MAT 128 Exam I Extra Credit Problems

Every little bit of work must be show and directions followed in order to earn credit. No partial credit will be given. It is important to answer all parts of each question. Read the directions very carefully.

  1. Solve by drawing a picture. Show and label all four steps of Polya’s four-step approach.

A fenced-in rectangular area has a perimeter of 40 ft. The fence has a post every 5 ft.

a)How many posts are there?

b)What is the length and width of the field?

c)Are there any other possible answers to the above? If so, what?

  1. Find two different ways this sequence can be extended. 1, 3, 9, . . .
  2. Show both sequences extended three more numerals.
  3. Identify each sequence as either arithmetic, geometric, or neither.
  1. A person applying for the position of college registrar submitted the following report to the college president on 101 students: 31 take math (M), 28 take chemistry (C); 42 take psychology (P); 9 take math and chemistry; 10 take chemistry and psychology; 6 take math and psychology; 3 take all three subjects; and 20 take none of these courses. The applicant was not hired. Explain and demonstrate why.
  1. Using the information from question #3 find the cardinal number for each of the following set operations.
  1. M ∩ C
  2. U – C __
  3. (P C) M
  1. Identify sets using roster notation that demonstrate the following;
  1. A ~ B
  2. C = D
  3. E F
  4. G H
  1. Identify the property that is illustrated in each of the following;
  1. (a + b) + c = c + (a + b)
  2. a + 0 = a
  3. (a + b) + c = (b + a) + c
  4. a(b + c) = ab + ac
  1. Write a division problem and perform a standard division algorithm where 63 is the divisor and the remainder is a 2 digit number. Show every step.
  1. Write and solve a problem with;
  1. 0 as the dividend
  2. 0 as the divisor
  3. Explain the two answers.
  1. Estimate by using two of the four different strategies. Identify the two strategies.

Show every step for each. 27 + 39 + 31 + 65 + 49

  1. Find the least non-zero whole number that is divisible by 3 different primes.
  1. Find a pair of 2-digit numbers whose GCD is 15. Now find the LCM of that pair of numbers.

Show all steps of the method you use.

  1. Find all the integers “x” satisfying the given equations;
  1. │x – 7 │= 7
  2. │x│ + 6 = 10
  3. │2 – x │= 10
  1. Place parentheses, but only if needed, to make each of the following equations true.
  1. -8 2 + 3 • - 4 = -16
  2. -2 – 5 • -3 = 13
  3. -5 – 2 + 4 = -3
  4. 3 • 2 – 8 – 4 = -52
  1. Provide a summary of the NCTM; what is the purpose of the organization, what have they accomplished over the past 3 decades, how can that help you as an educator?