Download Math-12 (Pre-calculus)

Common Core Mathematics: Pre-Calculus
School Year:
Teacher Name:
Number and Quantity (N)
The Complex Number System (N-CN)
N-CN 1
N-CN 2
N-CN 3
N-CN 4
N-CN 5
N-CN 6
N-CN 7
N-CN 8
N-CN 9
N-VM 2
N-VM 3
N-VM 4
N-VM 5
Explicitly
Taught/
Assessed
Introduced
Explicitly
Taught/
Assessed
Understand what the complex number i means (i2=-1) and that every number can be written in the form
𝑎 + 𝑏𝑖.
Add, subtract, multiply, and divide complex (imaginary) numbers.
Find the conjugates of complex numbers. Use conjugates in multiplying and dividing complex numbers.
Graph complex numbers on coordinate and polar graphs. Explain how the graphs show the same thing.
Add, subtract, multiply, and divide complex numbers on coordinate or polar graphs.
Find the distance and mid-point between complex numbers on a graph.
Solve quadratic equations that have complex (imaginary) answers.
Factor numbers that include complex (imaginary) numbers both before and after factoring.
Know the Fundamental Theorem of Algebra
Vector and Matrix Quantities (N-VM)
N-VM 1
Introduced
Understanding the meaning of a vector and show the magnitude and direction of vectors. Use correct
notation for vectors.
Given two points, find the components of a vector.
Solve problems using vectors.
Add and subtract vectors.
a. Add vectors end-to-end, in a similar direction, and using the parallelogram rule
b. Add vectors in different forms.
c. Subtract vectors.
Multiply a vector by a scalar.
a. Multiply a vector by a scalar using both graphs and equations.
Common Core Mathematics: Pre-Calculus
Vector and Matrix Quantities (N-VM)
N-VM 6
N-VM 7
N-VM 8
N-VM 9
N-VM 10
N-VM 11
N-VM 12
Introduced
Explicitly
Taught/
Assessed
Introduced
Explicitly
Taught/
Assessed
Introduced
Explicitly
Taught/
Assessed
b. Find the magnitude and direction of a vector times a scalar.
Know how to use matrices.
Multiply a matrix by a scalar.
Add, subtract, and multiply matrices.
Explain how multiplying a matrix is the same and different from normal multiplying.
Explain the meaning of an identity and zero matrix.
Multiply a vector and a matrix.
Use a 2x2 matrix to find the area of a plane.
Algebra (A)
Arithmetic with Polynomial and Rational Expressions (A-APR)
A-APR 4
A-APR 5
A-APR 6
A-APR 7
Use polynomial identities. (Example: 𝑎2 − 𝑏 2 = (𝑎 + 𝑏)(𝑎 − 𝑏))
Know and use the Binomial Theorem to find the expanded form for expressions that look like (𝑥 + 𝑦)𝑛 .
Write rational (fraction) expressions in different forms.
Add, subtract, multiply, and divide rational (fraction) expressions.
Reasoning with Equations and Inequalities (A-REI)
A-REI 5
A-REI 6
A-REI 7
A-REI 8
A-REI 9
Solve systems of equations by substitution and elimination/combination.
Solve systems of linear equations exactly and approximately.
Solve a system of equations with both a linear and quadratic equation by algebra (by hand) and graphing.
Write a linear equation as a matrix and vector.
Use matrices to solve systems of equations.
Common Core Mathematics: Pre-Calculus
Functions (F)
Interpreting Functions (F-IF)
F-IF 1
F-IF 4
F-IF 5
F-IF 7
F-IF 9
F-BF 3
F-BF 5
Explicitly
Taught/
Assessed
Introduced
Explicitly
Taught/
Assessed
Understand the meaning of a function. Use the right words and notation to talk about functions.
With a function modeling a situation, explain the information in the equation, graph, and table.*
Pick the correct domain for a function and its graph.*
Graph functions both by hand and using technology and explain the meaning of the graph.*
a. Graph linear and quadratic functions. Show the intercepts and maximum/minimum points.
b. Graph square root, cube root, step functions, absolute value, and piecewise functions.
c. Graph polynomial functions. Find zeros and the end behavior of the graph.
d. Graph rational functions. Find zeros and asymptotes.
e. Graph exponential, logarithmic, and trigonometric functions. Find the features of the graphs.
Given two functions in different forms (equation, graph, table, or description), compare the functions.
Building Functions (F-BF)
F-BF 1
F-BF 4
Introduced
c. Compose functions.
Find inverse functions.
b. Use composition to prove two functions are inverses.
c. Use a graph or table to find an inverse.
d. Find an inverse from a function that needs a limited domain.
