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<h1 align="center">Calculus Curriculum</h1><p>Below are skills needed, with links to resources to help with that skill. We also encourage plenty of exercises and book work. <a href="index-curriculum.html">Curriculum Home</a></p><div class="center80"><p align="center"><i>Important: this is a guide only.<br />Check with your local education authority to find out their requirements.</i><br/></p></div><div style="font-size: 21px; margin-top: 10px; padding: 18px 5px 2px 5px;">Calculus | Functions</div><div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Introduction to continuity</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/intermediate-value-theorem.html" target="MathIsFun">Intermediate Value Theorem</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/polynomials-behave.html" target="MathIsFun">How Polynomials Behave</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/continuity.html" target="MathIsFun">Continuous Functions</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../sets/functions-piecewise.html" target="MathIsFun">Piecewise Functions</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Intermediate Value Theorem and Extreme Value Theorem</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/intermediate-value-theorem.html" target="MathIsFun">Intermediate Value Theorem</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Understand how the behavior of the graphs of polynomials can be predicted from the equation, including: continuity, whether the leading term has an even or odd exponent, the size of the factor of the leading term, the number of turning points, and end behavior.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/polynomials-bounds-zeros.html" target="MathIsFun">Polynomials: Bounds on Zeros</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/polynomials-behave.html" target="MathIsFun">How Polynomials Behave</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/polynomials-rule-signs.html" target="MathIsFun">Polynomials: The Rule of Signs</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/functions-odd-even.html" target="MathIsFun">Even and Odd Functions</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Understand what is meant by saying that a function is increasing, strictly increasing, decreasing or strictly decreasing.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../sets/functions-increasing.html" target="MathIsFun">Increasing and Decreasing Functions</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Understand what is meant by the following terms for a function: Local Maximum, Local Minimum, Global Maximum and Global Minimum.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/functions-maxima-minima.html" target="MathIsFun">Maxima and Minima of Functions</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../sets/graph-equation.html" target="MathIsFun">Graph of an Equation</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../activity/soup-can.html" target="MathIsFun">Activity: Soup Can</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Understand what is meant by a continuous function and how continuity can depend upon the domain.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/continuity.html" target="MathIsFun">Continuous Functions</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../sets/functions-piecewise.html" target="MathIsFun">Piecewise Functions</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/asymptote.html" target="MathIsFun">Asymptote</a></div>
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<div style="font-size: 21px; margin-top: 10px; padding: 18px 5px 2px 5px;">Calculus | Derivatives</div><div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Introduction to derivatives</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-dy-dx.html" target="MathIsFun">Derivatives as dy/dx</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-introduction.html" target="MathIsFun">Introduction to Derivatives</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/introduction.html" target="MathIsFun">Introduction to Calculus</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ From average rate of change to instantaneous rate of change</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-dy-dx.html" target="MathIsFun">Derivatives as dy/dx</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-rules.html" target="MathIsFun">Derivative Rules</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Derivatives and continuity</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../sets/functions-increasing.html" target="MathIsFun">Increasing and Decreasing Functions</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/functions-maxima-minima.html" target="MathIsFun">Maxima and Minima of Functions</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/intermediate-value-theorem.html" target="MathIsFun">Intermediate Value Theorem</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../algebra/polynomials-behave.html" target="MathIsFun">How Polynomials Behave</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/continuity.html" target="MathIsFun">Continuous Functions</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/differentiable.html" target="MathIsFun">Differentiable</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Slope of a curve at a point: where there is a vertical tangent, or no tangents</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../geometry/slope.html" target="MathIsFun">Slope of a Straight Line</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/differentiable.html" target="MathIsFun">Differentiable</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Approximating rate of change (graphs and tables)</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../data/function-grapher.html" target="MathIsFun">Function Grapher and Calculator</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-introduction.html" target="MathIsFun">Introduction to Derivatives</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Differentiate functions using the Derivative Rules</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-rules.html" target="MathIsFun">Derivative Rules</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-introduction.html" target="MathIsFun">Introduction to Derivatives</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-dy-dx.html" target="MathIsFun">Derivatives as dy/dx</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Find the second derivative of a function using the rules of differentiation</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/second-derivative.html" target="MathIsFun">Second Derivative</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-introduction.html" target="MathIsFun">Introduction to Derivatives</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-rules.html" target="MathIsFun">Derivative Rules</a></div>
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<div style="font-size: 21px; margin-top: 10px; padding: 18px 5px 2px 5px;">Calculus | Integrals</div><div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Introduction to Integration. Understand that integration is the inverse of differentiation, and recognize the importance of the constant of integration.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-introduction.html" target="MathIsFun">Introduction to Integration</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Integrate functions using the Integration rules.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-introduction.html" target="MathIsFun">Introduction to Integration</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-rules.html" target="MathIsFun">Integration Rules</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-by-parts.html" target="MathIsFun">Integration by Parts</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-by-substitution.html" target="MathIsFun">Integration by Substitution</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Integrate products of functions using Integration by Parts, and know how this method can sometimes be applied to integrating single functions.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-by-parts.html" target="MathIsFun">Integration by Parts</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Integration by Substitution</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-by-substitution.html" target="MathIsFun">Integration by Substitution</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Calculate definite integrals and know how they relate to areas.</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/integration-definite.html" target="MathIsFun">Definite Integrals</a></div>
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<div style="font-size: 21px; margin-top: 10px; padding: 18px 5px 2px 5px;">Calculus | Limits</div><div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Introduction to limits</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits.html" target="MathIsFun">Limits</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Evaluating limits</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-evaluating.html" target="MathIsFun">Limits - Evaluating</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-infinity.html" target="MathIsFun">Limits to Infinity</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-introduction.html" target="MathIsFun">Introduction to Derivatives</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits.html" target="MathIsFun">Limits</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Formal definition of limits</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-formal.html" target="MathIsFun">Limits</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/derivatives-introduction.html" target="MathIsFun">Introduction to Derivatives</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Estimating limits (graphs and tables)</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits.html" target="MathIsFun">Limits</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../data/function-grapher.html" target="MathIsFun">Function Grapher and Calculator</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-evaluating.html" target="MathIsFun">Limits - Evaluating</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-infinity.html" target="MathIsFun">Limits to Infinity</a></div>
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<div style="padding: 10px 8px 6px 8px; text-indent: -18px; margin-left: 18px;">☐ Continuity and Limits</div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../numbers/infinity.html" target="MathIsFun">What is Infinity?</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits.html" target="MathIsFun">Limits</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-infinity.html" target="MathIsFun">Limits to Infinity</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-evaluating.html" target="MathIsFun">Limits - Evaluating</a></div>
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<div style="padding: 3px 1px 3px 35px;">☐ <a href="../calculus/limits-formal.html" target="MathIsFun">Limits</a></div>
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