Pre-Calculus

 
 
Pre-Calculus                                                          

Semester I   [29 August 2016 - 13 Jan  2017]

 

Pre-Calculus provides students an honors-level study of trigonometry, advanced functions, analytic geometry, and data analysis in preparation for calculus. Applications and modeling will be included throughout the course of study. Appropriate technology, from manipulative to calculators and application software, will be used regularly for instruction and assessment.

Prerequisites

Describe phenomena as functions graphically, algebraically and verbally; identify independent and dependent quantities, domain, and range, input/output, mapping.

  • Translate among graphic, algebraic, numeric, tabular, and verbal representations of relations.
  • Define and use linear, quadratic, cubic, exponential, rational, absolute value, and radical functions to model and solve problems.
  • Use systems of two or more equations or inequalities to solve problems.
  • Use the trigonometric ratios to model and solve problems.
  • Use logic and deductive reasoning to draw conclusions and solve problems.

 

Number and Operations

Competency Goal 1

The learner will describe geometric figures in the coordinate plane algebraically.

 

Objectives

1.01 Transform relations in two dimensions; describe the results algebraically and geometrically.

1.02 Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.

  1. Solve using tables, graphs, and algebraic properties.
  2. Interpret the constants and coefficients in the context of the problem.

1.03 Operate with vectors in two dimensions to model and solve problems.

Geometry and Measurement

Competency Goal 2

The learner will use relations and functions to solve problems.

 

Objectives

2.01 Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.

  1. Solve using graphs and algebraic properties.
  2. Interpret the constants, coefficients, and bases in the context of the problem.

2.02 Use trigonometric and inverse trigonometric functions to model and solve problems; justify results.

  1. Solve using graphs and algebraic properties.
  2. Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.
  3. Develop and use the law of sine and the law of cosines.

2.03 For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions.

  1. Interpret the constants, coefficients, and bases in the context of the data.
  2. Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions.

2.04 Use the composition and inverse of functions to model and solve problems.

2.05 Use polar equations to model and solve problems.

  1. Solve using graphs and algebraic properties.
  2. Interpret the constants and coefficients in the context of the problem.

2.06 Use parametric equations to model and solve problems.

2.07 Use recursively-defined functions to model and solve problems.

  1. Find the sum of a finite sequence.
  2. Find the sum of an infinite sequence.
  3. Determine whether a given series converges or diverges.
  4. Translate between recursive and explicit representations.

2.08 Explore the limit of a function graphically, numerically, and algebraically

 

 

2003 Standard Course of Study and Common Core State

Standards for Pre-calculus North Carolina Assessment Specifications

 

Purpose of the Assessments

Measures of Student Learning: North Carolina’s Common Exams for Pre-calculus will measure students’ academic progress in the2003 Standard Course of Study (SCS) . Common Exam scores (along with any other relevant end-of-course or end-of-grade

assessment scores) will be used in the Educational Value Added Assessment System

(EVAAS) to produce student growth measures to satisfy Standards 6 and 8 of the North

Carolina Educator Evaluation System.

Common Exams were developed to replace locally developed assessments, providing

teachers and principals with a common measure for all students state-wide during a given testing window. For more information on the North Carolina Educator Evaluation System go to

http://www.ncpublicschools.org/educatoreffect/.

2012–2013: First year of operational administration of Common Exams in Pre-calculus.

Tables 2 describe the percentage of test questions that will appear on the Common

Exams forms in  Pre-calculus. The majority of the

items will be multiple-choice{MC} (78% to 86%), while a minority will be constructed response{CR} (14% to 22%). Students will probably take 20% to 25% of the available testing time to answer the CR items. As such, CR items will be worth up to three points each.

 

                                                         Table 2.

Test Specification Weights for the Common Exams in Pre-calculus

2003 Standard Course of Study

                MC                                                             CR

Numbers and Operations

1.01,   1.03 0%                                                     3%  to 6%

1.02    6%_to_9%                                                 0 %  to 3%

Geometry and Measurement

2.01, 2.05 12% to 16%                                       3% to 6%

2.02, 2.04, 2.07, 2.08 54% to 58%                           0%

2.03, 2.06 0%                                                       6%_to_9%

Total %of items 78-86%                                     14-22%

Total % of score points 56-66%                            34-44%

Cognitive Rigor
 

Pre-calculus items were aligned to the content standards using Marzano’s Thinking Skill Levels. To read more about North Carolina’s Thinking Skill Levels and how they were used to align items to the 2003 SCS

read http://www.ncpublicschools.org/docs/accountability/testing/eog/asb_thkskl.pdf.

Types of Items
 

The Common Exams for  Pre-calculus will consist of four-response-option multiple-choice items and short constructed response items.

The MC and CR items will align to the 2003 SCS content as shown in Tables  2.

 

 Students will be allowed to use calculators for all items.

Testing Structure and Time


The Common Exams will contain between 35 and 40 items. The test will be presented in
two forty-five minute parts. Students will be given forty minutes to complete each part.

Part one will contain MC items. Part two will contain some MC items and the CR items.Students should monitor the clock to ensure they allow themselves adequate time to respond to the questions.

Delivery Mode

The Common Exams in  Pre-calculus is designed for paper/pencil mode. 

 
Students are expected to work hard from day 1 of the semester to be successful in new assessment common core which is implemented by WCPS .

 

 

 

 

 


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