Outline of Math 142 Test I

 

Chapter 10 -- Statistics

 

  1. Different types of graphs and what type of information best displayed by each.  Stem and leaf, bar graph, line graph, circle graph, pictograph, and scatter plot.  Summary page 425.

 

  1. Measures of central tendency – mean, median, and mode.  Create a box and whiskers plot.  Understand and apply:  standard deviation, z-score, percentile, and normal distribution.

 

  1. Understand and discuss ways in which graphs and statistics can be misleading.

 

Chapter 11 – Probability

 

  1. Understand and apply the basic vocabulary and definitions of probability.  Understand theoretical probability and experimental probability.

 

  1. Be able to use probability tree diagrams and the Fundamental Counting Property to find the probability of more complex situations that involve successive events.  Summary page 507.  Pascal’s triangle can be used when counting any event in which only two equally likely possibilities exist.  See pages 507-9 and pages 534-535.

 

  1. There will be a series of short questions on simulations, expected value, odds, and conditional probabilities.

 

  1. Use the Fundamental Counting Property to count the number of permutations.  To determine the number of combinations, find the permutations and divide by “the number in the group” factorial.  Also be familiar with factorial notation and how to use it to calculate permutations and combinations using the formulas in the text.

 

 

 

 

Review using your class notes, quizzes, and the vocabulary lists in the chapter reviews.

Do problems in the Chapter reviews, check your answers with those in the back of the text.

 

Take the chapter tests as though they are practice tests.  Do not use your text to help answer any of the questions.  After doing as many of the problems as possible, check your answers with those in the back of the text.  Use this to help evaluate what topics you need to study further.

 

 

 

 

 

 

Outline of Math 142 Test II

 

Chapter 12 – Geometry

 

Section 1:  Understanding basic geometry shapes, their properties, definitions and relationships between different shapes.

 

Section 2:  Analyzing shapes:  Lines of symmetry, rotational symmetry, regular polygons, convex and concave shapes.

 

Section 3:  Basic definitions and relationships of lines, planes, angles, sum of angles in a triangle.

 

Section 4:  Regular polygons and tessellations.  Angle measures for vertex angles, exterior angles, and central angles of regular polygons.   How the vertex angles of regular polygons determine what tessellations, if any, it is possible to create with them.  How to name and discuss semiregular tessellations. 

 

Section 5:  3-dimensional geometry:  Understanding planes, skew lines, dihedral angles, pyramids, prisms and regular polyhedra.  Be able to give examples from the classroom of 3-dimenstional concepts.  Be able to draw pyramids and prisms and identify the number of vertices, edges and faces they have.

 

 

Chapter 13 – Measurement

 

Section 1:  Metric system:  Understand the units used in the metric system, using common examples as in homework problems.  Be able to give classroom examples of common metric units.  Be able to do conversions within standard English units and within metric units.

 

Section 2:  Understand differences between perimeter and area of polygons and circles.  Understand all the formulas to calculate perimeter and area of polygons and circles.  Know the Pythagorean Theorem and how to use it to find measurements for sides or heights of various polygons.  Be able to explain how the area formulas for simple figures are all related to the area of a parallelogram.

 

Review your class notes, homework problems and quizzes.

Practice the concepts by doing the chapter reviews.

Check your understanding by doing the chapter tests as a practice test.

 

 

 

 

 

 

 

 

 

 

Outline of Math 142 Test III

 

 

Chapter 13 – Measurement

 

Section 1:  Metric system.  Understand the basic units of measure for the metric system, be able to give classroom examples of the common units, and be able to convert from one type of unit to another, including square and cubic units.  Also know conversions between cubic centimeter, milliliter, and gram.

 

Section 2:  Perimeter and area of polygons and circles.  Understand all formulas and be able to use them to calculate areas of various polygons and circles.  Be able to explain how the area formulas are all related to the area of a parallelogram.  Know the Pythagorean theorem and how to apply it to find a missing length in a variety of figures.

 

Section 3:  Surface Area.  Be able to describe (with a picture and verbally) the surface area of any prism, pyramid, cylinder, and cone.  Calculate the surface area of any of those polyhedra.

 

Section 4:  Volume.  Be able to describe and calculate the volume of any prism, pyramid, cylinder, and cone.

Summary of formulas on page 678 – more compact than those inside the back cover of the text.

 

 

Chapter 14 – Geometry Using Triangle Congruence and Similarity

 

Section 1: Congruence of triangles.  Be able to verify that two triangles are congruent using SAS, ASA, or SSS.

 

Section 2:  Similarity of triangles.  Triangles are similar if corresponding angles are congruent and corresponding sides are proportional.  Be able to show this using SAS, AA, or SSS.  Use similarity to find “missing” lengths in similar triangles and for indirect measurement problems.

 

Section 5:  Geometric Problem Solving Using Triangle Congruence and Similarity.  I will put a simple proof from this section on the test. 

 

Review your class notes, homework problems and quizzes.

Practice the concepts by doing problems from the chapter reviews.

Check your understanding by doing the chapter tests as thought they are real tests.

 

 

 

 

 

 

 

 

 

 

 

 

Outline of Math 142 Final Exam

 

The final exam is cumulative and will thus be a summary of the major concepts in the course.

In addition to using the outlines above, think about how the concepts are connected, especially the geometry concepts in chapters 12-14 and 16.

For example, knowing the definition of a prism and how to draw one (section 12.5), helps in being able to calculate the surface area for a prism (section 13.3) and volume of a prism (section 13.4).

 

Chapter 16 – Geometry Using Transformations

Please bring paper to use as tracing paper to do problems for this chapter.

 

Section 1:  Transformations.  Be able to perform a translation (slide), reflection (flip), rotation (turn), size transformation and combinations of these.  Use tracing paper and a straight edge.

 

Section 2:  Congruence and Similarity Using Transformations.   A summary of notation for transformations is on page 822.  Know properties of transformations and which produce congruent figures and which yield similar figures. 

 

Section 3:  Geometric Problem Solving Using Transformations.  Use transformations to solve geometric problems and do simple proofs.

 

Chapter 16 Review  Pages 848-850

 

Chapter 16 Test  Pages 850-853 # 1-21.  These are especially good problems to use as practice for the final exam.