MYSTICAL ROSE COLLEGE OF SCIENCE AND TECHNOLOGY

Pogonlomboy Mangatarem, Pangasinan

Achievement Test
Mathematics 8
Name: Score:
Grade & Section: Date:

I. MULTIPLE CHOICES. Read and analyze each statement carefully then write the letter of the
correct answer on the space provided.
____1. What is the Greatest Common Factor of 24 ____18. What is the complete factored form of 4𝑥2
and 54? + 16𝑥𝑦 + 16𝑦2?
a. 1 b. 2 c. 3 d. 6 a. (2𝑥 + 4𝑦)2 b. (2𝑥 + 4𝑦)(2𝑥 − 4𝑦)
____2. What is the GCF of 20, 24, and 40? c.(2𝑥 − 4𝑦)2 d. (2𝑥 − 4𝑦)(2𝑥 − 4𝑦)

____3. What is the GCF of 𝑥2 and 𝑥9?

a. 1 b. 4 c. 8 d. 20 ____19. What are the two numbers whose sum is

a. 𝑥2 b. 𝑥7 c. 𝑥11 d. 𝑥 18
1 and whose product is -12?

____4. What is the GCF of 𝑥𝑦10,4𝑦6, 𝑥9𝑦9, and

a. 3 and -4 b. -3 and 4 c. -3 and -4 d. 3 and 4

𝑥10𝑦10?
____20. What are the two expressions whose sum

a. 𝑥𝑦 b. 𝑥𝑦 c. 𝑥 𝑦 d. 𝑥 𝑦
is 7x and whose product is 10𝑥2?
6 4 4 4 6
a. 2x and 5x b. -2x and 5x
____5. What are the complete factors of the c. 2x and -5x d. -2x and – 5x

a. 7(𝑥 − 1) b. 7(1 − 𝑥) c. 7𝑥 – 1 d.
polynomial 7𝑥 − 7? ____21. What do you call an expression in fraction
form in which the numerator and the
7(𝑥 − 7) denominator are polynomials?
____6. What are the complete factors of 2𝑥 - 12𝑥 6 4 a. rational algebraic equation
? b. linear algebraic expression
c. rational algebraic expression
6) d. 𝑥 (2𝑥 − 12)
4 4 5
a. 2(𝑥 - 6𝑥 ) b. 2𝑥 (𝑥 − 6𝑥) c. 2𝑥 (𝑥 − 4 2

6 2 d. linear algebraic equation

in the form of 𝑃/𝑄, where 𝑃 and 𝑄 are

____7. Which of the following is a perfect square ____22. In a rational algebraic expression written

polynomials, the polynomial 𝑄 must not be equal

expression?
a. 3𝑥 2
b. 4𝑥 c. 9𝑥 3
d. 16𝑥 4

____8. If one factor of the difference of two to ____.

a. 0 b. 1 c. 2 d. 3
a. 𝑥 – 2 b. 𝑥 – 2 c. 𝑥 – 2
squares is x + 2, what is the other factor?
____23. Which of the following is a rational
____9. What is the complete factored form of 𝑧 −
2 2 2
d. (𝑥 − 2) 2

2 algebraic expression?
16? a. 6/𝑥−1 b. 2− √𝑥/4−𝑥 c.4+3/𝑥/𝑦−2 d.
a. (𝑧 − 4)2 b. (𝑧 − 8)2 c. (𝑧 − 4) (𝑧 − 4) 1−𝑥/1+1/𝑥
d. (𝑧 + 4) (𝑧 − 4) ____24. What value of x will make the rational
algebraic expression 5𝑥+3/𝑥−6 undefined?
expression 𝑦 − 49?
____10. What is the complete factored form of the
4 a. -6 b. -3/5 c. 6 D. 3/5

expression 2𝑥+1𝑥 when 𝑥 = 1?

