Math 201 Prof. Brick
section 51 Spring 02
Math Elem Ed Exam 1
Do the problems in order in your bluebook. Show your work.
1. Suppose f(x)=4x−5 and g(x) = x2. Draw a black box diagram for the composite
function g◦f(x) and compute its value when x= 3.
2. Consider the following trick: “think of a number, multiply it by 3, add 6, divide by 3,
subtract 2.” What happened ? Using algebra explain why it works.
3. Use both a partition model and repeated subtractions to describe 11 ÷3
4. Add 3425+ 4245working only in base 5. Explain your steps.
5. Explain why the commutative law of multiplication holds using areas of rectangles.
6. Use a Venn diagram to determine if the following is valid:
Math classes are always a lot of fun.
Watching TV is a lot of fun.
Therefore, watching TV is a Math class
7. Use a truth table to determine when if ever the formula p→(¬q) is true ?
8. List the nonempty subsets of the set B={∅, a, 21}.
9. Write the contrapositive of the statement “if Resistance is futile then the Borg win”.
10. Find the cardinality of the set {x|x=i2−j, where i, j ∈ {1,2} }