Shared Gizmo List: Calculus and Vectors

Grade 12 Calculus and Vectors MCV4U
12th Grade Math

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Shared by a high school math teacher in Ontario.

Adv Functions Knowledge

Polynomials and Linear Factors Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function.
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Rational Functions Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.
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Graphs of Polynomial Functions Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior.
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Dividing Polynomials Using Synthetic Division Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division.
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Translating and Scaling Sine and Cosine Functions Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function.
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Exponential Functions Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.
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Logarithmic Functions Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function.
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Logarithmic Functions: Translating and Scaling Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.
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Graphs of Polynomial Functions Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior.
  5 Minute Preview   Lesson Info

CALCULUS

Absolute Value with Linear Functions Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response.
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Riemann Sum Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of rectangles and explore how the graph of the rectangles and curve change in response.
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VECTORS

Vectors Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors.
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Adding Vectors Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.
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Distance Formula Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation.
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Uniform Circular Motion Measure the position, velocity, and acceleration (both components and magnitude) of an object undergoing circular motion. The radius and velocity of the object can be controlled, along with the mass of the object. The forces acting on the object also can be recorded.
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Quadratics in Polynomial Form Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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Parallel, Intersecting, and Skew Lines Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects.
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