// In secondary classrooms

# Calculus

## Course Focus

CA.1
Identify SDA Christian principles and values in correlation with mathematics.

CA.1.1 | Recognize God as Creator and Sustainer of an ordered universe. |
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CA.1.2 | Value God’s inspired writings and created works as a revelation of His precision, accuracy, and exactness. |

CA.1.3 | Develop accountability as expressed in God’s word and laws |

CA.1.4 | Employ Christian principles as a basis for learning and growth. |

CA.1.5 | Broaden intellectual abilities through the study of mathematics. |

CA.1.6 | Make biblically-based choices when dealing with mathematical data. |

CA.1.7 | Apply biblical principles of Christian morality, integrity, and ethical behavior to mathematical processes. |

## Course Abilities

CA.2
Develop abilities in mathematics

CA.2.1 | Understand mathematical concepts (number sense, algebraic and geometric thinking, measurement, data analysis, and probability). |
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CA.2.2 | Utilize the problem-solving process (explore, plan, solve, verify). |

CA.2.3 | Develop higher-order thinking skills (analyze, evaluate, reason, classify, predict, generalize, solve, relate, interpret, simplify, model, synthesize). |

CA.3
A.3 Be able to apply mathematical knowledge and skills to a variety of purposes

CA.3.1 | Use a variety of strategies in the problem-solving process (i.e. patterns, tables, diagrams). |
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CA.3.2 | Conduct research (locate, observe/gather, analyze, conclude). |

CA.3.3 | Perform calculations with and without technology in life situations. |

CA.3.4 | Read critically and communicate proficiently with mathematical vocabulary. |

## Course Content

CA.4
Be able to understand concepts of differentiation and integration.

CA.4.1 | Understand limits of functions (i.e. definition, graphs, calculating, properties, behaviors, finite, infinite, one-sided). |
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CA.4.2 | Identify continuity of functions (i.e. intuitively, definition in terms of limits, and graphically). |

CA.4.3 | Demonstrate knowledge of the derivative (i.e. concept, definition, at a point, as a function, applications, linearization and second derivatives). |

CA.4.4 | Demonstrate knowledge of the integral (i.e. concept, definition of anti-derivatives, techniques, fundamental theorems of calculus, and numerical approximations). |

CA.4
Be able to understand concepts of differentiation and integration

CA.4.1 | Understand limits of functions (i.e. definition, graphs, calculating, properties, behaviors, finite, infinite, one-sided). |
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CA.4.2 | Identify continuity of functions (i.e. intuitively, definition in terms of limits, and graphically). |

CA.4.3 | Demonstrate knowledge of the derivative (i.e. concept, definition, at a point, as a function, applications, linearization and second derivatives). |

CA.4.4 | Demonstrate knowledge of the integral (i.e. concept, definition of anti-derivatives, techniques, fundamental theorems of calculus, and numerical approximations). |

CA.5
Be able to represent mathematical relationships and situations using calculus.

CA.5.1 | Interpret applications of the derivative in various situations (i.e. optimization, velocity, speed, acceleration, increasing/decreasing, concave up/down and points of inflection. |
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CA.5.2 | Solve a variety of situations (physical, biological, or economic) and represent their limits as definite integrals. |

CA.5.3 | Identify, graph, and interpret various derivatives and integrals in applied contexts. |

CA.5.4 | Present solutions resulting from applications of derivatives and integrals in conjunction with substitution techniques in finding anti-derivatives. |

CA.6
Be able to apply appropriate techniques, tools, and formulas to interpret and solve problems.

CA.6.1 | Compute the derivatives of functions using the sum, product, quotient, and chain rules. |
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CA.6.2 | Use the integral in specific applications to give accumulated change, find the area of a region, the volume of a solid with known cross sections, the average value of a function, and the distance traveled by a particle along a line. |

CA.6.3 | Demonstrate mathematical mastery of a graphing utility. |

CA.7
Be able to analyze results and draw appropriate conclusions.

CA.7.1 | Find and interpret information from graphs, charts, and numerical data. |
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CA.7.2 | Predict patterns and generalize trends. |

CA.7.3 | Judge meaning, utility, and reasonableness of findings in a variety of situations, including those carried out by technology. |