ZAMBOANGA DEL SUR NATIONAL HIGH SHOOL
SENIOR HIGH SCHOOL STAND ALONE
Sta. Maria District, Pagadian City
SECOND QUARTER EXAM
GENERAL MATHEMATICS
Name: __________________________________
Section: _________________
Direction: Choose the letter of the correct answer. Write your answers in capital letters on the
space provided.
_____a 1. The graph is a function if it satisfy/satisfies the
A. vertical line test
B. horizontal line test
C. both vertical and horizontal line test
D. none of the above
_____ 2. The motorcycle fare in Pagadian City costs P10.00 for the first kilometer and an
additional of P1.00 for every additional integer kilometer. How much will you pay if
you have travelled 32.4 km?
A. P40.40
B. P41.00
C. P43.00
D. P44.40
1
_____b 3. Evaluate the function 𝑓(𝑥) = 3𝑥 2 + 2𝑥 − 1 for 𝑓 ( ).
2
A.
1
B.
4
1
C.
2
3
D. 1
4
_____b 4. In the function 𝑓(𝑥) = 2𝑥 + 1, what value is substituted to x to have a 5 as the value
of the function?
A. 1
B. 2
C. 3
D. 4
𝑥−4
2𝑥+1
_____a 5. Given that 𝑓(𝑥) =
and
𝑔(𝑥) =
, find (𝑓 + 𝑔)(𝑥).
8
8𝑥−11
11𝑥−8
6
11𝑥+8
8𝑥+11
A.
B.
C.
D.
24
24
48
48
_____a 6. The sum of the function of 𝑓(𝑥) and 𝑔(𝑥)is defined by
A. (𝑓 + 𝑔)(𝑥) = 𝑓(𝑥) + 𝑔(𝑥)
C. (𝑓 − 𝑔)(𝑥) = 𝑓(𝑥) − 𝑔(𝑥)
B. (𝑓 ∙ 𝑔)(𝑥) = 𝑓(𝑥) ∙ 𝑔(𝑥)
D. (𝑓 ÷ 𝑔)(𝑥) =
𝑓(𝑥)
𝑔(𝑥)
_____b 7. Let 𝑓(𝑥) = 2𝑥 and 𝑔(𝑥) = 𝑥 + 1 be functions. What is the value of (𝑓 ∘ 𝑔)(2)?
A. 5
B. 6
C. 7
D. 8
_____a 8. Which of the following is an example of a rational inequality?
𝑥−4
𝑥−4
2𝑥+1
2𝑥+1
8𝑥+11
A.
<𝑥
B.
=
C. 𝑦 =
D. 𝑓(𝑥) =
8
_____
9. If 𝑃(𝑥) =
2𝑥 2 +800
𝑥
8
6
6
48
is the function representing the perimeter of the fencing material
required to enclose a rectangular vegetable farm with 𝑥 as the length of one side of the
fence, what is the perimeter of the fence if one side has length of 10 meters?
A. 80 m
B. 90 m
C. 100 m
D. 110 m
_____a 10. Which of the following is TRUE in solving rational equations?
A. All the values of 𝑥 are the solutions of the equation.
B. Extraneous roots are not part of the solution set.
C. Some rational equations do not have a solution.
D. if the denominator of the rational equation is 0, the answer is 0.
_____a 11. Which of the following interval is the equivalent of the set notation {𝑥|𝑎 < 𝑥 < 𝑏}?
A. (𝑎, 𝑏)
B. [𝑎, 𝑏]
C. (𝑎, 𝑏]
D. [𝑎, 𝑏)
_____ 12. Which of the following is/are rational expression/s?
𝑥 2 −3𝑥+2
I.
𝑥+2
A. I only
_____d 13. Solve for 𝑥:
−8
√𝑥+1
II.
3𝑥+4
B. I, II, and IV
𝑥
1
8
−
= 2 .
𝑥+2
𝑥−2
III.
𝑥 3 −1
C. I and III
𝑥 2 +5𝑥−9
IV.
4
D. I, II, and III
𝑥 −4
A. -5
B. -2
C. 2
D. 5
_____a 14. The values of x that can satisfy the rational function is a
A. range
B. x-intercept
C. vertical asymptote
D. domain
𝑥−2
_____
15. Based on the definition of domain, what is the domain of 𝑓(𝑥) =
_____
A. {𝑥|𝑥 < −2}
B. {𝑥|𝑥 > −2}
C. {𝑥|−2 < 𝑥 < 2}
D. {𝑥|𝑥 < −2 𝑜𝑟 𝑥 > −2}
16. The real numbered zeroes are also the x-intercepts of the graph of the function.
What is the x-intercept of 𝑓(𝑥) =
𝑥−3
𝑥+4
?
𝑥+2
?
A. 2
B. 3
C. 4
D. 5
_____ 17. If 𝑛 and 𝑚 are the degrees of the numerator and denominator, respectively, what is
the value of the horizontal asymptote of a rational function if 𝑛 < 𝑚?
A. 𝑦 = 1
B. 𝑦 = 0
C. 𝑥 = 0
D. no horizontal asymptote
_____
_____
_____
_____
18.Which of the following is an example of a one-to-one function?
