, and divide expressions containing radicals.
11.4 I can use properties of roots and rational exponents to evaluate and simplify expressions.
11.5 I can rationalize denominators containing radicals and find the simplest common denominator.
11.6 I can solve equations containing nth roots or rational exponents.
11.7 I can solve radical equations and show how extraneous solutions may arise.
11.8 I can solve radical equations given a formula for a real-world situation.
11.9 I can graph radical functions with and without technology.
11.10 I can simplify radicals that have various indices.
11.11 I can add and subtract expressions containing radicals.
Unit 12: Rational Expressions and Equations
12.1 I can graph a rational function with and without technology.
12.2 I can find the vertical and horizontal asymptotes
12.3 I can simplify rational expressions
12.4 I can multiply and divide rational expressions.
12.5 I can add and subtract rational expressions.
12.6 I can solve rational equations.
12.7 I can use rational equations to solve real world problems.
Unit 13: Composition of Functions and Inverses
13.1 I can add and subtract functions
13.2 I can multiply and divide functions
13.3 I can perform the composition of functions.
13.4 I can find the inverse of functions.
13.5 I can determine the domain and range for the given function, the composition function, or the inverse function.
Unit 14: Exponential & Log Functions
14.1 I can graph exponential functions with and without technology.
14.2 I can graph logarithmic functions with and without technology.
14.3 I can convert exponential equations to logarithmic form.
14.4 I can convert logarithmic equations to exponential form.
14.5 I can apply the properties of logarithms.
14.6 I can solve logarithmic equations.
14.7 I can solve problems related exponential growth and decay.
Unit 15: Conic Sections
15.1 I can solve quadratic equations and inequalities by completing the square.
15.2 I can graph circles and their translations from given equations or characteristics with and without technology.
15.3 I can graph parabolas and their translations from given equations or characteristics with and without technology.
15.4 I can determine characteristics of circles from their equations and graphs.
15.5 I can determine characteristics of parabolas from their equations and graphs.
15.6 I can identify and write equations for circles from given characteristics and graphs.
15.7 I can identify and write equations for parabolas from given characteristics and graphs.
15.8 I can identify and write equations for ellipses from given characteristics and graphs.
15.9 I can identify and write equations for hyperbolas from given characteristics and graphs.
15.10 I can identify conic sections and their properties (e.g., parabola, circle, ellipse, hyperbolas) from their equations in standard form.
Unit 16: Right Triangle Trigonometry, Laws of Sines and Cosines
16.1 I can use sine, cosine, and tangent ratios to find the sides of right triangles
16.2 I can use sine, cosine, and tangent ratios to find the angles of right triangles
16.3 I can use sine, cosine, and tangent ratios to solve real-world problems including those using angles of elevation and angles of depression.
16.4 I can use the law of sines to find the lengths of sides and measures of angles of triangles in mathematical and real-world problems.
16.5 I can use Law of Cosines to find the lengths of sides and measures of angles of right triangles in mathematical and real-world problems.