____25. What is the value of the rational
2 2 2 2
a. (𝑦 ) − (7 ) b. (𝑦 − 7) 2 2 2
c. (𝑦 + 7) 2

2
d. (𝑦 − 7) (𝑦 + 7) 2
a. 2 b. 3 c. 4 d. 5
____11. What is the result when you square a

𝑥2+5𝑥/𝑥2+1when 𝑥 = −1?
____26. What is the value of the expression
binomial?
a. binomial b. sum of two squares c.
difference of two squares d. perfect square a. −2 b. −1 c. 0 d. 1
trinomial ____27. Which of the following represents a ratio
For items 12 –14. Expand (2x − 4) 2 of two polynomials?
____12. What is the last term? a. (𝑥 + 1) + (𝑥 − 3) b. (𝑥 + 1) − (𝑥 − 3)
a. 4𝑥 2
b. -16 c. 16 d. −4𝑥 2 c. (𝑥 + 1)(𝑥 − 3) d. (𝑥+1)/(𝑥−3)
____13. What is the middle term? ____28. Which of the following is a rational
a. 8x b. -8x c. 16x d. -16x algebraic expression with a monomial in the

a. 𝑑/𝑡 b. 𝑥+1/𝑦 c. 𝑥/6𝑥−5 d.

____14. What is the first term? numerator and a binomial in the denominator?
a. 4x 2
b. −4x 2
c. 2x 2
d. −2x 2

____29. A speedy biker can travel 5 km per 𝑡

____15. Which of the following is the expanded 3𝑥−9/𝑥−3
form of (𝑥 − 5)2?
2 2
a. x − 25 b. x − 5x − 25 c. x − 10x + 2 hours. Which of the following expressions best

a. 5𝑡 b. 5𝑡1/2 c. 𝑡/5 d. 5/𝑡

25 illustrates the situation?
d. x2 − 10x + 25

𝑥 hours. What part of the activity can be

____16. Which of the following is a perfect square ____30. Vince can complete his school activity in

a. 𝑥 − 2𝑥 + 4
trinomial?

c. 𝑥 − 4𝑦 + 2𝑦 d. 9𝑥 − 6𝑥𝑦 − 𝑦 a. 4𝑥 b. 4𝑥 c. 𝑥 – 4 d. 𝑥 + 4
2 2
b. 4𝑥 + 12𝑥 + 9 completed by Vince after 4 hours?
2 2 2 2

____17. All of the following are perfect square _____31. 7/28

trinomials EXCEPT one. Which is it? a. ½ b. 4/5 c. 7/9 d. ¼
_____32. 2/4
c. 𝑥2𝑦2 − 4𝑥2𝑦2 + 4𝑥2𝑦2 d. 𝑎2𝑏2 + 4𝑎3𝑏 +
a. 4𝑥2 + 12𝑥𝑦 + 9𝑦2 b. 9𝑎2 − 36𝑎 + 36
a. ½ b. 4/5 c. 7/9 d. 7/3
4𝑎 2 _____33. 10/25
a. 7/9 b. 7/3 c. ¼ d. 2/5
_____34. 14/18
a. 7/9 b. 7/3 c. ¼ d. 2/5
_____35. 28/12
a. 7/9 b. 7/3 c. ¼ d. 2/5
_____36. 7𝑝2 − 7𝑝= 7𝑝 (______________)
a. 7x3y(1-2xy-3x-5x2y) b. 3xy
c. 15t(1-t+t ) 2
d. (p-2)
_____37. 18𝑥𝑦 + 3𝑦= (________________) (6𝑥 + 1)
a. 3xy b. 15t(1-t+t2) c. 17x d. 3y
_____38. 15𝑡3 − 15𝑡2 + 20𝑡= 5𝑡 (_________)
a. 7x3y(1-2xy-3x-5x2y) b. 3xy c. 15t(1-t+t2) d.

