Free Printable Quiz No. 1 - Quick Mathematical Review

1.

Arises in data structure and algorithm because the running times of loops naturally give rise to summations.

a)

Summation

b)

Loop Invariant

c)

Logarithms and Exponents

2.

This summation is the same as which series?

a)

1 + 2 + 3 + 4 + 5 + 6

b)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2) + (5 - 2) + (6 - 2)

c)

(1 - 2) + (6 - 2)

d)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2)

3.

The summation is the same as which series?

a)

(4+10) + (4+20) + (4+30) + (4+40) + (4+50) + (4+60) + (4+70) + (4+80) + (4+90) + (4+100) + (4+110)

b)

1+2+3+4+5+6+7+8+9+10+11

c)

4 + 110

d)

4 + 10

4.

Calculate the final sum/total of the series.

a)

6

b)

21

c)

9

d)

2

5.

Calculate the sum.

a)

66

b)

14

c)

704

d)

114

6.

This summation is the same as which series?

a)

(1/4) + (1/5) + (1/6) + (1/7) + ...

b)

4+5+6+7+8+...

c)

(1/4) + (2/4) + (3/4) + (4/4) + (5/4) + (6/4) + ...

7.

is a boolean statement that is true at the start of the loop (beginning) and at the end of each iteration (the loop invariant must be immediately true after exiting the loop)

a)

Summation

b)

Loop Invariant

c)

Logarithms and Exponents

8.

Some claims are of the generic form, “There is an element x in a set S that has property P”. To justify such a claim, we need only produce a particular x ∈ S that has property P. Likewise, some hard-to-believe claims are of the generic form, “Every element x in a set S has a property P.” To justify that such a claim is false, we need to only produce a particular x from S that does not have property P.

a)

Counterexample

b)

Contrapositive

c)

Contradiction

9.

Requires a bool condition satisfied

a)

Pre condition

b)

Post condtion

c)

Loop condition

10.

Ensures a bool condition is satisfied

a)

Pre condition

b)

Post condtion

c)

Loop condition

11.

Determine the sum of the series.

a)

144

b)

180

c)

176

d)

68

12.

Determine the sum of the series.

a)

8.25

b)

9

c)

5

d)

2.25

13.

Determine the sum of the series.

a)

194

b)

388

c)

197.5

d)

216

14.

Determine the sum of the series.

a)

45

b)

49

c)

90

d)

47

15.

Determine the sum of the series.

a)

-1

b)

244

c)

270

d)

255

16.

Determine the sum of the series.

a)

1091

b)

1149

c)

540

d)

1235

17.

If it is a number, then it is either positive or negative. What is an appropriate counterexample?

a)

10

b)

-2

c)

0

d)

True. There is no counterexample.

18.

The product of two negative numbers is greater than the sum of the two numbers. What is an appropriate counterexample?

a)

-3 and -3

b)

True. There is no counterexample

c)

-1 and -1

d)

4 and 6

19.

What does this mean?

a)

Conditional

b)

Converse

c)

Inverse

d)

Contrapositive

20.

p→q
What is the contrapositive?

a)

q→p

b)

∼p→∼q

c)

∼q→∼p

d)

p→∼q

21.

Analyze the following code.
int count = 0;
while (count < 100) {
// Point A
System.out.println("Welcome to Java!");
count++;
// Point B
}
// Point C

a)

count < 100 is always true at Point B

b)

count < 100 is always false at Point B

c)

count < 100 is always true at Point A and count < 100 is always false at Point C

d)

count < 100 is always true at Point Coint C

22.

is a sample space S together with a probability function, Pr, that maps subsets of S to real numbers in the interval [0, 1].

a)

Probability Space

b)

Probability Sample

c)

Probability Function

23.

You pick a marble from this bag.
What is the probability you will choose either a black or a white marble?
*remember to simplify*

a)

3/5

b)

4/10

c)

3/10

d)

6/10

24.

What is the probability of spinning and landing on green?

a)

3/12

b)

1/4

c)

3/4

d)

9/12

25.

which is defined as the set of all possible outcomes from some experiment.

a)

Sample Space

b)

Probability Space

c)

Probability Function

26.

Which of the following statements are true?

I. Sample Space = All possible outcomes

II. Sample Point = Each outcome (Each die from 1 to 6) or One possible outcome

III. Event = One or more of the possible outcomes (e.g. Probability <3 then 1 and 2 would be the only event)

a)

I and III only

b)

I and II only

c)

II and III only

d)

I, II, and III are all true

27.

Theorem 1.13: For any integer n ≥ 1, we have $\sum_{i=1}^ni\ =\frac{n\left(n+1\right)}{2}$

a)

True

b)

False

28.

Which of the following statements are true?

a)

2,4,6,8 only

b)

1,3, 5, 7 only

c)

1,4,5,8 only

d)

All of the above

29.

Theorem 1.12: For any integer n ≥ 0 and any real number 0 < a ≠ 1, consider $\sum_{i=0}^na^i\ =\ 1\ +\ a\ +\ a^2\ +....\ a^n$ remebering that a^0if a>0. This summation is equal to $\frac{\left(1-a^n\right)+1}{1-a^n}$

a)

True

b)

False

30.

$\sum_{i=a}^bf\left(i\right)=f\left(a\right)+f\left(a+1\right)+f\left(a+2\right)+...+f\left(b\right)$

a)

True

b)

False

Quiz No. 1 - Quick Mathematical Review

Total questions: 30

Worksheet time: 1hrs 7mins

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