Unit 17: Unit Circles & Trigonometric Identities
17.1 I can identify and draw angles in degrees and radian.
17.2 I can identify coterminal angles.
17.3 I can define the terminal and initial side of an angle on the unit circle.
17.4 I can convert between a radian measure and a degree measure.
17.5 I can find the side lengths of any special right triangle.
17.6 I can label coordinate points on the unit circle using special right triangle properties.
17.7 I can use the coordinate points on the unit circle to identify the sine and cosine values.
17.8 I can find the arc length of a sector of a circle.
17.9 I can find the tangent using sine and cosine.
17.10 I can apply the Pythagorean Theorem to derive the Pythagorean Identity: .
17.11 I can manipulate the basic trigonometric equation to evaluate other trigonometric functions.
Unit 18: Graphing Trigonometric Functions
18.1 I can identify and draw angles in degrees and radian.
18.2 I can identify coterminal angles.
18.3 I can define the terminal and initial side of an angle on the unit circle.
18.4 I can convert between a radian measure and a degree measure.
18.5 I can find the side lengths of any special right triangle.
18.6 I can label coordinate points on the unit circle using special right triangle properties.
18.7 I can use the coordinate points on the unit circle to identify the sine and cosine values.
18.8 I can find the tangent using sine and cosine.
18.9 I can apply the Pythagorean Theorem to derive the Pythagorean Identity.
18.10 I can manipulate the basic trigonometric equation to evaluate other trigonometric functions.
Unit 19 Probability
19.1 I can use the Fundamental Counting Principle to count the number of ways an event can happen.
19.2 I can find combinations for an event.
19.3 I can find permutations for an event.
19.4 I can find the probability of mutually exclusive and non-mutually exclusive events.
19.5 I can find the probability of independent and dependent events.
19.6 I can use unions, intersections, and complements to find probabilities.
19.7 I can solve problems involving conditional probability.
5.1 I can add and subtract matrices.
5.2 I can multiply matrices
5.3 I can use addition, subtraction, and multiplication of matrices to solve real-world problems.
5.4 I can calculate the determinant of 2x2 and 3x3 matrices
5.5 I can find the inverse of a 2x2 matrix.
5.6 I can solve systems of equations with 2 and 3 variables by using inverses of matrices or determinants.
5.7 I can use technology to perform operations on matrices, find determinants, and find inverses.
Unit 6: Graphing Systems of Linear Inequalities& Linear Programming
6.1 I can graph a system of linear inequalities in two variables with and without technology to find the solution set for the system.
6.2 I can solve linear programming problems by finding maximum and minimum values of a function over a region defined by linear inequalities.
Unit 7: Quadratics Analytical
7.1 I can multiply monomials.
7.2 I can multiply binomials
7.3 I can factor trinomials of the form ax2 + bx + c, including special forms.
7.4 I can solve quadratic equations by factoring.
7.5 I can solve quadratic equations using the quadratic formula
7.6 I can solve application problems involving quadratics.
7.7 I can use the discriminant to determine the number and type of roots for a given quadratic function.
7.8 I can solve quadratic equations with complex number systems.
7.9 I can identify complex numbers and write their conjugates.
7.10 I can add and subtract complex numbers.
7.11 I can multiply complex numbers.
7.12 I can simplify quotients of complex numbers.
Unit 8: Graphing Quadratic Functions.
8.1 I can identify quadratic functions and graphs.
8.2 I can graph quadratic functions in vertex form.
8.3 I can graph quadratic functions in standard form.
8.4 I can graph quadratic functions in intercept form.
8.5 I can determine the domain and range of quadratic functions.
8.6 I can solve quadratic systems graphically with and without technology.
8.7 I can solve quadratic systems algebraically with and without technology.
8.8 I can use transformations to draw the graph of quadratic functions.
8.9 I can explain the transformations of quadratic functions.
8.10 I can determine a quadratic function that fits a graph.
8.11 I can graph and analyze real-world problems involving quadratics.
8.12 I can graph a system of quadratic inequalities with and without technology to find the solution set to the system.
Unit 9: Polynomial Functions
9.1 I can classify polynomial expressions and equations.
9.2 I can evaluate and simplify polynomial expressions and equations.
9.3 I can factor polynomials using a variety of methods (factor theorems, synthetic division, long division, sums and differences of cubes, grouping.)
9.4 I can determine the number and type of rational zeroes for a polynomial function.
9.5 I can find all rational zeroes of a polynomial function.
9.6 I can recognize the connection among zeroes of a polynomial function, x-intercepts, factors of polynomials, and solutions of polynomial equations.
