Question 1

Approximately how many high school students took the Advanced PlacementCalculus exam in 2018?

Accepted Answer

A) 25,000. 
B) 37,000. 
C) 168,000. 
D) 448,000. 
E) 613,000.

Question 2

Which of the following represents the advice given by the American StatisticalAssociation for students who are exploring probability?

Accepted Answer

A) Students should have experiences with both physical and technologicalsimulations of probabilistic situations. 
B) Students should have experience with physical simulations of probabilisticsituations, but technological applications are not necessary. 
C) Students should have experience with technological simulations of probabilisticsituations, but physical simulations are not necessary. 
D) Students should spend more time with experimental probability and considerablyless time determining theoretical probabilities. 
E) Students should spend more time with theoretical probability and considerablyless time determining experimental probabilities.

Question 3

Which of the following would be considered teaching tools in a geometry class?

Accepted Answer

A) Pattern blocks. 
B) Algebra tiles. 
C) Paper folding. 
D) Geoboards. 
E) All of these.

Question 4

Which of the following refers to the initial image on which a fractal image isgenerated?

Accepted Answer

A) Initial Value. 
B) Seed. 
C) Term. 
D) Koch. 
E) Image.

Question 5

The Common Core State Standards for Mathematics calls for the introduction ofprobability in the curriculum at which grade level?

Accepted Answer

A) Grade 5. 
B) Grade 6. 
C) Grade 7. 
D) Grade 8. 
E) Grade 9.

Question 6

Which of the following describes a geometric shape that is generated by starting withan initial image and then applying successive iterations of a rule?

Accepted Answer

A) Fractal. 
B) Tessellation. 
C) Seed. 
D) Function Image. 
E) Pre-Image.

Question 7

By how much did undergraduate course taking in statistics increase in the decadebetween 1990 and 2000?

Accepted Answer

A) 15% increase. 
B) 25% increase. 
C) 45% increase. 
D) 65% increase. 
E) 85% increase.

Question 8

Which of the following includes the three categories of discrete mathematicsproblems?

Accepted Answer

A) Existence, graphing, and optimization. 
B) Existence, counting, and optimization. 
C) Establishing an algorithm, counting, and optimization. 
D) Establishing an algorithm, graphing, and counting. 
E) Existence, establishing an algorithm, and counting.

Question 9

Explain the difference between the expectations of students - including grade level recommendations - for the areas of statistics and probability in the Common Core State Standards when compared to NCTM's Principles and Standards for School Mathematics.

Accepted Answer

The answer of Explain the difference between the expectations of...

Question 10

Which of the following statements is specifically included in the Common Core StateStandards for Mathematics for what a high school student should be able to do ingeometry?

Accepted Answer

A) Develop proofs. 
B) Use precise definitions. 
C) Work with 2-dimensional shapes. 
D) Work with 3-dimensional shapes. 
E) All of these.

Question 11

Which of the following connects the LEAST to the study of probability?

Accepted Answer

A) Geometry. 
B) Fractions. 
C) Percents. 
D) Equations. 
E) Tables.

Question 12

Which of the following most accurately characterizes the position of the NCTM andthe Mathematical Association of America in terms of taking a calculus course in highschool?

Accepted Answer

A) All high school students should study calculus in preparation for post-secondarymathematics. 
B) High school students should not study calculus and, instead, should preparethemselves for the study of calculus in college. 
C) High school students should have an introductory calculus course that includessome of the fundamentals of calculus but not with the rigor of a college-levelcourse. 
D) The study of algebra, geometry, and trigonometry is more important to a highschool student than being exposed to fundamentals of calculus. 
E) Calculus should be avoided at the high school level since there is no agreed uponsyllabus for such a course.

Question 13

The authors of the Common Core State Standards for Mathematics note that data doesnot always send a clear message due to which of the following?

Accepted Answer

A) Miscalculations. 
B) Errors in collection. 
C) Variability. 
D) Lack of technology. 
E) Context.

Question 14

Which of the following content areas is LEAST likely to have been part of mostpeople's mathematical experiences?

Accepted Answer

A) Discrete Mathematics. 
B) Algebra. 
C) Measurement. 
D) Geometry. 
E) Statistics

Question 15

The exploration of geometry without using coordinates is referred to as which of thefollowing?

Accepted Answer

A) Integrated. 
B) Analytic. 
C) Transformational. 
D) Synthetic. 
E) Dimensional.

Question 16

According to the College Board's Standards, which of the following topics is NOTsuggested for a Pre-Calculus course?

Accepted Answer

A) Conic sections. 
B) Families of functions. 
C) Congruence. 
D) Trigonometry. 
E) Vectors.

Question 17

Determining how much money would be in a bank account at the end of a period oftime is typical of which type of discrete mathematics problem?

Accepted Answer

A) Combinatorics. 
B) Iteration and Recursion. 
C) Matrices. 
D) Social Choice. 
E) Graph Theory.

Question 18

Which of the following educational theorists studied the way that children learngeometry?

Accepted Answer

A) van Hiele. 
B) Piaget. 
C) Bruner. 
D) Skemp. 
E) Bloom.

Question 19

Discuss what it means to teach "geometry" in the secondary and middle schools.Be sure to include the influence of the research of the van Hieles.Also, describe the types of skills and competencies that are developed in the Common Core State Standards for Mathematics.

Accepted Answer

The answer of Discuss what it means to teach "geometry"...

Question 20

The sample lesson in Chapter 11 in which students use protractors leads them to theexploration of which geometric concept?

Accepted Answer

A) Similarity. 
B) Congruence. 
C) Sum of angles in a polygon. 
D) Area of a polygone.Perimeter.

Exam 11: Teaching Geometry, Statisticsprobability, and Discrete Mathematics