College Preparatory Mathematics - CCSD Course Goals
First Semester: Units 1 – 7 (18 weeks)
Unit 1 Quadratics (2 weeks)
1.1
1.2
1.3
1.4
1.5
1.6
To graph quadratic functions in both standard and vertex form, with and without technology.
[ A.APR.B.2, A.APR.B.3, F.IF.A.1, F.IF.A.2, F.IF.C.7a ]
To solve quadratic equations by graphing, factoring, completing the square, and the quadratic
formula. [ A.SSE.B.3a, A.SSE.B.3b, A.REI.B.4a, A.REI.B.4b, F.IF.C.8a ]
To predict and analyze the nature of the roots of a quadratic using the discriminant. [ A.REI.B.4b ]
To identify, simplify, and perform operations with complex numbers. [ N.CN.A.1, N.CN.A.2, N.CN.A.3 ]
To solve quadratic equations with complex numbers. [ N.CN.C.7 ]
To solve and graph solutions of single variable and two variable quadratic inequalities. [ A.CED.A.1-1,
A.CED.A.2-1 ]
Unit 2 Polynomial Functions (3 weeks)
2.1
2.2
2.3
2.4
2.5
2.6
2.7
To use long division and synthetic division to divide polynomials. [ A.APR.D.6 ]
To analyze graphs of polynomial functions determining the characteristics of the graph, including zeroes and
end behavior. [ A.APR.B.3, F.IF.A.1, F.IF.B.4-2 ]
To graph polynomial functions using characteristics determined by the equation of the function. [ F.IF.C.7c ]
To use transformations to sketch graphs of quadratic and polynomial functions. [ G.CO.A.2, F.BF.B.3-2 ]
To use the Fundamental Theorem of Algebra to determine the number of zeroes of polynomial functions.
[ N.CN.C.9 ]
To find all zeroes of a polynomial function using the Remainder Theorem and the Rational Roots Theorem.
[ A.APR.B.2, F.IF.C.8a ]
To solve and graph solutions of single variables and two variable polynomial inequalities. [ A.CED.A.1-2,
A.CED.A.2-2 ]
Unit 3 Rational Functions (2 weeks)
3.1
3.2
3.3
3.4
3.5
3.6
To identify a relation as direct, inverse, or joint variation and to write equations modeling such
relations. [ A.APR.D.6, A.APR.D.7, A.APR.A.1-2 ]
To simplify, add, subtract, multiply, and divide rational expressions. [ A.SSE.A.1a, A.APR.D.7,
A.SSE.A.1b-2 ]
To solve equations involving rational expressions. [ A.REI.A.2 ]
To identify vertical and horizontal asymptotes of rational functions. [ A.REI.D.11-2, F.IF.B.4-2 ]
To identify the domain and range of rational functions. [ A.REI.D.11-2, F.IF.B.5-2 ]
To graph rational functions with and without technology. [ F.IF.C.7d, A.REI.D.11-2 ]
Unit 4 Radicals & Functions (2 weeks)
4.1
4.2
4.3
4.4
4.5
To simplify and perform operations with radical expressions by applying properties of radicals.
[ N.RN.A.1, N.RN.A.2 ]
To use properties of rational exponents to simplify and evaluate expressions. [ N.RN.A.1, N.RN.A.2 ]
To solve equations containing radicals or rational exponents. [ N.RN.A.2, A.REI.A.2 ]
To derive and verify inverse functions both algebraically and graphically. [ F.IF.A.1, F.IF.A.2,
F.BF.B.4b, F.BF.B.4c, F.BF.B.4a-2 ]
To graph square root and cube root equations using “parent” functions, inverse functions and
transformations. [ G.CO.A.2, A.CED.A.2-2, F.IF.C.7b-2, F.BF.B.3-2 ]
Unit 5 Triangle Trigonometry & Vectors (2.5 weeks)
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
To write the six trigonometric functions in terms of the sides of a right triangle. [ G.SRT.C.6 ]
To use the special right triangles to write trigonometric functions. [ G.SRT.C.8 ]
To write a given angle in terms of its reference angle. [ G.SRT.C.7 ]
To develop strategies for solving right triangles. [ G.SRT.C.8 ]
To solve triangles using the law of sines and the law of cosines. [ G.SRT.D.10 ]
To calculate the area of a triangle using A=1/2 ab sin C or Heron’s Formula. [ G.SRT.D.9 ]
To solve real world applications involving trigonometric functions. [ G.SRT.D.11 ]
To solve real world application problems using bearing and vectors. [ N.VM.A.1 ]
Unit 6 Radians & Circle Trigonometry (3 weeks)
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
To distinguish between the radian measure and degree measure of an angle. [ F.TF.A.1 ]
To establish a correspondence between points on the real number line and points on the unit circle by
interrelating the wrapping (winding) process. [ F.TF.A.2 ]
To determine values for the circular functions using the unit circle. [ F.TF.A.3 ]
To describe graphical characteristics of the six trigonometric functions. [ F.TF.A.4 ]
To sketch the graphs of the six trigonometric functions. [ F.TF.B.5 ]
To graph transformations of the six trigonometric functions. [ F.TF.B.6 ]
To solve real world applications of the basic trigonometric functions. [ F.TF.B.5 ]
To model real world applications involving graphs of the trigonometric functions. [ F.TF.B.5 ]
Unit 7 Identities & Trigonometric Equations (3 weeks)
7.1
7.2
7.3
7.4
7.5
7.6
