# Pre-Calculus

## Pre-Calculus Standards

##### Semester 1:
1. 12.M.A.APR.D.07: I can simplify rational expressions.

2. 12.M.F.BF.A.01bc: I can create a function describing the relationship between two quantities using arithmetic operations. I can compose functions that describe relationships between two quantities.

3. 12.M.F.BF.B.03: I can identify transformations for functions using their parent graphs as reference.

4. 12.M.F.BF.B.04: I can find and write inverse functions.

5. 12.M.F.BF.B.05: I can use the relationship between functions exponential and logarithmic functions, which are inverses, to solve problems.

6. 12.M.F.IF.B.06: I can calculate and interpret the rate of change between two variables in a function.

7. 12.M.F.IF.C.07ab: I can graph linear and quadratic functions. I can graph radical, piece-wise and step functions.

8. 12.M.F.IF.C.07cd: I can graph polynomial functions. I can graph rational functions.

9. 12.M.F.IF.C.07e: I can graph exponential and logarithmic functions showing intercepts, maximums and minimums.

10. 12.M.G.GMD.A.02: I can give an informal argument using Cavalieris principle for the formulas for the volume of a sphere and other solid figures. Give an informal argument using Cavalieris principle for the formulas for the volume of a sphere and other solid figures.

11. 12.M.G.GPE.A.01: I can derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

12. 12.M.G.GPE.A.02: I can derive the equation of a parabola given a focus and directrix.

13. 12.M.G.GPE.A.03: I can derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

14. 12.M.N.CN.A.01-03: I can identify the standard form of a complex number. I can add, subtract, and multiply complex numbers. I can find the conjugate of a complex number and use the conjugate to find a quotient and moduli of a complex number.

15. 12.M.N.CN.C.08: I can extend polynomial identities to complex numbers and write in factored form.

16. 12.M.N.CN.C.09: I can know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

##### Semester 2:
1. 12.M.F.IF.C.07e (trig): I can graph trigonometric functions.

2. 12.M.F.TF.A.01-04: I understand that the radian measure of an angle is the length of the arc on the unit circle subtended by the angle and can apply this. I understand how coordinates for the angles on the unit circle relate to sine and cosine ratios of a right triangle. I can solve problems using special triangles and the unit circle to obtain exact answers. I can use the unit circle to explain symmetry and periodicity of trigonometric functions.

3. 12.M.F.TF.B.05-07: I can choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. I can use domain restrictions on trigonometric functions to construct inverse functions. I can use inverse functions to solve trigonometric equations that arise in modeling contexts and evaluate the solutions using technology, interpreting them in terms of the context.

4. 12.M.F.TF.C.08-09: I can prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. I can prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

5. 12.M.G.SRT.D.09-11: I can derive and use the formula A = 1?2 ab sin(C) for the area of a triangle. I can prove the Laws of Sines and Cosines and use them to solve problems. I can apply the law of cosines and sines to find unknown measurements.

6. 12.M.N.VM.A.01: I can recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

7. 12.M.N.VM.A.02: I can find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

8. 12.M.N.VM.A.03: I can solve problems involving velocity and other quantities that can be represented by vectors.

9. 12.M.N.VM.A.04: I can add and subtract vectors.

10. 12.M.N.VM.A.05: I can multiply a vector by a scalar.

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