A. The relation pairing an SSS member to his or her SSS number.
B. The relation pairing a book to a student.
C. The relation pairing a classroom to a teacher.
D. The relation pairing a guard to a school.
19. Which of the following is a one-to-one function?
A. 𝑥 = 𝑦 2
B. 𝑦 = 𝑥 2
C. 𝑦 = 2𝑥 − 1
D. 3𝑥 = 𝑥 2 − 1
20. The graph is a one-to-one function if it satisfy/satisfies
A. vertical line test
B. horizontal line test
C. both vertical and horizontal line test
D. none of the above
2𝑥+1
4𝑥+1
21. If the inverse of a one-to-one function 𝑓(𝑥) =
is 𝑓 −1 (𝑥) =
, what is
𝑓 −1 (𝑓 −1 (𝑥))?
2𝑥+1
A. 𝑓(𝑥) =
3𝑥−4
3𝑥−4
B. 𝑓(𝑥) =
4𝑥+1
3𝑥−2
C. 𝑓(𝑥) =
𝑥+1
3𝑥−4
2𝑥+1
3𝑥−2
D. 𝑓(𝑥) =
3𝑥−2
4𝑥+1
_____
22. The rational function 𝑓(𝑥) =
_____
inverse of the function?
A. ℝ
B. ℝ − {1)
C. ℝ − {−1}
D. (∞, 1)
3𝑥+2
23. If the domain and range of 𝑓(𝑥) =
are(−∞, 3) ∪ (3, ∞) and (−∞, 4) ∪ (4, ∞),
_____
respectively, what is the domain of the inverse of the function?
A. ℝ
B. ℝ − {4}
C. (−∞, 3) ∪ (3, ∞) D. (−∞, 4) ∪ (4, ∞)
3𝑥+2
24. If the domain and range of 𝑓(𝑥) =
are (−∞, 3) ∪ (3, ∞) and (−∞, 4) ∪ (4, ∞),
_____
respectively, what is the range of the inverse of the function?
A. ℝ
B. ℝ − {4}
C. (−∞, 3) ∪ (3, ∞) D. (−∞, 4) ∪ (4, ∞)
25. Which of the following graphs represent the graph of a function and its inverse?
_____
_____
_____
𝑥−4
𝑥−4
26.Suppose you are to cut a string into half on the first step, how many strings are
there in the fourth step?
A. 2
B. 4
C. 8
D. 16
27. Which of the following is NOT an example of an exponential function?
A. 𝑓(𝑥) = 2𝑥
B. 𝑓(𝑥) = −3
C. 𝑦 = 𝑒 𝑥
D. 𝑓(𝑥) = 4𝑥+1
28. For any numbers a and b, and any nonzero real numbers m and n, what is the
value of 𝑎𝑚 𝑎𝑛 ?
A. 𝑎𝑚+𝑛
_____
𝑥−1
is a one-to-one function. What is the domain of the
29. If 𝑎
−𝑛
B. 𝑎𝑚𝑛
=
1
𝑎𝑛
, what is the value of
C. 𝑎𝑚−𝑛
2
2−3
D.
𝑎𝑚
𝑎𝑛
?
A. -4
B. 4
C. 8
D. 16
30. In solving 3𝑥 = 92𝑥−1 , what should be the value of the base to apply the one-to-one of
exponential equation?
A. 3
B. 4
C. 5
D. 6
_____ 31. The exponential function 𝑓(𝑥) = 𝑏 𝑥 has the domain
A. ℝ
B. 0
C. (0, ∞)
D. (−∞, 0)
𝑥
_____ 32. The exponential function 𝑓(𝑥) = 𝑏 has a range in the set (0, ∞), what is the
horizontal asymptote of the function?
A. 𝑦 = 0
B. 𝑦 = 1
C. 𝑥 = 0
D. no horizontal asymptote
1
_____ 33. In the properties of exponential function, the domain of 𝑓(𝑥) = ( ) 𝑥 is
_____
2
A. ℝ
B. 0
C. (0, ∞)
D. (−∞, 0)
_____ 34. Natural logarithms are denoted by ln. What is the base of the natural logarithms?
A. 0
B. 1
C. 10
D. e
_____ 35. If you have an exponential form 𝑏 𝑐 = 𝑎, what is its equivalent in logarithmic form?
A. 𝑙𝑜𝑔𝑐 𝑏 = 𝑎
B. 𝑙𝑜𝑔𝑏 𝑐 = 𝑎
C. 𝑙𝑜𝑔𝑎 𝑏 = 𝑐
D. 𝑙𝑜𝑔𝑏 𝑎 = 𝑐
_____b 36. Which of the following is the equivalent of ln 4?
A. 𝑙𝑜𝑔4 𝑒
B. 𝑙𝑜𝑔𝑒 4
C. 4 log 𝑒
D. 𝑙𝑜𝑔4 𝑒 4
3 4
_____d 37. Evaluate ln(𝑒 𝑒 ).
A. 𝑒 7
B. 𝑒 12
C. 7
D. 12
_____ 38. What is the range of logarithmic functions?
A. {𝑦|𝑦 > 1}
B. {𝑦|𝑦 < 1}
C. {𝑦|𝑦 = 0}
D. {𝑦|𝑦 ∈ ℝ}
_____ 39. What is the x-intercept of a logarithmic function?
A. 𝑥 = 1
B.𝑥 = 0
C. 𝑥 = −1
D. no x-intercept
_____ 40. Evaluate the x-intercept of 𝑦 = 2𝑙𝑜𝑔2 𝑥.
A. 0
B. 1
C. 2
D. 3