To derive and apply the Pythagorean, co-function, quotient, reciprocal, sum and difference, double
angle and half angle identities. [ F.TF.C.8 ]
To evaluate expressions containing combinations and compositions of circular functions and their
principal inverses. [ F.TF.B.7 ]
To simplify trigonometric expressions. [ F.TF.C.8 ]
To prove trigonometric identities. [ F.TF.C.9 ]
To verify solutions using circular functions and their inverses. [ F.TF.B.7 ]
To solve trigonometric equations. [ F.TF.B.7 ]
Second Semester: Units 8 – 13 (18 weeks)
Unit 8 Exponential & Logarithmic Functions (3 weeks)
8.1
8.2
8.3
8.4
8.5
8.6
To recognize and evaluate exponential and logarithmic expressions. [ A.SSE.A.2-2 ]
To simplify and evaluate logarithmic expressions using the properties of logarithms and change of
base. [ A.SSE.B.3c ]
To solve exponential and logarithmic equations. [ A.SSE.B.3c, F.IF.C.8b, F.BF.B.5, F.BF.B.4a-2 ]
To graph exponential and logarithmic functions with and without technology using “parent”
functions and transformations. [ G.CO.A.2, A.REI.D.11-2, F.BF.B.3-2, F.IF.C.7e-2 ]
To graph the inverse of an exponential or logarithmic function. [ F.IF.A.1, F.IF.A.2, F.BF.B.4b,
F.BF.B.4c, F.BF.B.4a-2 ]
To develop mathematical models using exponential and logarithmic functions to solve application
problems. [ N.Q.A.1, N.Q.A.2, N.Q.A.3, F.IF.C.8b, F.LE.A.1a, F.LE.A.1b, F.LE.A.1c, F.LE.B.5,
A.CED.A.1-2, F.IF.C.7b-2, F.IF.C.9-2, F.IF.C.7e-2 ]
Unit 9 Matrices (2.5 weeks)
9.1
9.2
9.3
9.4
9.5
To define, add, subtract, scalar multiply, and multiply matrices. [ N.VM.C.7, N.VM.C.8, N.VM.C.9,
N.VM.C.11 ]
To find the determinant of a matrix with and without technology and to interpret the absolute value
of the determinant in terms of area. [ N.VM.C.10, N.VM.C.12 ]
To find inverse matrices with and without technology. [ A.REI.C.9 ]
To use inverse matrices to solve systems of equations. [ A.REI.C.8, A.REI.C.9 ]
To organize data into matrices to solve real world application problems using matrices. [ N.VM.C.6,
A.REI.C.8, A.REI.C.9 ]
Unit 10 Conics (3 weeks)
10.1
10.2
10.3
10.4
10.5
To define and identify the conic relations. [ A.REI.D.10, G.GMD.B.4 ]
To put conic relation equations into standard form by completing the square. [ A.SSE.B.3b ]
To graph conic relations both using center and vertices; and by using transformations. [ G.CO.A.2,
A.CED.A.2-2, F.BF.B.3-2 ]
To write equations of conic relations when given characteristics of their graphs. [ A.CED.A.2-2 ]
To solve real world application problems using conic relations. [ N.Q.A.1, N.Q.A.2, N.Q.A.3, G.MG.A.1 ]
Unit 11 Measures of Central Tendency & Variation (3 weeks)
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
To define and calculate measures of central tendencies (mean, median and mode). [ S.ID.A.2 ]
To compare and contrast pros and cons of each measure of central tendency. [ S.ID.A.3 ]
To define and calculate measures of variation (variance, standard deviation, range and interquartile range).
[ S.ID.A.4 ]
To graph frequency and relative frequency histograms. [ S.ID.B.5 ]
To classify histogram shapes (uniform, bimodal, skewed right, etc.). [ S.ID.A.3 ]
To calculate mean and standard deviation of grouped data [ S.ID.A.4 ]
To compute the 5-number summary of a data set (low, Q1, median, Q3, high). [ S.IC.B.6 ]
To graph and interpret box-and-whisker plots. [ S.IC.B.6 ]
To consider effects of outliers. [ S.ID.A.3 ]
Unit 12 Probability & Combinations (3 weeks)
12.1
12.2
12.3
12.4
12.5
To define and apply experimental, theoretical and empirical probabilities. [ S.CP.A.1 ]
To calculate simple probabilities (P(roll a 7)), (P(draw an ace)). [ S.CP.A.2 ]
To calculate compound probabilities (P(roll a 7 or an 11)), (P(roll a 7 and then an 11)), (P(draw a king or
red)), (P(draw a queen then a king without replacement)). [ S.CP.A.3 ]
To apply the multiplication rule of counting to determine the number of outcomes of an event. [ S.CP.B.9 ]
To use the formulas for permutations and combinations to determine the number of outcomes of an
event. [ S.CP.B.9 ]
Unit 13 Binomial Probability & Residuals (3 weeks)
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
To graph discrete probability distributions. [ S.ID.A.1 ]
To use probability distributions to compute simple probabilities. [ S.MD.A.1 ]
To define and find the expected value of a probability distribution. [ S.MD.A.2 ]
To define and use a binomial experiment to find binomial probabilities. [ S.MD.A.3 ]
To find the mean and standard deviation of a binomial probability distribution. [ S.MD.A.2 ]
To use scatter plots to find the line of best fit. [ S.ID.B.6c ]
To interpret scatter plots and investigate positive or negative trends. [ S.ID.B.6c ]
To determine the residual of a scatter plot. [ S.ID.B.6b ]