MetroWest School of Mathematics

Algebra 3 / Precalculus  
(Recommended for 10-11th grade students)

1.      Linear equations and inequalities - review.  

2.      Quadratic equations. Quadratic inequalities – review.

3.      Systems of linear equations. Different approaches to solving them.

4.      Systems of non-linear equations.

5.      Long division of polynomials. Solving equations of higher order.

6.      The remainder theorem. The factor theorem. Solving equations of higher order.

7.      Sequences and series. Sigma notation.

8.      Equation of a circle. The circle formula.

9.      Finding the x- and y-intercepts of an equation.

10.  Identifying Functions. Vertical line test.

11.  Function notation and finding function values.

12.  Determining intervals over which a function is increasing/decreasing.

13.  Domain and range of a function.

14.  Piecewise-defined functions.

15.  Sketching the graphs of basic polynomial functions.

16.  Rational functions. Vertical and horizontal asymptotes.

17.  Graphing rational functions.

18.  Logarithms and logarithmic function (basics).

19.  Solving exponential and logarithmic equations.

20.  Functions and their graphs.

21.  Inverse function.

22.  Elements of trigonometry. Basic trigonometric functions, their graphs, properties. Trigonometric equations.

23.  Probability and statistics – random variables, expected value. Binomial, uniform and normal distributions.

Calculus 1

(The students will be asked to purchase a book).

1.      Functions and their graphs - review.  

2.      Limits and rates of change

-          The Limit of a sequence

-          The Limit of a function

-          Calculating Limits using the Limit Laws

-          The precise definition of a Limit

-          Continuity

-          Tangents, Velocities, and other rates of change.

3.      Derivatives

-          Definition

-          Differentiation formulas

-          Derivatives of trigonometric functions

-          Word problems

-          The Chain Rule

-          Implicit differentiation

-          Higher derivatives

-          Differentials and Linear Approximations

-          Newton’s method

4.      Maximum and minimum values.

5.      The Mean Value Theorem.

6.      Monotonic functions. First derivative test.

7.      Concavity and points of inflection.

8.      Asymptotes.

9.      Curve sketching.

10.  Applied maximum and minimum problems.

11.  Antiderivatives.

12.  Integration.

-          Sigma notation

-          Area

-          The Definite Integral

-          Properties of the Definite Integral

-          The Fundamental Theorem of Calculus

-          The Substitution Rule

13.  Application of Integrals (areas between curves, volumes, work).

14.  Techniques of Integration (integration by parts, substitutions, partial fractions).

15.  Improper integrals.

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