_____39. 17𝑥5 − 51𝑥4 − 34 𝑥= (________) (𝑥4 −

17x
_____51. Which points lie in Quadrant II?
3𝑥3 − 2) a. A, B b. C, D c. D, G d. E, H
a. 7x3y(1-2xy-3x-5x2y) b. 3xy _____52. Which of the following illustrates the

_____40. 35𝑥5𝑦2 + 21𝑥4𝑦 + 14𝑥3𝑦2 = 7𝑥3𝑦

c. 15t(1-t+t2) d. 17x coordinates of point G?
a. (-7,8) b. (-8, -7) c. (-8,7) d. (8, -7)
(___________) For items 13-15, refer to Figure 2.
a. 2xy+3x+5x2y b. 3xy
c. 15t(1-t+t2) d. 7p(p-2)
_____41. What is a Rectangular Coordinate
System?
a. It is a coordinate system that is used for
naming points in a plane.
b. It is a coordinate system that is used for
graphing linear functions.
c. It is a coordinate system that is used to
determine the location of a point by using a
single number.
d. It is a coordinate system that is composed of
two perpendicular number lines that meet at a
point of origin.
_____42. How many quadrants does a Rectangular
Coordinate System have?
a. 2 b. 4 c. 6 d. 8 _____53. At what location is the butterfly located?
_____43. Which among these mathematicians was a. (5,6) b. (-5, -6) c. (6,5) d. (-6, -5)
the Cartesian Plane named after? _____54. The ant is located at what quadrant?
a. Euclid b. Pythagoras a. Quadrant I b. Quadrant II
c. Blaise Pascal d. Rene Descartes c. Quadrant III d. Quadrant IV
_____44. What do you call the vertical number line _____55. Which of the following illustrates the
in the Cartesian plane? position of the bee?
a. y-axis b. x-axis c. origin d. quadrant
_____56. If 𝐴, 𝐵, and 𝐶 are real numbers and if 𝐴
a. (4,4) b. (4,5) c. (-4,4) d. (-4,5)
_____45. For the coordinates of the point in
and 𝐵 are both not equal to 0 then A𝑥 + 𝐵𝑦 = 𝐶
quadrant IV, the x value and y value are always
_____ and ______, respectively.
is called a __________.
a. negative, positive b. negative, negative
a. linear equation in one variable
c. positive, negative d. positive, positive
b. linear equation in two variables
_____46. The coordinates of the origin in the
c. system of linear equations
coordinate plane are________.
d. system of linear inequalities
a. (0,1) b. (1,0) c. (0,0) d. (1,1)
_____57. Which of the following is the standard
_____47. Point (3, 4) is an example of _______.
a. 𝑦 = 𝑚𝑥 + 𝑏 b. 𝑦 = 𝑚𝑥 – 𝑏
form of a linear equation in two variables?
a. labels b. fraction
c. 𝐴𝑥 + 𝐵𝑦 = 𝐶 d. 𝐴𝑥 − 𝐵𝑦 = 𝐶
c. ordered pair d. point of origin

_____58. What is 𝐶 in the equation 𝐴𝑥 + 𝐵𝑦 = 𝐶?

_____48. Which of the following is true about the
point (8, 1)?
a. It lies in Quadrant I. a. coefficient b. constant c. slope d.
b. It lies in Quadrant II. variable

value of 𝐵 in the equation 4𝑦 − 5 = 𝑥?

