MATH 110 EXAM 1 QUESTIONS AND
ANSWERS 2025
Mathematical Problem - ANSWERSonly a problem if you do not know how to solve it.
Otherwise it is an exercise.
Four steps for solving problems - ANSWERS1. understanding the problem
2. Reflecting on your problem solving strategies
3. explaining the solution
4. justifying that you are both done and correct.
Connection to Elementary Education #1 - ANSWERSstudents need to engage in
problem solving that are oral and written
mathematicians need to explore patterns, explain results, justify solutions
inductive reasoning - ANSWERScoming to a conclusion based on example; example,
the sun has come up every day so it will come up tomorrow
deductive reasion - ANSWERSa conclusion based on logic; like explaining the true
reason why the sun will come up
conjecture - ANSWERShypothesis or a guess about what is true; like guessing that by
multiplying you will get a number that is larger than the other two numbers
counterexaple - ANSWERSexample that shows that a conjecture is false;
proof - ANSWERSa mathematical proof consists of a deductive argument that
establishes the truth of a claim
theorem - ANSWERSa mathematical statement that has been proved to be true. like a
product of two odd numbers is always odd
solve an equation - ANSWERSfind all values for the unknown
graphic method of solving an equation - ANSWERSthink of the equation as a function;
then where the line crosses the horizontal line is the answer
numeric methods - ANSWERSinvolves a technique to estimate the solution by "smart"
or iterative guessing and checking
ANSWERS 2025
Mathematical Problem - ANSWERSonly a problem if you do not know how to solve it.
Otherwise it is an exercise.
Four steps for solving problems - ANSWERS1. understanding the problem
2. Reflecting on your problem solving strategies
3. explaining the solution
4. justifying that you are both done and correct.
Connection to Elementary Education #1 - ANSWERSstudents need to engage in
problem solving that are oral and written
mathematicians need to explore patterns, explain results, justify solutions
inductive reasoning - ANSWERScoming to a conclusion based on example; example,
the sun has come up every day so it will come up tomorrow
deductive reasion - ANSWERSa conclusion based on logic; like explaining the true
reason why the sun will come up
conjecture - ANSWERShypothesis or a guess about what is true; like guessing that by
multiplying you will get a number that is larger than the other two numbers
counterexaple - ANSWERSexample that shows that a conjecture is false;
proof - ANSWERSa mathematical proof consists of a deductive argument that
establishes the truth of a claim
theorem - ANSWERSa mathematical statement that has been proved to be true. like a
product of two odd numbers is always odd
solve an equation - ANSWERSfind all values for the unknown
graphic method of solving an equation - ANSWERSthink of the equation as a function;
then where the line crosses the horizontal line is the answer
numeric methods - ANSWERSinvolves a technique to estimate the solution by "smart"
or iterative guessing and checking
