COLLEGE ALGEBRA

1. Which of the following statements is FALSE? a−1

a. In the equation y=f(x), x is the independent d.
a≫
variable.
10. Perform the indicated operation and reduce the
b. All relations are functions.
result to simplest form:
c. All functions are relations.
3x» 5y
d. A relation is any set of ordered pairs.
---- a --
2. Form of linear equation in one variable
4y» x»
a. ax +b=0
b. ax 2 +bx +c=0 15 y
a.
c. ax 2−by 2+ dx+ ey +f =0 4x
d. ax +by + c=0 5x
3. Find the zero of the linear function b.
4y
−5𝑥+10=0 15 x
c.
4y
a. -2
b. 0
4x
d.
c. 2 15 y
d. 5
4. Find the zero of the linear function 11. Find the smaller root of the quadratic equation x» -
7x + 10 = 0.
8𝑥+24=0 a. x = 7
a. 3 b. x = 2
b. -3 c. x = 5
c. 0 d. x = 10
d. 2 12. How long will it take Carol and Tessa together, to
5. Express z as a function of x and y if z is directly finish encoding a manuscript which can be done by
proportional to the difference of x and y. Carol alone in 6 days and Tessa alone in 3days?
a. 2/3 days
a. z=c ( x− y )
b. 3/2 days
1 c. 4 days
b. z=
x+ y d. 2 days
c 13. Which equation can approximately solve this
c. z= problem. The average of two friends is 19, one of
x− y them is 17 years old, how old is the other?
c a. x = (2) (19) +19
d. z=
z− y b. x = (2) (19) +17
6. Find the range of the function of y = 3x -5. c. x = (2) (19) -19
a. y = 5 d. x = (2) (19)-17
b. y = 3 14. A water tank is 2/3 full. After drawing out 15 liters of
c. all real numbers water from it, it became one-half full, what is the full
d. y is not equal to 5 capacity of the tank in liters?
7. Perform the indicated operation and reduce result to a. 10
simplest form: b. 90
x»-2xy+y» x»+xy+y c. 45
------------- a ----------- d. 80
x^3 - y^3 x–y 15. Three fourths of the participants in a regional training
program are from private universities. Two thirds of
a. x these are from Teacher Education Institutions. If
b. x + y there are 96 participants, how many of them
c. 1 represent private Teacher Education Institutions?
d. x – y a. 72
8. If f(x) = 2x – 3 and g(x) = x» -1, find (g o f) (x). b. 24
a. 4x-9 c. 18
b. x^ - 2x» d. 48
c. 4x»-12x+8 16. Find the equation of the x-axis.
d. 2x»-5 a. x = 0
9. Perform the indicated operation and reduce to b. x + y = 0
lowest terms: c. y = 0
a» - 1 a» d. x – y = 0
---------- - --------- 17. If m<0 and n>0 , which of the following is true?
a^3 + 1 a»-a+1 m
a. =0
n
a−3 1 1
a. b. <
3 m n
a+1 c. mn>0
b.
2 1 1
d. >
2 m n
c.
a+1

| MARCH 2025
COLLEGE ALGEBRA
 COLLEGE ALGEBRA

18. Express (y-3)/4y+(y+6)/y as a single fraction in 26. Find the inverse of the function.
simplest form.
2 x+5
y−3 y+ 6 f ( x )=
+ x−3
4y y
3 x −5
2 a.
a.
−5 y x+ 2
4y 3 x +5
b.
5 y+ 21 x−2
b.
4y 3 x +5
c.
2 y +3 x+2
c.
4y 3 x −5
2 d.
d.
5 y −21 y x−2
4y 27. Given that p varies directly as q and the square of r
19. How many roots does the function f(x) = x»-3x+4 and inversely as s, and p=40 when q=5, r=4 and
a. no real roots s=6, find s, when p=10, q=5 and r=2.
b. 1 a. s = 6
c. 2 b. s = 3
d. 3 c. s = 1/6
20. The tens digit of a certain two-digit number is 4 more d. s=9
than the unit’s digit; the sum of the squares of two 28. Given that z varies jointly as x and y and z=60 when
digits is 26. Find the number. x=5 and y=6, determine y when z=80 and x=4.
a. 51 a. y = 5
b. 54 b. y = 15
c. 15 c. y = 10

29. If 𝑓(𝑥) = 2𝑥 + 3 and 𝑔(𝑥) = 𝑥^2 − 1. Find (𝑔∘𝑔)(𝑥).

d. 45 d. y = 20
21. The roots of an equation are 4 and 5. Determine the
equation. a. 2 x 2+2
a. x 2+ 9 x+20 b. x 2+ 2 x
b. x 2+ 2 x +15 c. x 4 −2 x 2
c. x 2+ 7 x+6 d. 4 x 2+12 x+ 8
d. x 2−9 x +20 30. If 8𝑥 + 5𝑥 + 2𝑥 + 4𝑥 = 114, what is the value of 5𝑥
22. Find the larger root in the given equation: + 3?
a. 12
2 1 1 b. 25
x − x− =0 c. 33
6 3
d. 47
1 31. Find the domain of the function:
a.
3 2
x −2 x
−2 y=
b. 3
4
4 a. All real numbers
c. b. y ≠3
3
2 2
d. c. y≥
3 3
23. The cubic equation with the roots 3, 2, -1. 3
d. y ≤
a. x 3−4 x 2+ x +6 2
b. x 3 +4 x 2−x−6 32. Find the range of the function
2
c. x 3−4 x 2+ x−6 y=2 x +3
a. All real numbers
d. x 3−4 x 2−x−6
b. y ≠3
24. Factor completely.
3 2 2 3 c. y ≥3
27 x −5 4 x y +36 x y −8 y d. y ≤3
a. ( 3 x+ 2 y )3 33. What is the solution of the equation:
b. ( 3 x−2 y )3 5 3
=
c. ( x +3 y )3 2(x+ 1) x+ 2
d. ( x−3 y )3 a. 4
b. 5
25. What is the degree of the given polynomial
c. 12
5 3 2 4 7 3 6 4 2 d. 6
2 x y z −3 x y z + 8 x y z 34. The solution y>=2 belongs to which inequality?

𝑦≥2
a. 7
b. 6
c. 12 a. y + 16 ≤ 2 – 8y
d. 14
b. y – 16 ≤ 2 – 8y

| MARCH 2025
COLLEGE ALGEBRA
 COLLEGE ALGEBRA

c. y – 16 ≤ 2 + 8y
d. y + 16 ≤ 2 + 8y
35. Find the solution of the given inequalities:

33𝑧+117<−4+11𝑧

11
a. z←
2
9
b. z ←
2
11
c. z ←
3
21
d. z ←
2
36. How many integers satisfy the inequality:

−16<(3𝑥−7) ≤ 14
a. 8
b. 9
c. 10
d. 11

| MARCH 2025
COLLEGE ALGEBRA