maths

In a classroom, students will receive a letter grade based on the percentage of points gained in the term out of the total points possible. There are 334 points possible. To get an A in the class, the student must have a percentage that is at least 90%.

1. Determine whether a student who earns 299 points will receive an A for the class if the teacher rounds the student’s percentage to a whole number.

a. Justify your answer to part A1.

2. Determine whether the same student from part A1 will receive an A for the class if the teacher instead truncates the student’s percentage to a whole number.

a. Justify your answer to part A2.

B. Explain how you would use rounding, truncating, and mental math in real-world scenarios by doing the following:

1. Explain how you would use mental math to calculate the exact tax, using a tax rate of 27.8% and an income of your choice.

2. Provide a real world example that uses rounding.

a. Justify why rounding is more appropriate for this example than truncating.

3. Provide a real-world example that uses truncating.

a. Justify why truncating is more appropriate for this example than rounding.

C. There are 20 boys and 24 girls in an Algebra I class. The class is so large that the teacher wants to divide the students into gender-specific groups (all boys or all girls). Each group needs to have the same number of students.

1. Explain the process the teacher will use to determine the largest number of students that can be in each group using appropriate mathematical terms from number theory.

D. Explain how to prove that there is an infinite number of primes.

E. Explain the concept of modular operations by doing the following (suggested length of 1–2 pages):

1. Discuss modular arithmetic and its relation to time (i.e., clock arithmetic).

2. Explain what is meant by 10 mod 6.

3. Explain how to add and multiply in mod 7, including the following:

• Appropriate examples for modular addition using positive integers

• Appropriate examples for modular addition using negative integers

• Appropriate examples for modular multiplication using positive integers

• Appropriate examples for modular multiplication using negative integers

F. When you use sources, include all in-text citations and references in APA format.

Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web link included in the Evaluation Procedures section.

Note: When using sources to support ideas and elements in an assessment, the submission MUST include APA formatted in-text citations with a corresponding reference list for any direct quotes or paraphrasing. It is not necessary to list sources that were consulted if they have not been quoted or paraphrased in the text of the assessment.