Shormann Precalculus with Trigonometry does teach most of what Georgia's Accelerated Precalculus Standards require.
The focus of Shormann Precalculus with Trigonometry is to prepare students for Calculus and the CLEP Precalculus Exam.The first 25 lessons also provide excellent preparation for the PSAT,SAT, and ACT.
AREAS SHORMANN PRECALCULUS DOES NOT MEET THE GEORGIA STANDARDS:
1. The Complex Number System
- MGSE9-12.N.CN.5: We cover everything listed, but instead of the words "modulus" and "argument," we use "magnitude" and "direction."
2. Vector and Matrix Quantities
- MGSE9-12.N.VM.5: We do not multiply a vector by a scalar.
- MGSE9-12.N.VM.11: We do not multiply a vector by a matrix.
- MGSE9-12.N.VM.12: We do not work with 2x2 matrices as transformations of the plane.
3. Making Inferences and Justifying Conclusions
- MGSE9-12.S.IC.3: We do lots of statistics\, but we do recognize purposes and differences listed in this standard.
4. Conditional Probability and Rules of Probability
- MGSE9-12.S.CP.8: We cover conditional probability (actually\, a review from Shormann Algebra 1 and 2)\, but we do not cover the Multiplication Rule described here.
5. Use Probability to Make Decisions
S.CP(Use Probability to Make Decisions): We do not cover using probability to make decisions in the ways described here that incorporate the use of a "random variable."
AREAS SHORMANN PRECALCULUS EXCEEDS THE GEORGIA STANDARDS:
This is just one man's opinion, but, for what it's worth, here's where I see the Georgia Standards are lacking. Note on p.2 of the Georgia Standards, first paragraph under Accelerated Pre-Calculus, they describe the purpose of Accelerated Pre-Calculus to be prep for AP Calculus AB and BC (which they do poorly), and AP Statistics (which they do well). Just like any normal Pre-Algebra course will cover some Algebra basics, a normal Pre-Calculus course should cover some calculus fundamentals. Key calculus fundamentals include basics of limits, derivatives, integrals, and infinite series. Also, an introduction to infinity, and infinitesimals, and partial fractions should be present. None of this is present in the Georgia Standards. Here are lessons where Shormann Precalculus covers these topics:
-Infinity: 1, 9, 13, 19, 21, 25, 51, 58, 88, 92, 100
-Infinitesimals("infinitely small"): 19, 20, 21, 24, 43, 51, 58, 85, 88,92, 95, 100
-Infinite Series: 2, 25, 42, 51, 90
-Limits: 19, 20, 21, 25, 58, 91, 92, 96, 100
-Derivatives: 20, 21, 58, 71, 91, 93, 94, 95, 96, 97, 98, 100
-Integrals: 21, 88, 92, 93, 100
-Partial Fractions: 85
As mentioned above, Georgia Standards appear to provide good prep for AP Statistics. Two areas they appear to be lacking include 1) regression analysis and 2) analysis of variance. Regression analysis helps students apply their skills with functions to model real data. Analysis of variance is a fundamental method for comparing experimental data between a control and one or more treatments. Although this might be covered in MGSE9-12.S.IC.5, it doesn't specify any techniques.
Here are lessons where Shormann Precalculus covers these topics:
Regression analysis: 23, 56, 61
Analysis of variance: 41
Other areas where Georgia Standards appear to be lacking are listed below. Shormann Precalculus lessons are listed in parentheses.
- Math as an attribute of God(throughout Shormann Precalculus)
- Connections to History and History of Mathematics(throughout Shormann Precalculus)
- Measurement and Conversion Factors (14, 15, 32, 70, 83, 84, 99). These topics are SO IMPORTANT, especially students pursuing STEM! Unfortunately,they are almost always lacking in state math standards.
- Computer Science (ALL Lessons on infinite series listed above, plus 24and 85)
- Advanced Algebra, Geometry *Systems of nonlinear equations (11, 12, 13) *Exponential and logarithmic functions and equations (5, 27, 65, 67) *Non-periodic functions (87) *Non-Euclidean geometry (7) *Proofs (7, 8, 18, 42)
- Logic fundamentals *Syllogisms (7) *Truth tables (7) *Converse, Inverse, Contrapositive (7)