Name: Nathaniel D. Andrade
BSIT 1-1
MATH MIDTERM EXAM
I.
DIRECTION: Write the letter of the your answer that best suit the statement
on the space before each number.
1. A
2. E
3. B
4. C
5. I
6. F
7. D
8. H
9. J
10. G
II. DIRECTION: Answer the following questions on the table below.
1. IVJ
2. 30 AND 31
3. STU
4. 512
5. 514, 229
6. 28, 657
7. 6, 561, 19,683, 59, 049
8. 4,096
9. HJI
10. 48, 96
III.
DIRECTION. Answer completely. (2 pts. each)
1. The exponential growth model A = 50e0.07t describe the population of a
city in the Philippines in thousands, years after 1997.
a. A = 50e0.07t
= 50e0.07(20)
= 50e (1.4)
= 50(2.718) (1.4)
= 202.730 or 202,730
= 202,730 after in 20 years (2017)
b. A = 50e0.07t
= 50e0.07(40)
= 50e (2,8)
= 50(2.718) (2.8)
= 821.993 or 821,993
= 821,993 after in 40 years (2037)
2. Substitute the given values in the formula A = Pert in finding the missing
quantity.
a. P = 1,250,555 (2.718)0.1111 (17)
= 8,265,511.5616383
= 8,265,512
b. A = 12,777,111/ (2.718)0.075 (25)
= 1,959,814.4003603
=1,959,814
3. 2.75 (1.60)
= 4.4
4.4/1.60
= 2.75
• So, the size of the plate base on the golden ratio is 4.4m
IV.
DIRECTION: Solve the problem below showing pertinent solution. (5 pts.
each)
For Square Packing
Area of Square: 14 x 14 = 196cm2
Area of Circle: 3.14 (7)2 = 153.94cm2
153.94 x 100%
= 78.5%
196cm2
For Hexagonal Packing
Area of Triangle: 142 √3/4 = 84.87 cm2
Area of Hexagon: 6 (84.87) = 509.22 cm2
Area of Circle: 3 (153.86 cm2) = 461. 58 cm2
461.58 x 100%
509.22 cm2
= 90. 64%
V.
DIRECTION: Answer the following questions.
1. SET A & SET B
2. 4 ≠ {4}
3. They have 3 elements
4. They have 2 elements
5. NO
6. NO
7. YES
8. NO
9. NO
10. NO
VI.
DIRECTION: Use the set-roster notation to indicate the elements in each of
the following sets.
1. { -1, 0, 1}
4. {3, 2, 1}
2. NONE or { }
5. {0, 1, 2}
3. { -2, -1, 0}
VII.
1.
2.
3.
4.
VIII.
DIRECTION: Solve the following using the Cartesian Product (2 pts. each)
{(2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6, 5)}
{(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}
{(1, 2), (1, 4), (1, 6), (3, 2), (3, 4), (3, 6), (5, 2), (5, 4), (5, 6)}
{(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}
DIRECTION: Determine the domain and range of the following. Write your
answer on the table below.
Domain: -2, -1, 0, 1, 2
Range: -3, -4, 0
Domain: 0, 1, 4, 9
Range: -3, -2, -1, 0, 1, 2, 3
Domain: -2, 0, 1, 2
Range: -8, -4, 2, 4, 8
Domain: x ∈ R
Range: y = 5
1.
2.
3.
4.
IX.
DIRECTION: Perform the indicated fundamental operations on a given
function. (4 points each)
1. f(x) = x3 + 2x2 + 1, g(x) = x – 2
Addition:
= x3 + 2x2 + 1 + x – 2
Final Answer:
= x3 + 2x2 + x – 1
Subtraction:
= x3 + 2x2 + 1 – x – 2
= x3 + 2x2 + 1 + (-x + 2)
Final Answer: = x3 + 2x2 – x + 3
Multiplication:
Division:
= (x3 + 2x2 + 1) (x – 2)
= x4 – 2x3 + 2x3 – 4x2 + x – 2
Final Answer:
= x4 – 4x2 + x – 2
= x3 + 2x2 + 1
x–2
Final Answer:
= x-1
2. f(x) = 3x + ½, g(x) = x – 1
Addition:
= 3x + ½ + x – 1
Final Answer:
= 4x + ½
Multiplication:
= (3x + ½) (x-1)
Final Answer:
Subtraction:
= 3x + ½ - x – 1
= 3x + ½ + (-x + 1)
Final Answer: = 2x + 1½
Division:
= (3x + ½)
(x-1)
= 3x 2 + 4x + 1½ x + 1½
3. f(x) = x2 + x – 6, g(x) = x + 3
Addition:
= x2 + x – 6 + x + 3
Final Answer:
= x2 + 2x – 3
Multiplication:
= (x2 + x – 6) (x + 3)
= x3 + 3x2 + x2 + 3x – 6x – 18
Final Answer:
= x3 + 4x2 – 3x - 18
Subtraction:
= x2 + x – 6 - x + 3
= x2 + x – 6 + (-x – 3)
Final Answer: = x2 - 9
Division:
= x2 + x – 6
x+3
= (x – 2) (x + 3)
x+3
Final Answer:
=x–2
X.
DIRECTION: Determine the composite of two functions. (2points each)
1. f(x) + g(x)
= x + 3 + 2x2 – 9
Final Answer:
= 2x2 + x – 6
2. f(x) • h(x)
= (x+3) (x2)
Final Answer:
= x3 + 3x2
3. g(x) / h(x)
= 2x2 - 9
x2
=2–9
Final Answer:
= -7
4. g(x)[f(x) + h(x)]
= (2x2 – 9) [x + 3 + x2]
= (2x2 – 9) [x2 + x + 3]
= 2x4 + 2x3 + 6x2 – 9x2 – 9x – 27
Final Answer:
= 2x4 + 2x3 – 3x2 – 9x – 27
5. h(x) • f(x) – g(x)
= (x2) (x + 3) – 2x2 – 9
= x3 + 3x2 – 2x2 – 9
= x3 + 3x2 + (-2x2 + 9)
Final Answer:
= x3 + x2 + 9