MAT 101 FINAL EXAM|COLLEGE
ALGEBRA|ACTUAL QUESTIONS AND
ANSWERS 100% CORRECT|2026
UPDATE|STRAIGHTERLINE.
Course
MAT 101
Linear Equations and Inequalities
1. Solve for x :
5 x−12=3 x +8
A. 8
B. 10
C. 12
D. 14
Answer: B. 10
Rationale:
Subtract 3 x :
2 x−12=8
Add 12:
2 x=20
Therefore:
x=10
2. Solve the inequality:
4 x−7>13
A. x >4
B. x >5
C. x <4
D. x <5
Answer: B. x >5
Rationale:
Add 7:
, 4 x> 20
Divide by 4:
x >5
3. What is the slope of the line passing through ( 2,5 ) and ( 6,13 ) ?
A. 1
B. 2
C. 3
D. 4
Answer: B. 2
Rationale:
13−5 8
m= = =2
6−2 4
4. Which equation has a slope of −3and a y-intercept of 7?
A. y=3 x +7
B. y=−3 x +7
C. y=−3 x −7
D. y=7 x−3
Answer: B. y=−3 x +7
Rationale:
Slope-intercept form is:
y=mx+b
where m=−3 and b=7.
5. Solve:
x
+3=8
4
A. 12
B. 16
C. 20
D. 24
Answer: B. 20
Rationale:
, x
=5
4
Multiply by 4:
x=20
Functions and Graphs
6. If f ( x )=3 x 2−2 x+ 1, find f ( 2 ) .
A. 7
B. 8
C. 9
D. 10
Answer: C. 9
Rationale:
f ( 2 ) =3 ( 2 )2−2 ( 2 )+ 1¿ 12−4+1=9
7. Which relation represents a function?
A. { ( 1,2 ) , ( 1,4 ) , ( 2,5 ) }
B. { ( 1,3 ) , ( 2,3 ) , (3,3 ) }
C. { ( 2,4 ) , ( 2,6 ) , ( 3,7 ) }
D. { ( 4,1 ) , ( 4,2 ) , ( 5,3 ) }
Answer: B. { ( 1,3 ) , ( 2,3 ) , (3,3 ) }
Rationale:
A function assigns exactly one output to each input. In choice B, every x-value has only one
corresponding y-value.
8. Find the x-intercept of:
y=2 x−10
A. ( 0 ,−10 )
B. ( 5,0 )
C. ( 0,5 )
D. (−, 50 )
Answer: B. ( 5,0 )
Rationale:
At the x-intercept, y=0:
, 0=2 x −102 x=10x=5
9. If f ( x )=x + 4and g ( x )=2 x, find ( f ∘ g ) (3 ).
A. 7
B. 10
C. 14
D. 18
Answer: B. 10
Rationale:
g ( 3 )=2 ( 3 ) =6
Then:
f ( 6 )=6+ 4=10
Quadratic Equations
10. Solve:
x 2−7 x+ 12=0
A. x=2,6
B. x=3,4
C. x=−3 ,−4
D. x=1,12
Answer: B. x=3,4
Rationale:
x 2−7 x+ 12=( x−3 )( x−4 )
Therefore:
x=3 , x=4
11. Solve using the quadratic formula:
x 2+ 2 x−8=0
A. x=2 ,−4
B. x=−2,4
C. x=1 ,−8
D. x=−1,8
Answer: A. x=2 ,−4
ALGEBRA|ACTUAL QUESTIONS AND
ANSWERS 100% CORRECT|2026
UPDATE|STRAIGHTERLINE.
Course
MAT 101
Linear Equations and Inequalities
1. Solve for x :
5 x−12=3 x +8
A. 8
B. 10
C. 12
D. 14
Answer: B. 10
Rationale:
Subtract 3 x :
2 x−12=8
Add 12:
2 x=20
Therefore:
x=10
2. Solve the inequality:
4 x−7>13
A. x >4
B. x >5
C. x <4
D. x <5
Answer: B. x >5
Rationale:
Add 7:
, 4 x> 20
Divide by 4:
x >5
3. What is the slope of the line passing through ( 2,5 ) and ( 6,13 ) ?
A. 1
B. 2
C. 3
D. 4
Answer: B. 2
Rationale:
13−5 8
m= = =2
6−2 4
4. Which equation has a slope of −3and a y-intercept of 7?
A. y=3 x +7
B. y=−3 x +7
C. y=−3 x −7
D. y=7 x−3
Answer: B. y=−3 x +7
Rationale:
Slope-intercept form is:
y=mx+b
where m=−3 and b=7.
5. Solve:
x
+3=8
4
A. 12
B. 16
C. 20
D. 24
Answer: B. 20
Rationale:
, x
=5
4
Multiply by 4:
x=20
Functions and Graphs
6. If f ( x )=3 x 2−2 x+ 1, find f ( 2 ) .
A. 7
B. 8
C. 9
D. 10
Answer: C. 9
Rationale:
f ( 2 ) =3 ( 2 )2−2 ( 2 )+ 1¿ 12−4+1=9
7. Which relation represents a function?
A. { ( 1,2 ) , ( 1,4 ) , ( 2,5 ) }
B. { ( 1,3 ) , ( 2,3 ) , (3,3 ) }
C. { ( 2,4 ) , ( 2,6 ) , ( 3,7 ) }
D. { ( 4,1 ) , ( 4,2 ) , ( 5,3 ) }
Answer: B. { ( 1,3 ) , ( 2,3 ) , (3,3 ) }
Rationale:
A function assigns exactly one output to each input. In choice B, every x-value has only one
corresponding y-value.
8. Find the x-intercept of:
y=2 x−10
A. ( 0 ,−10 )
B. ( 5,0 )
C. ( 0,5 )
D. (−, 50 )
Answer: B. ( 5,0 )
Rationale:
At the x-intercept, y=0:
, 0=2 x −102 x=10x=5
9. If f ( x )=x + 4and g ( x )=2 x, find ( f ∘ g ) (3 ).
A. 7
B. 10
C. 14
D. 18
Answer: B. 10
Rationale:
g ( 3 )=2 ( 3 ) =6
Then:
f ( 6 )=6+ 4=10
Quadratic Equations
10. Solve:
x 2−7 x+ 12=0
A. x=2,6
B. x=3,4
C. x=−3 ,−4
D. x=1,12
Answer: B. x=3,4
Rationale:
x 2−7 x+ 12=( x−3 )( x−4 )
Therefore:
x=3 , x=4
11. Solve using the quadratic formula:
x 2+ 2 x−8=0
A. x=2 ,−4
B. x=−2,4
C. x=1 ,−8
D. x=−1,8
Answer: A. x=2 ,−4
