The Coordinate Plane (1.1, 1.2)

1. Be able to find the equation of a line given:
   1. two points on the line
   2. a point on the line and its slope
   3. a picture of the line.
2. Given the equation of a line in any form (not necessarily y=mx + b), sketch the line.
3. Understand what the Pythagorean Theorem means and use it to find the distance between two points.
4. Given the center and radius of a circle, write down its equation, and vice versa.

Functions (1.3, 1.4)

1. Know what a function is, give examples of different kinds of functions.
2. Calculate the domain of a function.
3. Understand what function composition means.
4. Give an example to show that function composition is not commutative.
5. Understand what it means for a function to be invertible; identify such functions.
6. Calculate the inverse of an invertible function.
7. Be able to draw graphs of functions by recognizing reflections, shifts, and dialations.
8. Be able to draw quadratic functions (parabolas) accurately.

Position + Velocity (2.2)

1. Explain what velocity is.
2. Draw a graph of a particle's velocity, given a graph of its position.
3. Given graphs of position and velocity of a particle, identify which is which.
4. Calculate average and instantaneous velocity.

Limits (2.3)

1. Explain what it means for a limit to exist, and why a particular limit exists or does not exist.
2. Calculate limits of rational functions.
3. Give examples of functions whose limits don't exist.

Derivatives (2.1, 2.2, 2.4, 3.2)

1. Know what the difference quotient is.
2. Know the limit definition of a derivative.
3. Calculate the derivative using the limit definition.
4. Find the equation of a tangent line given a point on the graph.

Continuity and Differentiability (2.5)

1. Define what it means for a function to be continuous, differentiable.
2. Give an example of a continuous function that is not differentiable.
3. Determine the parameters of a piecewise function to make it continuous, differentiable.
4. State the Intermediate Value Theorem, give examples of function for which it does not apply.
5. Use the Intermediate Value Theorem to estimate the roots of function, including non-polynomial functions.

The Power Rule (3.1)

1. Explain why the term (a + b)ⁿ may be expanded into a polynomial of a and b.
2. Show why the Power Rule holds, based on the expansion above.
3. Use the Power Rule to differentiate functions that are sums of the form cxⁿ, where n is an integer and c is a constant

The Product and Quotient Rules (3.3, 3.4)

1. Given a proof of the product or quotient rule, explain a step of the proof.
2. Differentiate products and quotients of polynomials.

The Chain Rule (3.5)

1. Given a proof of the Chain Rule, explain a step of the proof.
2. Explain, using an example, why the Chain Rule is plausible.
3. Differentiate compositions of functions.

Trigonometry (4.1, 4.5)

1. Define the functions sin(x) and cos(x) in terms of the unit circle and right triangles.
2. Understand and sketch the graphs of sin(x), cos(x).
3. Know radian measurements and their relation to sin(x), cos(x).
4. Know the derivatives of sin(x), cos(x).

Exponentials and Logarithms (4.6, 4.7)

1. Be able to manipulate and simplify exponents.
2. Define the number e, the natural logarithm, and sketch e^x, ln(x).
3. Know the derivatives of e^x, ln(x).
4. Differentiate functions of the form f(x)^g(x).
5. Explain why exponential and logarithmic functions are useful in terms of modelling and differential equations.

Tangent Lines

1. Given a function and an x-value, calculate the equation of the tangent line and the normal line.
2. Find the x-value where the tangent line of a graph is:
   1. horizontal
   2. parallel to another line
   3. perpendicular to another line
3. Use tangent and normal lines to find the center of a circle.
4. Use tangent lines to find the maximum/minimum, axis of symmetry of a parabola
5. Use the point on a parabola where the tangent line is parallel to y = x to find the focus of the parabola.

Binomials and Induction

1. Be able to compute small binomial coefficients.
2. Understand how the binomial relates to Pascal's Triangle.
3. Use the binomial to answer questions about choosing elements out of a group.
4. Be able to list the steps of an inductive proof, and set one up.