# TExES Physics/Math 7-12: Number Theory Chapter Exam

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Question 1
1.
The factored form of a polynomial function is *f*(*x*) = (*x* + 4)(*x* - 2)(*x* - 1)(*x* + 1). According to the Fundamental Theorem of Algebra, what is the degree of this function?

#### Question 2 2. How long is the proof for Fermat's Last Theorem?

#### Question 3 3. Why is 5 a prime number even though it ends in a 5?

#### Question 4 4. The following graph is of a polynomial function of degree 4. Which of the following best describes the solutions?

#### Question 5 5. How many factors does a prime number have?

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#### Question 6 6. What is the next odd number after 621?

#### Question 7 7. How could you make the prime number 3 a composite number?

#### Question 8 8. What is the greatest common factor between 9 and 18?

#### Question 9 9. Which of the following shows the correct method for evaluating the integral below?

#### Question 10 10. Which of the following is NOT a prime number?

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#### Question 11 11. What is the prime factorization of 420?

#### Question 12 12. Which integral would be evaluated using the following expression (given that F'(x) = f(x))?

#### Question 13 13. What is the prime factorization of 17?

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Question 14
14.
Two solutions of the function *f*(*x*) = *x*^3 + 5*x*^2 - 9*x* - 45 are *x* = 3 and *x* = -3. How many solutions and what types of solutions remain?

#### Question 15 15. Sam has 40 blue balloons and 30 white balloons. He wants to split each set of balloons equally. What is the largest number of groups that Sam can split the balloons into so that both the blue balloons and the white balloons are shared equally between the groups? The number of blue and white balloons in each group do not have to match.

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#### Question 16 16. Which of the following is a prime number?

#### Question 17 17. What is the least common multiple between 5 and 15?

#### Question 18 18. What is the prime factorization of 24 with exponents?

#### Question 19 19. Why is 57 a composite number?

#### Question 20 20. Which of these is NOT a prime number?

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#### Question 21 21. Evaluate the following integral.

#### Question 22 22. What number can you divide a prime number evenly by besides itself?

#### Question 23 23. When was Fermat's Last Theorem successfully proved?

#### Question 24 24. A _______ is one that has only two factors, 1 and itself, and factors are simply two numbers you ____ together to get a product.

#### Question 25 25. The following graph is of a polynomial function of degree 2. Are the solutions of this function real or imaginary and why?

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#### Question 26 26. What is the least common multiple of 8 and 33?

#### Question 27 27. What is the sum of all the even numbers?

#### Question 28 28. Which of the following is a composite number?

#### Question 29 29. Use the fundamental theorem of calculus to solve the problem below.

#### Question 30 30. How many factors does the composite number 24 have?

#### TExES Physics/Math 7-12: Number Theory Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!