c. It lies in both Quadrant II and III. _____59. If written in standard form, what is the
d. Both statements A and C are correct.
For numbers 9-12, use Figure 1. a. −5 b. −4 c. 0 d. 1
_____49. Which of the following is true about the _____60. On his notes on linear equation in two
points in Figure 1? variables, Joshua found an equation 2𝑥 +3𝑦 =10.
a. Point D lies in the y-axis. If you were Joshua, how would you describe the
b. Poin t C has all positive coordinates. equation according to its form?
c. Point G has all negative coordinates. a. It has constant
d. Points A and B are located in Quadrant III. b. It has variables
_____50. Which point lies in the origin? c. It is in standard form
a. D b. E c. F d. H d. It is in slope-intercept form
____61. 7𝑝2 − 7𝑝
a. 7p(p-1) b. 7𝑝2 c. 7𝑝2 − 7𝑝 d. − 7𝑝 a. 1 b. 2 c. 3 d. 4
____62. 18𝑥𝑦 + 3𝑦 ____86. a4b3-2c2d6
a. 3y(6x+1) b. 3𝑦 c. 18𝑥𝑦 d. 18x(y+3y) a. 6 b. 7 c. 8 d. 9
____63. 15𝑡3 − 15𝑡2 + 20𝑡 ____87. 5e5f7 +7g8h5
a. t(15t2-15t+20) b. 2t(15t2-15t+20) c. 20t d. a. 5 b. 12 c. 13 d. 14
____88. 9-x6
____64. 17𝑥5 − 51𝑥4 − 34 𝑥
2/5
a. 3 b. 4 c. 5 d. 6
a. x(17x4-51x3-34) b. 17x(x4-51x3-34) c. 34x ____89. 12x2-x3y5+7xy5
a. 2 b. 3 c. 8 d. 6
____65. 35𝑥5𝑦2 + 21𝑥4𝑦 + 14𝑥3𝑦2
d. 2x
____90. abc+abcd
a. x3y(35x2y+21x+14y) b. (35x2y+21x+14y) a. 1 b. 3 c. 4 d. 5
c. ¼ d. 2/5 ____91. (1,100)
____66. x+3 a. Q1 b. Q2 c. Q3 d. Q4
a. polynomial b. not polynomial c. maybe d. ____92. (-25, 27)
dot a. Q1 b. Q2 c. Q3 d. Q4
____67. x-4 ____93. (45,-78)
a. polynomial b. not polynomial c. maybe d. a. Q1 b. Q2 c. Q3 d. Q4
dot ____94. (71, 99)
____68. 2d a. Q1 b. Q2 c. Q3 d. Q4
a. polynomial b. not polynomial c. maybe d. ____95. (89,96)
dot a. Q1 b. Q2 c. Q3 d. Q4
____69. 3c2+2c ____96. Find the slope of (1,100)
a. polynomial b. not polynomial c. maybe d. a. 1/100 b. 100/1 c. ¼ d. 2/5
dot ____97. Find the slope of (-25, 225)
____70. 3d-2+1 a. -1/25 b. -25 c. ¼ d. 2/5
a. polynomial b. not polynomial c. maybe d. ____98. Find the slope of (45,-8)
dot a. -5/1 b. -1/5 c. ¼ d. 2/5
For 71-80, find the coordinates of the following ____99. Find the slope of (81, 99)
places in the figure. a. 9/11 b. 11/9 c. ¼ d. 2/5
_______71. Agusan del Norte ____100. Find the slope of (14, 28)
a. (-2, 1) b. (-1, 0) c. (-2, 2) d. (-1, -3) a. 1/2 b. 2 c. ¼ d. 2/5
_______72. Cabadbaran City
a. (-2, 1) b. (-1, 0) c. (-2, 2) d. (-1, -3)
_______73. Surigao City
a. (-2, 1) b. (-1, 0) c. (-2, 2) d. (-1, -3)
_______74. Agusan del Sur
a. (-2, 1) b. (-1, 0) c. (-2, 2) d. (-1, -3)
_______75. Bislig City
a. (3, -3) b. (0, 1) c. (2, -2) d. (-1, 3)
_______76. Surigao del Norte
a. (3, -3) b. (0, 1) c. (2, -2) d. (-1, 3)
_______77. Surigao del Sur
a. (3, -3) b. (0, 1) c. (2, -2) d. (-1, 3)
_______78. Dinagat Islands
a. (3, -3) b. (0, 1) c. (2, -2) d. (-1, 3)
_______79. Butuan City
a. (1, -1) b. (0, -1.5) c. (-2, 2) d. (-1, -3)
_______80. Bayugan City
a. (1, -1) b. (0, -1.5) c. (-2, 2) d. (-1, -3)
Choose the highest degree of the polynomial
equation in the blank.
____81. x3-9x-3x2+27
a. 1 b. 2 c. 3 d. 4
____82. x2-6x+9
a. 1 b. 2 c. 3 d. 4
____83. b4
a. 1 b. 2 c. 3 d. 4
____84. c-3
a. 1 b. 2 c. 3 d. 4
____85. f2-9