Republic of the Philippines
Department of Education
REGION II – CAGAYAN VALLEY
SCHOOLS DIVISION OF CAGAYAN
STO. NIÑO DISTRICT
Lipatan Integrated School
Lipatan, Sto. Niño, Cagayan
THIRD QUARTER EXAMINATION
MATHEMATICS 8
S.Y. 2023 – 2024
Name:______________________________________Date:____________Score:______Parent’s
Signature:___________
Directions: Read the questions carefully. Write you answers on the space provided. Use CAPITAL
LETTER in answering.
1. Which of the following is in the form of the difference of two squares?
A. 16 + a2
B. 4 + a2b2
C. 100 a2 + b2
D. b2 – 4
2. Uwu is tasked to factor 5𝑥 2 + 20𝑥. If one factor is 5𝑥, then the other factor is _____.
A. ( x + 4 )
B.
5x2 ( x + 4 )
C. 5x ( x2 + 4x )
D. x – 4
3. Which of the following is a rational expression?
√2𝑥
9
A.
B.
5𝑥+𝑦
𝑥−5𝑦
C.
𝑥 2 +3𝑥
4
4. Which of the following is the equivalent rational expression of
A.
10𝑥 4
2𝑥
5. What is the quotient of
A.
3
𝑏
B.
𝑎
2𝑏
5𝑥 6
25𝑥
÷
B.
C.
𝑎𝑏
6
2
𝑏
5𝑥 3
𝑥5
5
D.
8𝑥
9𝑥
D.
25𝑥 4
5
D.
3
𝑏2
?
10𝑥
=.
C.
2
𝑏2
6. He is a French Mathematician who created the cartesian plane and the father of modern
mathematics.
A. René Descartes
B. Euclid
C. Pythagoras
D. Isaac Newton
7. What quadrant do points (-3, 3), (-4, 7), and (-9, 1) belong in?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
8. Kristine used the cartesian plane to arrange her things inside the bedroom. Where can you find her
bag?
A. (-4, 3)
B. (0, 0)
C. (1, 5)
D. (3, -4)
9. Which of the following is written in slope-intercept form?
A. 3x + 2y=8
B. y= 8x-10
C. y-8= 3(x-5)
D. 6x+7y+20=0
10. Which of the following equation(s) is /are considered as a linear equation in two variables?
I.y=3+2x
II. xy=3
III. x2+2y=3
IV. 2x +3y=5
A. I only
B. I and II only
C. II and III only
D.III and IV only
11. What is the equation of the line whose slope is 5 and
A.
?
C.
B.
D.
12. Your section has a graded recitation in Math. You were tasked to give the formula for finding the
slope of the line given the linear equation. What will be your answer?
A. m=
𝐴
B. m=
𝐵
−𝐴
𝐵
C. m=
𝑋2 −𝑋1
𝑌2 −𝑌1
D. m=
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
13. Samuel is preparing for his skateboarding competition. His skateboard formed a line with an
equation y=3x + 6. What is the slope of his trick shown on the right?
A.
B.
C.
D.
m=
m=
m=
m=
6
-6
3
-3
14. Jose, Mari and Chan are having a review in Math 8 in preparation for the First Periodical Test. The
three boys were discussing about the graph of a linear equation whose slope is negative. Who among
them has a true statement?
Jose:
Mari:
Chan:
The direction of the graph of a The direction of the graph of a The direction of the graph of a
linear equation whose slope is linear equation whose slope is linear equation whose slope is
negative is
negative is
negative is
A. Jose only
B. Jose and Mari
C. Mari and Chan
D. Chan only
15. Write the standard form of linear equation 3x+2y=12 into slope –intercept form.
3
A. y= 2x+6
3
3
B. y= -2x+6
C. y= 2x+12
3
D. y= -2x+12
16. Rewrite 2x + 5y = 10 in the slope-intercept form.
2
A. y= -5 x+2
B. y=
2
5
x+2
2
C. y= − 5x+10
D. y=
2
5
x+10
17. Which is the standard form of 6 -5y = 3x ?
A. 3x+5y= -6
B. 3x-5y=-6
C. 3x-5y=6
D.3x+5y=6
18. Marites is doing her assignment in graphing linear equations given the equation y = -2x + 4.
Which of the following is the correct graph of the linear equation?
19. Suho and Kai are trying to graph a linear equation using two points. Their solution is presented
below. Who is right?
