Fall ’02 Math 201 Exam 1 Review Prof. Brick
1. Find the 19th odd integer.
2. Without adding all the terms up by hand, compute the sum 2 + 4 + 6 + 8 + . . . + 300.
3. Give an example where inductive reasoning doesn’t work.
4. How many nonempty subsets does the set B={∅, a, 12}have ?
5. How many 1:1 correspondences are there from {1,2,3}to {a, b, c}. Make up a tree
diagram showing them.
6. Think of a number. Multiply it by 2. Add 2. Divide by 2. Subtract 1. Explain the
trick and why it works.
7. Draw a Venn diagram showing two nonempty sets Aand Bfor which A∪B=A.
8. Suppose A={1,2,9}and B={a, 2}. Find A×B.
9. Suppose f(x) = 3x+ 1 and the domain is {−3,2,5}. Describe f(x) using two sets with
directed arrows and as a collection of ordered pairs.
10. Use a truth table to determine when if ever the formula p→ ¬qis true ?
13. Write the contrapositive of the statement “if I am hungry then I will eat”.
14. Find the cardinality of the set {x|x=i−j, where i, j ∈ {1,2,3} }
15. Using flats, longs and units explain how to compute 6257−467in base 7.
16. Suppose f(x)=2x−3 and g(x) = x2. Draw a black box diagram for the composite
function g◦f(x) and compute its value when x= 5.
17. Use a Venn diagram to determine if the following is valid:
College classes are always a lot of fun.
Math 201 is a college class.
Therefore, Math 201 is always a lot of fun.
18. Use a numberline model to describe 6 −2.
19. Use both a partition model and repeated subtractions to describe 14 ÷5
20. Express the decimal number 43 in base 5 and in binary.
21. Explain how to add 2438+ 7568working only in base 8.
22. Explain why division by zero isn’t allowed, using an appropriate model.
23. Explain why the commutative law of multiplication holds using areas of rectangles.
24. What do you call the property that says 5 ·(2 + 4) = (5 ·2) + (5 ·4) and how would
you explain it using a model ?
25. Explain why we study arithmetic in other bases in this class.
26. Consider the relation “is at least as tall as” on the set of people in the room. Is it
reflexive, symmetric and/or transitive ?
27. Review all the homework, all the quizzes, and your notes from class.
