SAN ISIDRO NATIONAL HIGH SCHOOL
San Isidro, Surigao del Norte
FIRST PERIODICAL EXAMINATION
Mathematics Grade 8
Name: ________________________________________
Grade/Section:____________________
DIRECTION: Read the questions carefully and choose the letter that corresponds to your answer. Write
the letter before the number.
1. These are special forms of algebraic expressions whose products are readily seen.
a. Factors
b. Special Products
c. Rational Number
d. Real Number
2. What do you call this expression (x+4)² ?
a. Square of Binomial
c. Square of Trinomial
b. Sum and Difference of Two Squares
d. Cube of Binomial
3. Which of the following does not belong to the group?
a. (¼)x² - 1
b. x² - 0.0001y²
c. 8(x-1)³ - 27
d. (x+2)²
4. It is a process of finding factors of an expression.
a. Prime Factorization b. Factoring
c. Common Factors
d. Monomial Factor
5. The result of squaring a binomial which the first and last term are perfect squares and the
middle term is twice the product of square root of the first and last term.
a. Perfect Square trinomials
c. Perfect Square Binomials
b. Cube of Binomials
d. Sum and Difference of Two Squares
6. Which of the following expression is a rational algebraic expression?
a. x/√3y
b. 3c² / √a+1
c. 4y² + z²
d. (a-b )/( b + a)
7. A ratio of two polynomials provided that the denominator is not equal to zero.
a. Rational Algebraic Expressions
c. Irrational Numbers
b. Rational Numbers
d. Real Numbers
8. What is the product of two rational expressions?
a. It is the product of the dividend and the reciprocal of the divisor
b. It is the product of the numerators divided by the product of the denominators
c. It is the product of the sum of numerators and denominator of rational expressions
d. It’s the product of the difference of numerator and denominator of a rational expressions
9. If the numerator or denominator, or both numerator and the denominator of a rational
algebraic expressions is also a rational expression then it is called…
a. Complex Numbers
c. Complex Rational Algebraic Expressions
b. Complex Fraction
d, Complex Radical
10. What is the Value of Non- zero polynomial raised to zero?
a. One
b. Two
c. Zero
d. Undefined
11. Which of the mathematical statement is true?
a. (2x-y)(3-y)= 6x² -5xy +y²
c. (3x-4)(2x+7)=6x² -13x – 28
b. (4x-5)(4x-5)=16x² -40x-25
d. (2x+5)²= 4x²+20x-25
12. Find the missing terms: (x+____)(3x+____)=3x²+27x+24
a. 6,4
b. 4,6
c. 8,3
d. 3,8
13. 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
14. The area of a rectangular garden is (12x²-8x-15)m². What are the dimensions?
a. (3x-5)m by (4x+3)m
c. (6x-3)m by (2x-5)m
b. (6x+5)m by (2x-3)m
d. (12x-15) m by (x+1)m
15. Which of the following values of k will make x²-5x+k factorable?
a. 5
b. 12
c. -10
d. -14
16. If one of the factors of 1/(a+1) is a-1/a²-2a+1, find the other factor?
a. a+1/a-1
b. a-1/1-a
c. a²-2a+1/a²-1
d. a²-1/a²-2a+1
17. The area of a rectangle is x²-3x-10, What is the length of the rectangle if the width is x+2?
a. (x+5)(x-2)
b. (x+5)(x-2)/(x-2)
c. (x+5)/(x-2)
d. x-5
18. What will be the result when a and b are replaced by 2 and -1 respectively, in the expression
(5a-2b)(3a-3b)?
a. 108
b. 106
c. 104
d. 102
19. What are the value of x²+2x-5, x=2
a. 2
b. 3
c. 4
d. 5
20. What is the equivalent of a²-b²
a. (a+b)(a-b)
b. a-b
c.a+b
d. a²-2a+b²
21. How do you find the cube of binomial of the (x+y)³?
a. Find the cube of each term to get the first and last term
b. The second term is three times the product of the square of the first and second term
c. The third term is three times the product of the first and the square of the second term
d. All of the above
22. Your classmate was asked to square (2x-3), he answered 4x²- 9. Is his answer correct?
a. Yes, because squaring a binomial always a produces a binomial product
b. Yes, because the product rule is correctly applied
c. No, because squaring a binomial always produces a trinomial product
d. No, because the answer must be 4x²+9
23. Factor 16x⁴-625y¹⁶ completely
a. (4x²-25y⁴)(4x²+25y⁴)
c. (2x+5y⁴)(2x-5y⁴)(4x²+25y⁴)
b. (4x⁴-25y⁸)(4x⁴+25y⁸)
d. (2x²+5y⁴)(2x²-5y⁴)(2x²+5y⁴)(2x²+5y⁴)
24. Which of the following is a possible base of a triangle whose area is (2x²-6x+9) square meters?
a. (2x-9)m
b. (4x-6)m
c. (2x+1)m
d. (4x-3)m
25. The reduced form of (4/5)ˉ³ is
a. 64/125
b. 125/64
c. -64/125
d. -125/64
26. (xˉ³yˉ⁴)⁰ is equivalent to
a. x³y⁴
b. 1/x³y⁴
c. 0
d. 1
27. Roger can do the project x number hours. Concepcion can do the same job in 2 hours less than
Roger does. Which of the choices is the difference of their rate?
