APARRI SCHOOL OF ARTS AND TRADES
FIRST PERIODIC EXAM IN MATHEMATICS 8
Name : _________________________________________
Section : ___________________________
Score: __________
Date : _________
Directions : Read each item carefully. Write the letter of your answer on the space
provided. USE CAPITAL LETTERS.
________1. These are special forms of algebraic expressions whose products are readily seen.
A. Algebraic Equations
C. Rational Algebraic Expressions
B. Special Products
D. Factoring
________2. Which of the following expresses as the square of a binomial?
A. (x + y) (x – y)
C. (x + y)2 or (x – y)2
B. (x2 + y2)2
D. (x + y) (x2 + y)
________3. (10y + 5) (10y – 5), what special product is illustrated?
A. Square of a binomial
C. Cube of a binomial
B. Difference of to squares
D. Sum and Difference of a trinomial
________4. Which of the following illustrates the product of the sum and difference of two
terms?
A. x2 – y2
C. (x –y)2
2
2
B. x + y
D. (x + y)2
________5. Which of the following is a perfect square trinomial?
A. x2 + 27x + 50
C. x2 - 7x + 5
2
B. x + 18x + 9
D. x2 + 13x – 16
________6. Which of the following illustrates difference of two cubes?
A. (a + b) (a2 – ab + b2)
C. (a + b) (a2 + ab + b2)
2
2
B. (a - b) (a – ab + b )
D. (a - b) (a2 + ab + b2)
________7. (s – 5)2 is equal to _______________.
A. s2 – 10 x + 25
C. s2 – 10 x - 25
2
B. s + 10 x + 25
D. s2 + 10 x – 25
________8. Find the greatest common monomial factor of 25x2 + 15x.
C. 5x
B. x
C. 10x
D. 10
________9. Which of the following gives a product of x2 + 5x + 4?
A. (x + 1) (x + 4)
C. (x + 5) (x – 1)
B. (x+ 2) (x + 2)
D. (x + 2) (x - 2)
________10. It refers to the largest monomial that is a factor of each term of the polynomial.
A. Greatest Common Monomial Factor
B. Least Common Monomial Factor
C. Greatest Common Denominator
D. Least Common Denominator
________11. One of the factors of 2a2 + 5a – 12 is a + 4. What is the other factor?
A. 2a – 3
B. 2a + 3
C. 2a – 8
D. 2a + 8
2
________12. In the expression 2x + 10x + 25, the leading term is ___________.
A. 2
B. 2x2
C. 10x
D. 25
________13. What are the factors of the expression 16m2 + 8m?
A. (8m + 1) (2m + 4)
C. (8m) (2m + 1)
B. (4m + 4) (4m + 2)
D. (4m) (4m + 2)
________14. It is a process of finding the factors of an expression.
A. Factoring B. Squaring
C. Cancelling D. Dividing
________15. Find the factors of the given expression m4n8 – 169.
A. (mn – 13) (mn – 13)
C. (m2n4 – 13) (m2n4 – 13)
B. (mn + 13) (mn + 13)
D. (m2n4 – 13) ((m2n4 + 13)
________16. One factor of the expression x3 + 64y3 is (x2 – 4xy + 16y2). What is the other factor.
A. (x – 4y)
B. (x + 4y)
C. (x2 – 4y)
D. (x2 + 4y)
________17. What is the missing term in the expression x2 - ____ + 144 to make it a perfect
square trinomial?
A. 12x
B. 24x
C. 36x
D. 28x
________18. Which of the following is a rational algebraic expression?
3
A.
B.
√5𝑦
−𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
C. 15abc
5
3
D. √4𝑦 𝑦
________19. It can be expressed as a ratio or quotient of two polynomials.
A. Factors
C. Expressions
B. Algebraic Fractions
D. Coefficients
________20. Simplify the expression:
x 3 y5
𝑥𝑦
1
A. x2
________21. Simplify:
B. 𝑥 2 𝑦
C. x2y4
D. xy
B. x + 4
C. x2 – 4
D. x2 + 4
B. 9f2g
C.
𝑥 2 − 16
𝑥−4
A. x – 4
________22. Simplify:
9𝑓+𝑓𝑔
4𝑓
A. 9fg
9𝑓 2 𝑔
4𝑓
D.
9+𝑔
4
________23. Simplify the expression:
4𝑥 3 +8𝑥 2 −10𝑥
2𝑥
A. 2x2 + 4x – 5
B. 2x2 + 4x – 10
5𝑚𝑛
________24. Simplify: 15𝑛
A. 3m
B.m/3
________24. Add: 13xy + 9xy + 4xy
A. xy
B. 26xy
3𝑥𝑦
4𝑥𝑦
________25. Find the sum of 𝑎 𝑎𝑛𝑑 𝑎 .
7𝑥𝑦
A.
B.
2𝑎
3𝑦
7𝑥𝑦
C. 8x3 + 4x2 - 5
D. 8x4 + 16x3 - 10x
C. 3m2
D. mn/3
C. 26 + xy
D. 13(3xy)
C.
𝑎2
5
7𝑥𝑦
D. 7xy
𝑎
________26. Subtract: 3𝑦−5 − 3𝑦−5.
3𝑦−5
A.
8𝑦
8𝑦
B. 3𝑦−5
3𝑦²−5
C. 3𝑦²−5
________27. What is the difference of the polynomials
5x2 − 4x + 3
A.
C.
2𝑎
5x2 − 6x + 3
B.
D.
2𝑎
21 16𝑦
________28. Find the product of (4𝑦)(
A. 12/y
________29. If
5𝑦²
6
________30.
(3x2 + x + 1)
2𝑎
–𝑥2−4𝑥−1
−
(2x2 − 5x + 2)
2𝑎
–𝑥2+6𝑥−1
2𝑎
).
