Grade 12
Math 4 - Precalculus
Unit — Quadratic, Polynomial, and Radical Functions and Relations
Essential Questions
How are the properties connected to the properties of radicals?
How can we check an equation for extraneous roots?
How do we use matrices to solve systems of equations?
Guiding Questions
How can we use structure in expressions to factor polynomials?
How can we use inequalities to model and solve real-llfe problems?
How can writing an equation in reduced row echelon form help us to solve a multivariable system?
Resources
Precalculus with Limits by Larson, Hostetler, and Edwards © 2008
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Number and Quantity: The Real Number System: N-RN.1, N-RN.2
Algebra: Seeing Structure in Expressions: A-SSE.2
Algebra: Arithmetic with Polynomials and Rational Expressions: A-APR..6
Algebra: Reasoning with Equations and Inequalities: A-REI.A.1, A-REI.2, A-REI.4, A-REI.4b
Number and Quantity: Vector and Matrix Quantities: N-VM.7, N-VM.8, N-VM.9
Unit — Advanced Functions and Relations
Essential Questions
How can functions apply to real-world situations?
How do you find the domain and asymptotes of a rational function?
How does exponential behavior apply to real world scenarios?
How are series and sequences useful in identifying patterns?
How do we recognize each conic section and solve problems involving parabolas?
Guiding Questions
How can we evaluate functions at certain values?
How do you determine the end behavior of a rational function?
What a the properties of logs?
How do we find the nth term of a partial sum or an arithmetic sequence?
How can we identify the foci and vertices of an ellipse?
Resources
Precalculus with Limits by Larson, Hostetler, and Edwards © 2008
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Algebra: Reasoning with Equations and Inequalities: A-REI.5, A-REI.6
Functions: Interpreting Functions: F-IF.1, F-IF.2, F-IF.4, F-IF.5, F-IF.7, F-IF.7a, F-IF.7b, F-IF.8
Functions: Building Functions: F-BF.1a, F-BF.1b, F-BF.2, F-BF.3, F-BF.4, F-BF.4a, F-BF.5
Functions: Linear, Quadratic, and Exponential Models: F-LE.4, F-LE.5
Geometry: Expressing Geometric Properties with Equations: G.GPE.1, G.GPE.2, G.GPE.3
Unit — Probability and Statistics
Essential Questions
How do we find the probability that a series of events will occur?
Guiding Questions
How can we find simple probability?
Resources
Precalculus with Limits by Larson, Hostetler, and Edwards © 2008
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Algebra: Arithmetic with Polynomials and Rational Expressions: A-APR.5
Statistics and Probability: Conditional Property and the Rules of Probability: S-CP.1, S-CP.2, S-CP.7, S-CP.8, S-CP.9
Unit — Trigonometry
Essential Questions
How can we use trig graphs to model real-world situations?
How do you rewrite trigonometric expressions in order to simplify and evaluate trigonometric functions and to verify trigonometric identities?
How do we use trigonometry to solve problems involving real-life situations?
How can we represent and perform operations on complex numbers by using trigonometry?
How do you describe the position of a point in a plane using distance and angle rather than x and y coordinates?
Guiding Questions
How do you evaluate trigonometric functions by using the unit circle?
How do we evaluate trig expressions that contain sums or differences of angles?
How do we use the Law of Cosines to solve oblique triangles?
How can we write a complex number in trigonometric form?
How do we eliminate the parameter in a set of parametric equation?
Resources
Precalculus with Limits by Larson, Hostetler, and Edwards © 2008
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Number and Quantity: The Complex Number System: N-CN.1, N-CN.2, N-CN.3, N-CN.4, N-CN.5, N-CN.7, N-CN.8, N-CN.9
Functions: Trigonometric Functions: F-TF.1, F-TF.2, F-TF.3, F-TF.4, F-TF.6, F-T.F.5, F-TF.7, F-TF.8, F-TF.9
Geometry: Expressing Geometric Properties with Equations: G-GPE.4
Geometry: Similarity, Right Triangles, and Trigonometry: G-SRT.9, G-SRT.10, G-SRT.11
Unit — Introduction to Calculus
Essential Questions
How do we evaluate limits that cannot be solved through the use of direct substitution?
Guiding Questions
How can we determine when a limit fails to exist?
Resources
Precalculus with Limits by Larson, Hostetler, and Edwards © 2008
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
EK-1.A.1, EK-1.A.2, EK-1.A.3, EK-1.B.1, EK-1.C.1, EK-1.C.2, EK-1.C.3