9.7 I can use technology to graph a polynomial function and approximate the zeroes, minimum, and maximum.
9.8 I can determine the domain and range of a polynomial function.
Unit10: Sequences and Series
10.1 I can differentiate between a sequence and a series.
10.2 I can find the nth term of an arithmetic sequence.
10.3 I can find the nth term of a geometric sequence.
10.4 I can find the sum of a finite arithmetic series.
10.5 I can find the sum of a finite geometric series.
10.6 I can write a rule for a sequence.
10.7 I can find the position of a given term of an arithmetic sequence.
10.8 I can find the position of a given term of a geometric sequence.
10.9 I can use sigma notation to express sums of sequences.
10.10 I can use sequences and series to solve real-world problems.
Unit 11: Radical Expressions and Equations
11.1 I can simplify radicals that have various indices.
11.2 I can add and subtract expressions containing radicals.
11.3 I can multiply, and divide expressions containing radicals.
11.4 I can use properties of roots and rational exponents to evaluate and simplify expressions.
11.5 I can rationalize denominators containing radicals and find the simplest common denominator.
11.6 I can solve equations containing nth roots or rational exponents.
11.7 I can solve radical equations and show how extraneous solutions may arise.
11.8 I can solve radical equations given a formula for a real-world situation.
11.9 I can graph radical functions with and without technology.
11.10 I can simplify radicals that have various indices.
11.11 I can add and subtract expressions containing radicals.
Unit 12: Rational Expressions and Equations
12.1 I can graph a rational function with and without technology.
12.2 I can find the vertical and horizontal asymptotes
12.3 I can simplify rational expressions
12.4 I can multiply and divide rational expressions.
12.5 I can add and subtract rational expressions.
12.6 I can solve rational equations.
12.7 I can use rational equations to solve real world problems.
Unit 13: Composition of Functions and Inverses
13.1 I can add and subtract functions
13.2 I can multiply and divide functions
13.3 I can perform the composition of functions.
13.4 I can find the inverse of functions.
13.5 I can determine the domain and range for the given function, the composition function, or the inverse function.
Unit 14: Exponential & Log Functions
14.1 I can graph exponential functions with and without technology.
14.2 I can graph logarithmic functions with and without technology.
14.3 I can convert exponential equations to logarithmic form.
14.4 I can convert logarithmic equations to exponential form.
14.5 I can apply the properties of logarithms.
14.6 I can solve logarithmic equations.
14.7 I can solve problems related exponential growth and decay.
Unit 15: Conic Sections
15.1 I can solve quadratic equations and inequalities by completing the square.
15.2 I can graph circles and their translations from given equations or characteristics with and without technology.
15.3 I can graph parabolas and their translations from given equations or characteristics with and without technology.
15.4 I can determine characteristics of circles from their equations and graphs.
15.5 I can determine characteristics of parabolas from their equations and graphs.
15.6 I can identify and write equations for circles from given characteristics and graphs.
15.7 I can identify and write equations for parabolas from given characteristics and graphs.
15.8 I can identify and write equations for ellipses from given characteristics and graphs.
15.9 I can identify and write equations for hyperbolas from given characteristics and graphs.
15.10 I can identify conic sections and their properties (e.g., parabola, circle, ellipse, hyperbolas) from their equations in standard form.
Unit 16: Right Triangle Trigonometry, Laws of Sines and Cosines
16.1 I can use sine, cosine, and tangent ratios to find the sides of right triangles
16.2 I can use sine, cosine, and tangent ratios to find the angles of right triangles
16.3 I can use sine, cosine, and tangent ratios to solve real-world problems including those using angles of elevation and angles of depression.
16.4 I can use the law of sines to find the lengths of sides and measures of angles of triangles in mathematical and real-world problems.
16.5 I can use Law of Cosines to find the lengths of sides and measures of angles of right triangles in mathematical and real-world problems.
Unit 17: Unit Circles & Trigonometric Identities
17.1 I can identify and draw angles in degrees and radian.
17.2 I can identify coterminal angles.
17.3 I can define the terminal and initial side of an angle on the unit circle.
17.4 I can convert between a radian measure and a degree measure.
17.5 I can find the side lengths of any special right triangle.
17.6 I can label coordinate points on the unit circle using special right triangle properties.
17.7 I can use the coordinate points on the unit circle to identify the sine and cosine values.
17.8 I can find the arc length of a sector of a circle.
17.9 I can find the tangent using sine and cosine.
17.10 I can apply the Pythagorean Theorem to derive the Pythagorean Identity: .
17.11 I can manipulate the basic trigonometric equation to evaluate other trigonometric functions.
Unit 18: Graphing Trigonometric Functions
18.1 I can identify and draw angles in degrees and radian.
18.2 I can identify coterminal angles.
18.3 I can define the terminal and initial side of an angle on the unit circle.
18.4 I can convert between a radian measure and a degree measure.
18.5 I can find the side lengths of any special right triangle.
18.6 I can label coordinate points on the unit circle using special right triangle properties.
18.7 I can use the coordinate points on the unit circle to identify the sine and cosine values.
18.8 I can find the tangent using sine and cosine.
18.9 I can apply the Pythagorean Theorem to derive the Pythagorean Identity.
18.10 I can manipulate the basic trigonometric equation to evaluate other trigonometric functions.
Unit 19 Probability
19.1 I can use the Fundamental Counting Principle to count the number of ways an event can happen.
19.2 I can find combinations for an event.
19.3 I can find permutations for an event.
19.4 I can find the probability of mutually exclusive and non-mutually exclusive events.
19.5 I can find the probability of independent and dependent events.
19.6 I can use unions, intersections, and complements to find probabilities.
19.7 I can solve problems involving conditional probability.