Integer Challenge Questions

1. On a college test, students receive 4 points for every question answered correctly and loses 7 points for every question answered incorrectly. On this particular test, Terry answered 87 questions correctly and 46 questions incorrectly. What is his score for the test?2. Use the following 4 integers -1, 4, 40 and -25 to create as many equations you can with an answer of 34. You can use each integer only once.3. Use the following 4 integers -1, -10, 40 and 50 to create as many equations you can with an answer of 45. You can use each integer only once.4. Complete the function table:

5. Solve the following equations for ?.a. ? (-96) = 190b.? (-2) = -12 (-3)c. (? + -2) x (? - -4) = 27 6.Solve: 6 + 5{4 9[10 + 10 (4 1) + 6] + 3} 7 + 5{6 10[10 + 4 (1 + 1) + 6] + 7}

7. Give 5 integers whose product is less than zero and whose sum is -26.

8. Give four ways to get from 9 to 21 without repeat any numbers.

9. Give 3 integers whose sum is -12. Use 2 negative integers and 1 positive integer.

10. Consecutive integers are integers that follow each other such as -9 and -8 or +4 and +5. The sum of two consecutive integers is 27. What are the two integers?

11. Two consecutive odd integers have a sum of 48. What are the two odd integers?

12. Two negative consecutive integers have a sum of -21. What are the integers?

13. One integer is 2 more than 5 times another integer. If the difference of the two integers is 26, what is the smaller integer?

14. Each term of a sequence, after the first term, is three less than the square of the previous term. If the first term of the sequence is 2, what is the 2011th term?

15. If a + 2b =11 and a - b = -4, what is the value of 4a - b?

16. If (n + 1)2 3 is equal to 22, what is the value of (n + 1)2 5 ?

17. If f(n) = 3n - 5, g(n)= n2 + 3n - 2 and h(n) = 15 - 0.3n, what is the value of f(4) x h(-10)? g(-3)18. What is the product of all integer values of x for which is a prime number?

19. Use the numbers 2, 4, 5, and 8 to write an expression that has a value of 5. You may use any operations and you must use each of the numbers at least once.

20. Make an order of operations problem with at least 8 steps, which uses positive and negative integers and has answer of -12.

Thinking Questions

Explain your answer in words and give a number example to prove what you are saying.

1. When you have a long string of positive and negative integers to add up, what is a good strategy to make things more efficient?

2. Why is taking away always like adding an opposite?

3. How does the commutative property help us with integer operations?

4. How do opposite operations help us with integer operations?