Suho:
Steps
1. Assign values of x to find the value of y.
2. Plot the points.
Kai:
Steps
1. Plot the points.
2. Assign values of x to find the value of y.
3. Connect the points with a line.
3. Connect the points with a line.
A. Suho only
B. Kai only
C. Suho and Kai
D. None of these
20. What is the trend of the graph of a linear equation that has a slope of 5?
A. The graph is a vertical line.
B. The graph is a horizontal line.
C. The graph is increasing from left to right.
D. The graph is decreasing from left to right.
21. How do you describe the graph of an equation with a slope of 7 passing through y – intercept 5?
A. The graph is parallel to the y – axis
B. The graph is parallel to the x – axis
C. The graph rises from the left to right
D. The graph rises from right to left
22. Based on the graph, which line has a negative slope?
A. Line A
B. Line B
C. Line C
D. Line D
23. What is the graph of the system of linear equations in two
variables whose slopes are equal and y-intercepts are equal?
A. Intersecting
C. Parallel
B. Coinciding
D. Perpendicular
24. Which of the following is NOT a system of linear equations in two variables?
25. Given the system
order to eliminate the variable
A. -3
B. 3
, by what number would you multiply the first equation in
when the equations are added?
C. 2
D. -2
26. What is the solution to the system of equations shown in the graph?
A. (0, −1)
B. (0,2)
C. (0,3)
D. (3,0)
27. Jane was asked by her Mathematics teacher to graph a system of linear equations in two
variables. After following all the steps in solving linear equations in by graphing, she was able to
draw lines that are parallel to each other.
Which of the following can Jane conclude about the solutions of the system?
A. It has no solution.
B. It has one solution.
C. It has two solutions.
D. It has infinitely many solutions.
28. What do you call the graph of a system of linear equations in two variables
which shows only one solution?
A. intersecting
B. coinciding
C. parallel
D. perpendicular
29. How do you describe the graphs of the system of linear equations in two variables which has no
solution?
A. coinciding
B. intersecting
C. parallel
D. perpendicular
30. What kind of system of linear equations in two variables is illustrated in?
A.
Dependent
B. Inconsistent
C. Independent
D. Consistent
31. Find the missing term so that ___-24x + 9 forms a perfect square trinomial.
A. 6x2
B. 16x2
C. 4x2
32. What is the factored form of
A.)
B.)
?
D. 3x2
C.)
D.)
33. What should be multiplied to (x - 2) to get x3- 8?
A. x-3
B. x2 + 2x + 4
C. x2+4
D. x2 - 4
34. Suppose the length of a rectangular room is (x + 6) meters and the width is (x – 6) meters,
what expression can be used to represent the area of the room?
A.(x – 6) m2
B. (x2 + 36) m2
C. (x + 6) m2
D. (x2 - 36) m2
35. If the area of a square garden is ( 9𝑥 2 – 54x + 81 ) square units, is it possible to find its sides ?
A. Yes, using factoring the difference of two squares
B. Yes, using factoring of perfect square trinomial
C. No, one of the sides must be given
D. No, the area is not factorable
36. The simplified form of the rational expression
A.
−5𝑏3
4𝑐 3
B.
−5𝑐 3
4𝑏3
37. Which of the following is equal to:
A.
10𝑥
(𝑥−2)
B.
−25𝑎 10 𝑏11 𝑐 12
20𝑎10 𝑏 8 𝑐 15
7𝑥 2 −3𝑥
𝑥−2
3𝑥 2
4𝑥 2
+
𝑥−2
𝑥−2
3𝑥
𝑥−2
-
.
C.
−4𝑏3
5𝑐 3
D.
−4𝑐 3
5𝑏3
C.
4𝑥
(𝑥−2)
D.
4𝑥
𝑥−2
.
38. Nena is making her assignment in adding dissimilar rational algebraic expressions. She recalled
that she needed to find the LCD first. Which of the following is the correct Least Common Denominator
4
9
for her to add 𝑥 5 𝑦 + 6𝑥8 𝑦5 ?
A. 𝑥 5 𝑦
B. 6𝑥 5 𝑦
C. 6𝑥 8 𝑦 5
𝑎 2 +𝑎
3𝑎−15
𝑎 2 +𝑎
.
3𝑎−15
39. Given the expression
A. The divisor is
𝑎 2 +2𝑎+1
6𝑎−30
÷
D. 6𝑥 5 𝑦
, which of the following statements is true?