B. 12
C. 12y
D. 3y
3𝑥
is multiplied to 10𝑦 , what is the product?
1
A. 2xy
-24x8
7
D. 1
B. 2𝑥𝑦
C. –xy
D. xy
C. -6x12
D. -6x4
C. 3xy
D. 1/3xy
, what is the quotient?
4x4
A. 6x4
________31. Divide:
81𝑥𝑧
36𝑦
A. 1/z
B. 6x12
÷
27𝑥 2 𝑧 2
12𝑥𝑦
B. z
.
2𝑎
?
________32. Evaluate the expression 3x2y if x=1 and y=0.
A. 3
B. 2
C. 1
D. 0
3
________33. Evaluate: 6bc – bc where b=1, c=1.
A. 3
B. 4
C. 6
D. 9
2
________34. Evaluate the expression 3w – 5z given that w=3 and z=-1.
A. 4
B. -4
C. 14
D. -14
________35. Evaluate: 4a2 + 5a where a=3.
A. 51
B. 61
C. 71
D. 81
________36. Laiza added two rational algebraic expressions and her solution is presented
below.
4𝑥+3
3𝑥−4
4𝑥+3+3𝑥−4
7𝑥+1
+ 3 =
= 5
2
5
Is there something wrong in her solution?
A. Yes. Solve first the GCF before adding the rational algebraic expression.
B. Yes. Cross multiply the numerator of the first expression to the denominator
of the second expression.
C. Yes. She may express first the expressions as similar fractions.
D. Yes. 4x-4 is equal to x.
_________37. Maica was asked by her teacher to simplify
solution on the board this way:
𝑎²−1
=
𝑎²−𝑎
A.
B.
C.
D.
(𝑎+1)(𝑎−1)
𝑎(𝑎−1)
𝑎²−1
𝑎²−𝑎
on the board. He wrote his
=1
Did he arrive at the correct answer?
Yes. The expressions that he crossed out all common factors.
Yes. The LCD must be eliminated to simplify the expression.
1
No. a2 must be cancelled out so that the answer is 𝑎.
No. a is not a common factor of the numerator.
For items 38-39,
The length of a principal’s office is x + 5 ft and the width is x ft.
_________38. Which of the following represent the area of the office?
𝑥+5
A. A= 𝑥
C. A= (x + 5)(x)
B. A=(x + 5) D. A= (x + 5) + x
_________39. What is the area of the office if x= 10?
A. 125 ft2
B. 130 ft2
C. 145 ft2
D. 150 ft2
_________40. Rowena has a square garden with sides of length x feet. If she increases the
length by 5 feet and decreases the width by 4 feet, what is the area of the rectangular garden in
terms of x?
A. x2 – x – 20 ft2
C. x2 + x – 20 ft2
2
2
B. x –x + 20 ft
D. x2 + x + 20 ft2
4
5
6
__________41. The lengths of the sides of a triangle are 𝑐 units, 𝑑 units, 𝑐𝑑𝑒 units. Find the
perimeter of the triangle.
15
4de+5ce+6
A. 𝑐𝑑𝑒 units
C.
units
𝑐𝑑𝑒
B.
4c+5d+6e
cde
units
__________42. The length of a rectangle is
of the rectangle.
A.
B.
𝑥²+𝑥+2
square units
15
𝑥²+3𝑥−2
15
square units
D.
𝑥+2
5
15𝑐𝑑
𝑐𝑑𝑒
units
units while the width is
C.
D.
𝑥²+3𝑥+2
15
𝑥²−𝑥+2
15
𝑥+1
3
units. Find the area
square units
square units
𝑥+2
__________43. If the measurement of the side of a square is
A.
B.
𝑥²+4𝑥+4
square units
C.
square units
D.
4
𝑥²−4𝑥−4
4
__________44. The area of the rectangle is
the rectangle.
5𝑥+50
5𝑥−50
A.
B.
4
4
𝑥²−100
8
units, what is its area?
2
𝑥²−4𝑥+4
4
𝑥²+4𝑥−4
4
square units
square units
while the length is
C.
2𝑥+20
20
. Find the height of
𝑥+25
2
D.
𝑥−25
2
For items 45-46,
Jay can paint a room in 15 hours while John can finish the same task in 10 hours.
__________45. What is the representation of the above problem?
𝑥
𝑥
A. 15 + 10 = 1
C. 15x+10x=1
15
10
15
10
B. 𝑥 + 𝑥 = 1
D. 𝑥 = 𝑥
__________46. How long will it take to paint the room if they work together?
A. 3 hours B. 4 hours
C. 5 hours
D. 6 hours
For items 47-48,
Pipe A can fill the tank in 2x minutes. Pipe B can fill the tank in x minutes.
__________47. What part of the tank is filled by pipe A if it is open for 10 minutes?
A. 1/2x
B. 2x
C. 20x
D. 10/2x
__________48. How about pipe B if it is open for 10 minutes?
A. 1/x
B. 10/x
C. 10x
D.x
For items 49-50,
The volume of a cube depends on the length of its side. The formula of volume of a cube
3
is V= s , where V stands for volume and s stands for the side.
__________49. Compute for the volume if the side measures 5 cm.
A. 125cm3 B. 150cm3
C. 200cm3
D. 225cm3
__________50. How are the volume and the side related to each other?
A. The volume of the cube depends on the measurement of the side.
B. The side of the cube depends on the measurement of the volume.
C. The volume is the dependent variable while the side is the independent
variable.
D. The side is the dependent variable while the volume is the independent
variable.
Prepared by:
Ma’am Jonamaica