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# Descrete Math Multiple Choice

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3.
A grammar that has no restrictions on production is called a:
A) phrase-structure grammar.
B) context-sensitive grammar.
C) context-free grammar.
D) regular grammar.

5.
A Karnaugh map for 6 variables will have __________ squares.
A) 16
B) 32
C) 64
D) 128

6.
A Turing machine exists with tape symbols 0, 1, and B, that takes a bit string as input and replaces all 0s with 1s; it does not change any of the 1s. Pick the Turing machine from the following:
A) (s0, 0, s0, 1, R), (s0, 1, s1, 1, R), (s1, 1, s1, 1, R), (s1, 1, s0, 1, R)
B) (s0, 0, s1, 1, R), (s1, 0, s0, 1, R)
C) (s0, 0, s0, 1, R), (s0, 1, s0, 1, R)
D) None of the above

8.
Bubble sort has worst case complexity of:
A) O(n log2 n)
B) O(n2)
C) O(n)
D) O(n!)

9.
Consider the following derivation tree:

What strings can be constructed using this derivation tree?
A) A large bunny hops wildly
B) A large bunny hops
C) A bunny hops wildly
D) A bunny hops
E) All of the above

10.
Every full binary tree with 61 vertices has __________ leaves.
A) 30
B) 31
C) 60
D) 61
E) none of the above

11.
How many different Boolean functions of degree 7 are there?
A) 27
B) 128
C) 228
D) 2128

12.
T is a tree with 999 vertices, therefore T has __________ edges.
A) 998
B) 999
C) 1000
D) none of the above

13.
The best comparison-based sorting algorithms for a list of n items have complexity of:
A) O(n log2 n)
B) O(n2)
C) O(n)
D) O(n!)

14.
The idempotent laws of Boolean algebra state that:
A) x + x = 2x
B) x * x = x2
C) x + x = x
D) x * x = 2x

15.
The identity, x + yz = (x + y)(x + z) is known as:
A) De Morgan's law.
B) distributive law.
C) associative law.
D) commutative law.

16.
The pairs of numbers define the input and output to and from each state. The machine starts in state s0. If the input value to s0 is a 0, then 1 is output and the machine transitions to state s1; if the input is a 1, then 0 is output and the machine transitions to state s3. If the machine is in state s1 and receives a 0 as input, it outputs a 1 and stays in state s1; if it receives a 1, it outputs a 1 and transitions to s2. The remainder of the machine diagram may be read in the same fashion.

The machine is started and receives the bit string 0000. What does it output?
A) 1111
B) 1000
C) 1010
D) 0000

17.
The pairs of numbers define the input and output to and from each state. The machine starts in state s0. If the input value to s0 is a 0, then 1 is output and the machine transitions to state s1; if the input is a 1, then 0 is output and the machine transitions to state s3. If the machine is in state s1 and receives a 0 as input, it outputs a 1 and stays in state s1; if it receives a 1, it outputs a 1 and transitions to s2. The remainder of the machine diagram may be read in the same fashion.

The machine is started and receives the bit string 101010. What does it output?
A) 010101
B) 011011
C) 001001
D) 000101

18.
The study of languages and grammars using discrete math focuses on:
A) syntactics.
B) semantics.
C) natural language.
D) none of the above.

19.
The sum-of-products expansion of F(x,y) = 1 is:
A)
B)
C)
D) none of the above

20.
The two outputs of a half adder are the sum, s and carry, c. What is the output for input values of 1 and 1?
A) s=1, c=1
B) s=1, c=0
C) s=0, c=1
D) s=0, c=0

21.
There are __________ non-isomorphic trees with 4 vertices.
A) 0
B) 1
C) 2
D) 3
E) 4

24.
What is the language recognized by the following nondeterministic finite-state machine?

A) { 0, 1 }
B) { 0, 00, 10, 01, 11 }
C) { 0, 00, 10 }
D) { 0, 10, 01 }

25.
What is the value of the following prefix notation arithmetic expression: - 5 / * 6 2 - 5 3
A) -1
B) 0
C) 1
D) none of the above

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#### Solution Summary

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## Understanding Mean, Median, Mode and Range

1. Peter, a sixth-grade mathematics teacher, recently administered an exam. He wants to report a measure of central tendency but he doesn't know what to do with the fact that two students have much lower scores than anyone else. What is the best measure of central tendency for Peter to report?
a. Range
b. Standard deviation
c. Median
d. Mean

2. Maricella has collected her thesis data that examines differences in PSAT math achievement in Latino boys and girls. However, upon a second look at the graphs of her raw scores, it appears that the boys' scores are more normally distributed and the girls' scores are somewhat more bunched together around the mean. Given this information, what can you conclude regarding the data set?
a. The standard deviation is likely smaller for girls.
b. The girls' distribution is likely unimodal.
c. The girls' mean score is more representative of the data.
d. The girls' median is higher than the boys' median.

Use the following scenario for Q. 3 and 4:

Anton collected survey data regarding teachers' use of technology in their teaching activities. He was pleased that his data are generally normally distributed. Among other data, he collected age, number of years teaching, highest degree held, amount of time spent in online office hours weekly, and whether the teacher reported using an electronic discussion board.

3. Anton will most likely report which of the following measures of central tendency for the variable number of years teaching?
a. Mode
b. Range
c. Mean
d. Median

4. Anton will most likely report which of the following measures of central tendency for the variable highest degree held?
a. Mode
b. Range
c. Mean
d. Median

5. Andy compared students' ability to transfer learning from three different types of instructional materials. He found that there were pre-existing group differences between his conditions. Which of the following is the appropriate analysis technique for Andy to use?
a. Nonindependent t test
b. Independent t test
c. MANOVA
d. ANCOVA

6. Nelson's recent study tested differences in problem-solving ability based upon science ability, treatment (instruction, no instruction), and gender. Of the following, which test should Nelson employ?
a. Chi Square
b. t test
c. ANOVA
d. Multiple Regression

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