EDUCATIONAL SYSTEMS TECHNOLOGICAL INSTITUTE

Murallon, Boac, Marinduque

MIDTERM EXAMINATION
GENERAL MATHEMATICS
S.Y. 2022-2023

Name: _______________________________________ Score: _____________

Grade & Strand: ___________________________ Date: _______________
I. In circle the letter that corresponds to the correct answer.
1. The type of relation that describes the pairing of a single x value to single y value is called.
A. one-to-one B. one-to-many C. many-to-one D. many-to-many
2. In how many points will a vertical line intersect the graph of a function.
A, only one point B. more than one point C. at most one-point D. no point at all
3. What is the range of the relation {(0,0), (1,1), (1,-1), (2,4), (2, -4), (3, 9), (3, -9)}?
A. set of real numbers B. {0,1,2,3} C. {-9,-4,-1,0,1,2,3,4,9} D. {-9,-4,-1,0,1,4,9}
2
4. If f(x) = x −2 x+3 , then f(1) equals.
A. -2 B. 2 C. 3 D. 0
5. What is the range of the relation {(1,3), (0,0), (-3,3)}?
A. (0,1,-3) B. (3,0,3) C. (3,0) D. (-3,0,3)
3x
6. What value of x are excluded from the domain of 2 ?
x −25
A. (0,1) B. (-2,2) C. (-3,3) D. (-5,5)
3 x−2
7. If g ( x )= , g(-2) equals
5
−4 4 −7 −8
A. B. C. D.
5 5 5 5
f (2) – f (1)
8. If f ( x )=2 x 2+ 5 x−1, then equals
2
A. -2 B. 5 C. 14 D. 2
2
9. If f ( x )=2 x −3, then f(3) is equal to
A. 33 B. 15 C. 9 D. 3
2
10. If f ( x )=x +5, then f(a+b) is equal to
A. a 2+ b2+ 5 B. a 2+ b2+ ab+5 C. a 2+2 ab+ b2 +5 D. a 2+b2+ 25
11. If and f ( x )=4 x−3 and g ( x )=4 +5 x , then f ( x ) + g(x ) is equal to
A. 9x + 7 B. x+1 C. 1-9x D. 9x + 1
12. If f ( x )=3 x +5 and g ( x )=x−2, then f(g(x)) =
A. 2 x2 +15 B. (3x-10) C. 3x-1 D. 3x-3
13. If f ( x )=2 x +3 and h ( x )=x +5, then f(x) • g(x) =
A. 2 x2 +15 B. 2 x2 +8 C. 3 x+ 15 D. 3 x 2+13 x +15
g ( x)
14. If g ( x )=15 x2 +2 x−8 and h ( x )=3 x−2, then =¿
h(x )
A. 5x – 4 B. 5x + 4 C. 5x – x +4 D. 3x + 4
2 x+3
15. Which of the following cannot be an element of the domain of the function f ( x )=
x−1
A. 0 B. 1 C. -1 D. ½
16. Which of the following cannot be an element of the domain of the function f ( x )= √ x +2
A. 0 B. -2 C. 3 D. -3
17. The sum of three and x is
A. 3x B. x+x+x C. 3 + x D. x 3
18. The product of 4 x2 y 5 and −5 x 3 y 2 is
A. 20 x 5 y 7 B. -20 x 5 y 7 C. -20 x 6 y 10 D. none of the above
19. The difference between (5x + 6) and (12x – 2) is
A. -7x + 8 B. 7x – 8 C. 17x + 2 D. 17x – 4
3 2
20. If x −2 x −8 x−2=0 is multiplied by -1, the result is
 A. −x 3−2 x 2−8 x−2=0 C. −x 3 +2 x 2+ 8 x+2=0
B. −x 3 +2 x 2−8 x=2=0 D. none of the above
3
21. When the expression 6 x −45 x is divided by 3x, the quotient is
A. 2x -15 B. 2 x2 −15 C. 2 x2 +15 D. 2x + 15
22. The product of (4a – 3b) and (4a + 3b) is
A. 16a -9b B. 16 a2 −9 b2 C. 16 a2 −12 ab−9b 2 D. none of these
23. The simplest form of the expression 6x + 2x – 4 – 1 is
A. 8x – 3 B. 8x – 4 C. 2 x2 −4 D. none of these
3 2
24. The factor of 8 x −12 x y is
A. 4 x2 ( 2 x −3 y ) B. 4 x2 ( 2 x +3 y ) C. 4 x ( 2 x−3 y ) D. none of thee
25. The inverse of f(x) = 3x + 6 is
−1 1 −1 1 −1 1
A. f −1 ( x )=6+3 x B. f ( x )= x −2 C. f ( x )=3 x− D. f ( x )= x−2
3 2 6
II. Mathematical Computation
A. Find the inverse of each function.
1. f(x) = 4x – 6
2. h(x) = 2x – 4
3. f(x) = x
4. f(x) = 3x – 6
5. 3x + 4y = 12
B. If f(x) = 5x – 4 and g(x) = 2x - x 2. Find the following:
1. f(3) + g(3) 6. f(x) - g(x)
2. f(2) - g(2) 7. f(x) • g(x)
3. f(1) • g(1) 8. (f օ g)(x)
f (5)
4. 9. (g օ f)(x)
g (5)
5. f(x) + g(x) 10. (g o f)(-1)
C. Perform the indicate operations. Reduce answers to lowest term.
a 3
1. a+5 − a
9 ab 7 ab
2. 2
+ 2
cd cd
3x 8
3. 4 • 9 x
x
4. 2 x •
10
3 4
5. 15 x • 2
10 x
D. Factor the following.
1. 16 x 2 y 3 +8 x y 2 +14 xy
2. 6 ax +3 a 2 b2 −36 ab
3. xy +2 xy 4 +5 x 2 y 2
4. 8 c 2 d 3+16 c3 d 2 +4 c 4 d
5. x 2+ 13 x + 42

“Mathematics give us hope that every problem has a solution.” – Unknown

Prepared by:
JAY L. NOVENARIO EDITO M. GARNIEL
High School Teacher High School Teacher

Checked by:
EMILIANA N. ACOSTA
Principal
Approved by:
DR. CITA J. LARGA
President

Answer Key: (Gen. Math)

I.
1. A 6. D 11. D 16. B 21. A
2. A 7. D 12. D 17. C 22. B
3. D 8. C 13. D 18. B 23. D
4. B 9. B 14. B 19. A 24. A
5. C 10. C 15. B 20. C 25. B

II.
A. B. C. D.
2
−1 x +6 a −3 a−15
1. f ( x )= 1. 8 1. 1. 2 xy (8 xy ¿¿ 2+ 4 y +7) ¿
4 a(a+ 5)
−1 x +4 16 ab
2. f ( x )= 2. 6 2. 2.
2 cd 2
3 a(2 x +ab¿ ¿2+12 b)¿
2
3. f −1 ( x )= y 3. 1 3. 3. xy (1+2 y ¿¿ 3+5 xy) ¿
3
2
−1 x +6 21 x
4. f ( x )= 4. 4. 4. 4 c 2 d (2 d 2 +4 cd +c 2)
3 −15 5
−1 4 x−12 x
5. f ( x )= 5. −x 2+ 7 x−4 5. 5. (x +7)( x+ 6)
3 2
6. x 2+ 3 x −4
7. −15 x 3 +14 x 2−8 x
8. 10 x−5 x 2−4
9. −25 x 2+50 x−24
10. – 99