Moodle M-1 Sample Finals

MATHEMATICS 1 SAMPLE FINALS

Write solutions and answers in the ANSWER SHEET. You my use the test paper for scratch but only those written on the answer sheet will be considered.

10. Elliptic geometry

j. If and only if

11. Sum of angles of k. Riemann a triangle is less 0 than 180 . 12. An equivalent l. Hyperbolic relation geometry of statements.

I. Match items in Column A to the corresponding letters in Column B. Write the letters in the ANSWER SHEET. (10 points)

II. If the statement is true, write TRUE. Otherwise write FALSE. (10 points). Write answers and solutions if any on the ANSWER SHEET.

Column A Column B 1. Secret messages a. Probability through secret formulas 2. Collection, b. Projective presentation Geometry & Analysis of data. 3. Slope of a curve. c. Euclidean Geometry 4. Area under a d. Cryptography curve.

1. In a valid argument the conclusion is always true.

5. Rubber geometry.

3. Complement of the universal set is the universal set. 4. Division of integers is not commutative. 5. The set of integers has an additive identity element.

sheet e. Derivative

6. { Z 4 , ⊕ } is closed with respect to the modular addition ⊕ .

f. Statistics

7. All Euclidean equilateral triangles are similar.

6. Ideal point. 7. An sets..

2. The empty set is a subset of any set.

operation

of g. Union

8. Ideal lines exist in Euclidean geometry.

8. Pythagorean h. Topology theorem. 9. Mathematics chance.

of i. integral

Definite

III. Write the letter corresponding to the correct answer. If there is no answer, write NONE. (10 points). Write answers and solutions if any on the ANSWER SHEET.

1. Which of the following sets of numbers is a group under multiplication? A) Positive integers B) Natural numbers C) Non-zero rational numbers D) {2, 4, 8} 2. If A ⊂ B and B is a subset of C, then D) A ∪ B = C A) A ⊂ C B) C ⊂ A C) A ∩ C = φ 3. Which of the following is converse of the statement: “No guts, no glory”? A) If you have glory then you have guts. B) If you have no glory then you have no guts. C) If you have guts then you have glory. D) If you have no guts then you have no glory. 4. Write in symbolic equation: “Four more than twice a number x is thrice y” A) 4 + 2x = 3y B) 2x = 3y + 4 C) 2x + 3y + 4 = 0 D) 2x + 3y = 4

A) 600 100

B) 700

C) 590

8. Which of the following is a measure of central tendency? A)Mean B)variance C)standard deviation D) Range 9. Given S = {1, 2, 3, 4, 5, 6, 7, 8}. What is the probability that an odd number is chosen from S? A)

3 8

B)

1 2

C)

5 8

D) 1

10. What is the median of the following set of scores: 9, 1, 2, 4. A) 2.5 B) 3 C) 6.5 D) 9

IV. Fill in the blanks: (10 points). Write answers and solutions if any on the ANSWER SHEET. 1. If statements p and q FALSE, then the truth ( p ∧ q) → ( p ∨ q) is _____. 2 – 6. Let

are both value of

y = f ( x) = x2 − 1 .

5. Which of the following is topologically equivalent to a needle? A) five centavo coin B) T C) plate D) M

2. The image of x = −3 is _____.

400 6. Which is equal to 10 A) 10tan500 B) 10sin400 x C) 10 cos400 D) 10cos500

4. The derivative of f is ____ x?

7. Two angles of an elliptic triangle are 800 and 400. Which is a possible third angle?

D)

3. The zero(s) of the function is(are) _____.

5. The antiderivative of f is _____. 6. The value of

1

∫0 f ( x)dx

is _____.

7 – 8. The nth term of a sequence is 2n + 1 . 3n

7. The first 2 terms of the sequence are _____.

8. The limit of the sequence is _____. 9. The number 121 (base 5) written in base 10 is _____. 10. The number 9 base 10 in binary system is _____.

V.

1.

Show complete solutions and answers on the ANSWER SHEET. (3 points) Using

{ Z 26 ,⊕, ⊗ } and

the

“secret formula” y = (11 ⊗ x ) ⊕ 17 . a) Encode the message “YES”. b) Find the decoding formula. c) Decode R. 2. (3

of

ACE

3. (2 POINTS) Test the validity of the following argument using Euler’s diagram: Some students are lazy. No lazy person is successful. Jose is successful. Therefore, Jose is not a student. 4. (2 POINTS) A record bar sells CD records at P400.00 each. If you buy one CD, a discount of 15% is given on the cost of one CD. If you buy a set of 3 CD’s, a 45% discount on the cost of 3 CD’s is given. If you are going to buy 3 CD’s, which is a better deal? Justify your answer. Total: 50 points

POINTS)

Given AC = 5, CD = 9, DE = 3 in the following

figure: A

B

C

D

E Find: a) BD b) Perimeter of

c) Area

ACE