Interactive MicroSims
These interactive simulations let you explore the mathematical concepts from each chapter hands-on. Click any title to launch the MicroSim.
Total: 28 MicroSims across 13 chapters
Chapter 1: Algebra Foundations
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Visualize nested number systems — integers, rationals, irrationals — with an interactive number line and classification tooltips.
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Interactive flowchart guiding you through choosing the right factoring technique for any expression.
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Build algebraic expressions from term tiles and watch them simplify in real time.
Chapter 2: Relations and Functions
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Click to place points on the coordinate plane. Quiz mode challenges you to find specific coordinates.
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Function vs Non-Function Mapping
Side-by-side mapping diagrams showing why some relations are functions and others aren't.
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Explore how division by zero and square roots create domain restrictions on a visual number line.
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Compare the constant function and identity function with adjustable parameters and a trace tool.
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Classify functions as continuous/discrete, bounded/unbounded from their graphs. Quiz with scoring.
Chapter 3: Graphing and Key Features
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Toggle intercepts, turning points, and increasing/decreasing intervals on function graphs.
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Learn why GDC window settings matter by adjusting the view and seeing which features are visible.
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Click on graphs to identify intercepts, maxima, minima, and inflection points. Scored quiz.
Chapter 4: Linear Functions
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Adjust the gradient and y-intercept with sliders and see the rise/run triangle update in real time.
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Simultaneous Equations Visualizer
Graph two lines and find their intersection. Detects parallel and perpendicular relationships.
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Match real-world scenarios to linear models by choosing the right gradient and y-intercept.
Chapter 5: Quadratic Functions
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See three solution methods side by side — factoring, completing the square, and the quadratic formula.
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Build sign diagrams for quadratic inequalities with the parabola and number line aligned.
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Launch a projectile and watch the parabolic trajectory with adjustable velocity, height, and gravity.
Chapter 6: Inverse and Composite Functions
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See a function and its inverse as reflections over the line y = x with traced corresponding points.
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Feed inputs through two function machines and see how composition order changes the result.
Chapter 7: Exponential Functions
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Exponential Growth & Decay Explorer
Adjust the base to see exponential growth morph into decay, with the transition at a = 1.
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Explore compound interest, population growth, and half-life models with adjustable parameters.
Chapter 8: Logarithmic Functions
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Solve exponential and logarithmic equations graphically — see both sides plotted with the intersection.
Chapter 9: Polynomial Functions
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Build polynomials by setting roots and multiplicities. See how the graph crosses or bounces.
Chapter 10: Rational Functions
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Graph (ax+b)/(cx+d) with adjustable parameters. See asymptotes, intercepts, and the hyperbola shape.
Chapter 11: Function Classifications
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Modulus Transformation Explorer
Compare |f(x)|, f(|x|), and [f(x)]² side by side in a 2×2 grid for multiple base functions.
Chapter 12: Transformations
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Apply translations, reflections, and stretches to any base function with four parameter sliders.
Chapter 13: Modeling and Applications
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Fit linear, quadratic, and exponential regression curves to real-world datasets. Compare R² values.
Learning Tools
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Explore the interactive concept dependency graph for the entire course.