a. 2x-2/x²-2x
b. -2/x²-2x
c. 2x/x²-2x
d. -2x-2/x²-2x
28. You have (x²+2) pesos to buy materials for your school project. You spent half of it in the first
store, then you spent one-third of your money less than you spent in the first store. In the third
store, you spent one-fourth of the remaining money from the two stores. What is the total cost
of the materials?
a. (4x²-8)/4
b. (3x²+6)/4
c. (5x²+20)/12
d. (7x²+14)/12
29. What is the surface area of the given cube below?
a. (6x+18y)cm²
b. (x²+6xy+9y²)
c. (6x²+26xy54y²)cm² d. (x²+9x²y+27xy²+27y³)cm²
30. Which statement is true?
a. The square of a binomial is also a binomial
b. The product of a sum and difference of two terms is a binomial
c. The product of a binomial and a trinomial is the square of a trinomial.
d. The terms of the cube of a binomial are all positive.
31. If there area of a square garden is (4x²-12x+9) square units, is it possible to find its sides?
a. Yes, using factoring of difference of two squares.
b. No, one of the sides must be given
c. Yes, the area is a perfect square trinomial
d. No, the area is not factorable
32. Below is the solution of Rogelio in factoring 3(x⁴-81). Is his solution correct?
3(x⁴-81)
(x²-9)(x²+9)
(x+3)(x+3)
a. No, because the other factors were omitted
b. No, because it lacks 3 as its factor
c. Yes, because 3x⁴-243 is divisible by x+3.
d. Yes, because the complete factorization of the expression is (x+3)(x-3)
𝑥ˉ³𝑦𝑐⁸
33. What is the value of the expression 𝑥²𝑦ˉ²𝑐⁷ when x=2,y=3 and c= -2?
27
27
32
a. - 16
b. 16
c. 27
34. The expression (2xˉ³y)ˉ² written with positive exponent equals
a.
1
(2𝑥²𝑦)²
𝑥⁶
2
b. 4𝑦²
c. 𝑥⁶𝑦²
32
d. - 27
𝑥⁵
d. (4𝑦)2
1
35. Which of the following is equivalent to
1
1
𝑥²+5𝑥+6
1
𝑥+3
?
1
1
a. 𝑥+2
b. 𝑥−2
c. 𝑥+3
d. 𝑥−3
36. A businessman invested his money and was assured that his money will increase using the
formula P(1+rn)ᵑᵗ where P is the amount of money invested (the Principal); r is the rate of
increase; n is the mode of increase in a year and t is the number of years. If the businessman
invested Php 10,000. How much can he get at the end of the year if the rate is 50% and will
increase twice a year?
a. Php 15,652
b. Php 16, 552
c. php 15,625
d. Php 15, 255
37. The product of (5x+7y) and (5x-7y) is
a. 25x²-70xy-49y²
b. 25x²+70xy-49y²
c. 25x²+49y²
d. 25x²-49y²
38. You own three hectares of land and you want to mow it for farming. What will you do to finish
it at a very least time?
a. Rent a small mower
c. Do kaingin
b. Hire three efficient laborers
d. Use germicide
39. Your SK chairman planned to construct a basketball court. As a contractor, what will you do?
a. Show a budget proposal
c. Present a feasibility study
b. Make a budget plan
d. Give a financial statement
𝑎 2 −1
40. Simplify 𝑎2 −𝑎
a.
𝑎+1
𝑎
b. a+1
c. a-1
d. 1
II. PROBLEM-SOLVING (For numbers 41-50 ). Show your solution on the space provided and you can use
the back page of this sheet.
1. Simplify
𝑥 2 +2𝑥−8
𝑥 2 −4
𝑎 2 −9
2. Find the product of 𝑎2 +𝑎−20 and
𝑎 2 −8𝑎+16
3𝑎−9
3. A square piece of land was rewarded by a master to his servant. They agreed that a portion of it
represented by the rectangle inside, should be used to construct a grotto. How large of the land
that is available for other uses.
2
222gg
5-2x
222gg
2x-1
4. Divide
5. Add
𝑥 2 +2𝑥−8
𝑥 2 −4
𝑥 2 +2𝑥−8
𝑥 2 −4
1−𝑥²
and 𝑥 2 +𝑥−2
𝑎𝑛𝑑
1−𝑥²
𝑥−2
2x-1