Understand what happens when you change numbers in equations. (Example: what happens to 𝑥 2 when
you have 𝑥 2 − 3 o =r 5𝑥 2 )
Understand the inverse relationship between exponents and logarithms.
Common Core Mathematics: Pre-Calculus
Trigonometric Functions (F-TF)
F-TF 1
F-TF 2
F-TF 3
F-TF 4
F-TF 5
F-TF 6
F-TF 7
F-TF 8
F-TF 9
Introduced
Explicitly
Taught/
Assessed
Introduced
Explicitly
Taught/
Assessed
Understand how to measure angles using radians.
Explain how to use a unit circle.
Find the values of sine, cosine, and tangent for π/3, π/4, π/6. Know how to use angles greater or less
than π and 2π.
Use the unit circle to explain the symmetry and period of a function.
Use trigonometric functions to model real-world situations.*
Find the inverse of a trigonometric function.
Use inverse trigonometric functions to solve real-world situations.*
Prove the trigonometric identity sin2 𝜃 + cos2 𝜃 = 1.
Prove the addition and subtraction formulas for sine, cosine, and tangent and use the formulas to solve
problems.
Modeling (M)
*Modeling standards are incorporated into other areas: see (*) symbol.
Geometry (G)
Similarity, Right Triangles, and Trigonometry (G-SRT)
G-SRT 9
G-SRT 10
G-SRT 11
Create and understand the formula 𝐴 = 1/2𝑎𝑏 sin 𝐶.
Prove the Law of Sines and Cosines and use them to solve problems.
Use the Law of Sines and Cosines to find missing sides and angles in both right and non-right triangles.
Common Core Mathematics: Pre-Calculus
Expressing Geometric Properties with Equations (G-GPE)
G-GPE 1
G-GPE 2
G-GPE 3
G-GMD 2
G-GMD 3
G-C 3
G-C 4
Introduced
Explicitly
Taught/
Assessed
Introduced
Explicitly
Taught/
Assessed
Explain how to find, use, and apply the formulas for the circumference of a circle, area of a circle, and
volume for cylinders, pyramids, and cones.
Explain how Cavalieri’s principle proves the formulas for the volume of a sphere and other shapes.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
Circles (G-C)
G-C 1
G-C 2
Explicitly
Taught/
Assessed
Create the equation for a circle given the center and radius.
Create the equation for a parabola given the focus and directrix.
Create the equations for ellipses and hyperbolas given the foci.
Geometric Measurement and Dimension (G-GMD)
G-GMD 1
Introduced
Prove that all circles are similar.
Explain the relationships for lines in circles: angles, radii, chords, central angles, inscribed angles,
circumscribed angles.
Draw the inscribed and circumscribed circles of a triangle.
Draw a tangent line for a circle.
Common Core Mathematics: Pre-Calculus
Statistics and Probability * (S)
Using Probability to Make Decisions (S-MD)
S-MD 1
S-MD 2
S-MD 3
S-MD 4
S-MD 5
S-MD 6
S-MD 7
Introduced
Explicitly
Taught/
Assessed
Find the conditional probability of an event.
Use the Addition Rule, P(A or B)=P(A) + P(B) – P(A and B).
Use the Multiplication Rule, P(A and B) = P(A)P(B|A) = P(B)P(A|B).
Use permutations and combinations to find probability.
Standards for Mathematical Practice
Note: These Practices are addressed every year in mathematics.
MP.1
Explicitly
Taught/
Assessed
Find the random variable for a sample space.
Find the expected value of a random variable.
Make a probability distribution for a random variable from theoretical probability.
Make a probability distribution for a random variable from empirical probability.
Find possible outcomes for a decision by using payoff values.
a. Find the expected payoff for a game of chance. (Example: find the expected winnings from
paying the lottery)
b. Pick strategies using probabilities. (Example: which insurance plan should you pick based on the
chance of you getting in a car wreck)
Use probabilities to make decisions.
Analyze decisions and strategies using probability concepts.
Conditional Probability and the Rules of Probability (S-CP)
S-CP 6
S-CP 7
S-CP 8
S-CP 9
Introduced
Make sense of problems and persevere in solving them.
Integrated into
teaching, activities,
assignments, and
assessments.
Common Core Mathematics: Pre-Calculus
Standards for Mathematical Practice
Note: These Practices are addressed every year in mathematics.
MP.2
MP.3
MP.4
MP.5
MP.6
MP.7
MP.8
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.
Integrated into
teaching, activities,
assignments, and
assessments.