Sheryl E.

Michigan State University

Biography

I graduated with a BS from Michigan State University in 1983 with High Honors (4.0) with a major in Mathematics Educations and a minor in Physical Science. I earned my MA from Michigan State University in Curriculum and Instructions in 1986. I taught mathematics at DeWitt High School in DeWitt MI for 36 years. I taught every level of math during those years: Basic Math, Algebra I, Geometry, Algebra 2, Trigonometry, Functions & Statistics, Precalculus, AP Statistics and AP Calculus AB. I retired from teaching in June 2020.

Education

BS Math Education

Michigan State University

MA Curriculum and Instruction

Michigan State University

Topics Covered

Functions

Trigonometry

Equations and Inequalities

Introduction to Trigonometry

Quadratic Functions

Systems of Equations and Inequalities

Introduction to Conic Section

Algebra and Trigonometry

Descriptive Statistics

Probability Topics

Sampling and Data

Confidence Intervals

Derivatives

Differentiation

Functions

Series

Introduction to Sequences and Series

The Normal Distribution

Introduction to Combinatorics and Probability

An Introduction to Geometry

The Language of Algebra

Rational Functions

Introduction to Conic Sections

Differential Equations

Introduction to Sequences and Series

Right Triangles

Circles

Applications of Trigonometric Functions

Graphing Trigonometry Functions

Polynomials

Linear Regression and Correlation

Probability and Counting Rules

The Nature of Probability and Statistics

Confidence Intervals and Sample Size

Correlation and Regression

Testing the Difference Between Two Means, Two Proportions, and Two Variances

Hypothesis Testing with One Sample

Polar Coordinates

Quadratic Equations

Exponential and Logarithmic Functions

Exponents and Polynomials

Graphs and Statistics

Decimals

Linear Functions

Introduction to Matrices

Complex Numbers

Linear Equations and Functions

Linear Equations and Inequalities

Percent

Ratio, Proportion, and Measurement

Introduction to Algebra

Solve Linear Inequalities

Graph Linear Functions

Vectors

Algebra Topics That are Reviewed at the Start of the Semester

Introduction to Combinatorics and Probability

Introduction to Vectors

Parametric Equations

Geometry Basics

Matrices

Congruent Triangles

Hypothesis Testing with Two Samples

The Central limit Theorem

Sampling and Simulation

Integration Techniques

Partial Derivatives

Functions of Several Variables

Area and Perimeter

Parallel and Perpendicular lines

Limits

Fractions and Mixed Numbers

The Integers

Vector Functions

Probability

inverse functions

Integrals

Integration

Applications of Integration

Polygons

Relationships Within Triangles

Geometric Proof

Properties of Quadrilaterals

Similarity

Surface Area

Volume

Transformations

Logic

Systems and Matrices

Discrete Random Variables

Continuous Random Variables

Sequences and Series

Algebra

Sequences

The Normal Distribution

The Chi-Square Distribution

Discrete Probability Distributions

Hypothesis Testing

Applications of the Derivative

Experiment

Vector Calculus

Other Chi-Square Tests

Multivariable Optimization

CHI-SQUARE TESTS AND THE F-DISTRIBUTION

SAT Math - Geometry

Sheryl's Textbook Answer Videos

Precalculus with Limits

From 1950 through 2005, the per capita consumption $ C $ of cigarettes by Americans (age 18 and older) can be modeled by $ C = 3565.0 + 60.30t - 1.783t^2, 0 \le t \le 55 $, where $ t $ is the year, with $ t = 0 $ corresponding to 1950.

(a) Use a graphing utility to graph the model.
(b) Use the graph of the model to approximate the maximum average annual consumption. Beginning in 1966, all cigarette packages were required by law to carry a health warning. Do you think the warning
had any effect? Explain.
(c) In 2005, the U.S. population (age 18 and over) was 296,329,000. Of those, about 59,858,458 were
smokers. What was the average annual cigarette consumption per smoker in 2005? What was the
average daily cigarette consumption per smoker?

Chapter 2: Polynomial and Rational Functions

Section 1: Quadratic Functions and Models

Precalculus with Limits

An open box with locking tabs is to be made from a square piece of material 24 inches on a side. This is to be done by cutting equal squares from the corners and folding along the dashed lines shown in the figure.

(a) Write a function $ V(x) $ that represents the volume of the box.
(b) Determine the domain of the function $ V $.
(c) Sketch a graph of the function and estimate the value of for which $ V(x) $ is maximum.

Chapter 2: Polynomial and Rational Functions

Section 2: Polynomial Functions of Higher Degree

Precalculus with Limits

The table shows the average daily high temperatures in Houston $ H $ (in degrees Fahrenheit) for month $ t $, with $ t = 1 $ corresponding to January. (Source: National Climatic Data Center)

(a) Create a scatter plot of the data.

(b) Find a cosine model for the temperatures in Houston.

(c) Use a graphing utility to graph the data points and the model for the temperatures in Houston. How well does the model fit the data?

(d) What is the overall average daily high temperature in Houston?

(e) Use a graphing utility to describe the months during which the average daily high temperature is above $ 86^\circ $ and below $ 86^\circ F $.

Chapter 5: Analytic Trigonometry

Section 3: Solving Trigonometric Equations

Precalculus with Limits

TRUSSES $Q$ is the midpoint of the line segment $\overline{PR}$ in the truss rafter shown in the figure. What are the lengths of the line segments $\overline{PQ}$, $\overline{QS}$, and $\overline{RS}$?

Chapter 6: Additional Topics in Trigonometry

Section 2: Law of Cosines

Precalculus with Limits

Fill in the blank to complete the trigonometric formula.

$ \cos u - \cos v $ = ________

Chapter 5: Analytic Trigonometry

Section 5: Multiple-Angle and Product-to-Sum Formulas

Precalculus with Limits

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure). The radius of each arc $ r $ (in feet) and the angle $ \theta $ are related by

$ \dfrac{x}{2} = 2r \sin^2 \dfrac{\theta}{2} $

Write a formula for $ x $ in terms of $ \cos \theta $.

Chapter 5: Analytic Trigonometry

Section 5: Multiple-Angle and Product-to-Sum Formulas

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