3𝑎−15
B. The reciprocal of the divisor is 𝑎2 +𝑎 .
C. The common factors that can be divided out are (a+1) (3a- 15).
2𝑎
D. The quotient obtained after dividing the expression is 𝑎+1
40. Your classmate multiplied rational algebraic expressions as presented below. Is your classmate’s
solution correct?
𝑏2 +𝑏
3𝑏−15
𝑥
𝑏2 +2𝑏+1
6𝑏−30
=
𝑏2 +𝑏
3𝑏−15
𝑥
6𝑏−30
𝑏2 +2𝑏+1
=
𝑏(𝑏+1)
3(𝑏−5)
𝑥
6(𝑏−5)
(𝑏+1)(𝑏+1)
=
2𝑏
(𝑏+1)
A. Yes. There is a need to get the reciprocal of the second factor.
B. Yes. The product obtained after multiplying the expressions is correct.
C. No. Getting the reciprocal is not applicable in multiplying rational expressions.
D. No. The product obtained after multiplying the rational algebraic expressions is wrong.
4
6
41. Mark can run at a speed of (𝑥+2 )kph and Angelo can run at a speed of (𝑥−3) kph. Both stopped
(x+2)(x−3)
running at [
] hours. The formula in finding the distance is Distance =
4
The solutions below provided for the distance covered by Mark’s alone.
I.
II.
4
Distance = (𝑥+2) [
= (x-3) km
4
(x+2)(x−3)
]
4
Distance = (𝑥+2) ÷ [ (
4
)
𝑥+2
=(
=
Speed
.
𝑇𝑖𝑚𝑒
(x+2)(x−3)
]
4
4
]
(𝑥+2)(𝑥−3)
16
km
(x2 +4x+4)(x−3)
∙[
Which of the following shows the correct solution?
A. I only
B. II only
C. I and II
D. neither I nor II
42. Of the following equations, which line passes through the points (3, 1) and (2, −4)?
A. 5𝑥 + 𝑦 = 14
B. 5𝑥 + 𝑦 = −14
C. 5𝑥 − 𝑦 = 14
D. 5𝑥 − 𝑦 = −14
43. Which of the following equations is represented by the given graph below?
A. 𝑦 = 2𝑥 + 3
B. 𝑦 = 3𝑥 + 2
C. 𝑦 = 2𝑥 − 3
D. 𝑦 = 3𝑥 – 2
For items 44-45
Pauline bought 18 pieces of fruits in two kinds, avocado (a) and banana (b). She paid a total of ₱108. A
piece of avocado (a) costs 8 pesos and a piece of banana (b) costs 5 pesos each.
44. Which of the following sets of equations represent the given problem?
45. How many avocados did she buy?
A. 6 pieces
B. 12 pieces
C. 10 pieces
D. 8 pieces
For items 46-48 Manuel’s Budget Snacks
Taehyung and Jennie went to All Day convenience store. Taehyung bought 3 coffee shakes (c) and 4
pieces of fudgee bar (f) for a total of 167 pesos. Jennie bought 2 coffee shakes and 3 pieces of fudgee
bar for a total of 114 pesos. Lisa needs to buy his snacks for recess and he went to the same
convenience store. He has 50 pesos and decided to buy a coffee shake and a fudgee bar.
What can Lisa afford to buy?
Circle “Yes” or “No” for each of the following options. (3 points)
Snacks
Coffee Shake
Fudgee Bar
Coffee Shake and Fudgee Bar
Full Credit- Gives 3 correct answers
Partial Credit- One or two correct answers
No Credit- Missing/ No response
Can Manuel buy the item/s with 50 pesos?
Yes / No
Yes / No
Yes / No
Items 49-50 Bicycle Rush!
Shoyo Hinata and Koshi Sugawara are riding a bicycle. They are rushing for their volleyball
tournament. For them to reach the venue of the tournament, they need to pass on a hilly road. Road 1
has a slope of 20 feet while Road 2 has a slope of 35 feet.
Which road will they take for them to reach the tournament on time? Why?
(2 points)
m= 20 ft.
m= 35 ft.
https://weheartit.com/entry/271026303
Road 1
Road 2
Prepared by:
Approved by:
Checked by:
Mary Jane M. Pacion
Subject Teacher
Marvin R. Romias
Head Teacher I
Full Credit- Gives the correct
answer with explanation.
Partial Credit- Gives the answer
but no explanation
No Credit- Missing/ No response
Marvin R. Romias
Head Teacher