Name: __________________________ Date: ________

Year and Section:__________________ Score:________

Mathematics 8 First Quarter

Pre-test
General Direction:
 Read and understand each statement carefully
 Use black or blue ball pen
 No alteration allowed
 Always keep your answer sheet neat. Do not fold, crumple nor write unnecessary works on it.
 Use the back of your papers for your solutions.

1. It is an algebraic expression that represents a sum of one or more terms containing whole number
exponents on the variables.
a. polynomials c. variables
b. linear equation d. constant
2 4
2. Simplify (x )(x )(x).
a. x6 c. x7
6
b. x (x) d. x7(x)
3. What do you call a polynomial with three terms?
a. Monomial c. Trinomial
b. binomial d. linear equation
4. What is the product of (9xa)(5xa)?
a. 45xa c. 45x2a
x
b. 45a d. 45xaa
5. Calculate the product of (x+2)(x+3).
a. x2+6x+6 c. 3x2+5x+6
2
b. x +5x+6 d. 2x2+3x+6
6. What is the product of 2x(x+2)?
a. 2x2+4x c. 2x2+2
b. 2x2+4 d. x2+2
2n n
7. What is the quotient of x /x ?
a. x3n c. 3xn
n
b. x d. 3x2n
8. Simplify -24x8/12x4.
a. -6x4 c. 6x4
b. -2x4 d. 2x2
2
9. Determine the quotient of x +3x-40/x+8.
a. x-4 c. x-5
b. x+5 d. x+4
10. Divide x2-1 by x-1.
a. x+1 c. x+2
b. x-2 d. x-1
11. Find the dividend of divisor x-5, quotient 5x+1 with the remainder of zero.
a. 5x2-26x-5 c. 5x2+26x-5
b. 5x2+24x-5 d. 5x2-24x-5
2
12. What is the remainder of 3x -14x-12 divided by x-2?
a. 28 c. 3x-8
b. -28 d. 3x+8
2
13. Expand (x+y) .
a. x2+2xy+y2 c. 2x2+xy+y2
2 2
b. x -2xy+y d. 2x2-xy+y2
14. Find the area of a circle having a radius of x-5 cm.
a. Πx2-10Πx+25Π cm2 c. Πx2-10Πx-25Π cm2
b. Πx +10Πx+25Π cm
2 2
d. Πx2+10Πx-25Π cm2
15. What is the GCF of x2+2x?
a. 1 c. x
b. 2 d. a
16. Find the greatest common factor of 12a and 36ab.
a. 12b c. 6a
b. 12a d. 6b
17. What is the factor of 5x+10?
a. 5(x-2)2 c. 5(x+2)
2
b. 5(x+2) d. 5(x-2)
18. Factor and simplify x2+4x/4x+16.
a. x/4 c. x
b. 4/x d. 4x
19. Identify which expressions is a difference of two squares.
a. 9x2-5 c. 3x2-25
2
b. 100-13x d. 9x2-25
20. Factor 1-16x8 using difference of two squares.
a. (1+4x2)(1+2x2)(1-2x2) c. (1-4x2)(1+2x2)(1-2x2)
b. (1+2x2)(1-2x2) d. (1+2x2)(1+2x2)
3
21. Factor a +27.
a. (a+3)(a2-3a+9) c. (a-3)(a2+3a+9)
b. (a+3)3 d. a2-3a+9
3 3
22. The pattern x -y is called _____.
a. sum of two cubes c. difference of two squares
b. difference of two cubes d. perfect cube
2
23. Factor out x +4x+4.
a. (x+1)2 c. (x-2)2
b. (x+2)2 d. (x-1)2
2
24. Find the length of a side of a square if its area is 4x +12x+9.
a. x+3 c. 3x+3
b. 2x+3 d. 2x-3
25. (a+n)(a+11), what is the value of n to complete the factor of a2+12a+11?
a. 1 c. 2n
b. 2 d. n
26. Determine one of the positive integral values of k in the trinomial n2+5n+k so that it can be factored.
a. 4 c. 6
b. 5 d. 3
27. Determine the negative integral values of k in the trinomial n2+5n+k so that it can be factored.
a. -2 c. -5
b. -4 d. -6
2
28. Factor x -9x+18 completely.
a. (x+3)(x-6) c. (x-3)(x+6)
b. (x-3)(x-6) d. (x+3)(x+6)
29. Determine the statement: The value of “a” in the trinomial 5x2-8x-7 is -7.
a. always true c. never true
b. sometimes true d. none of the above
30. Fill in the box to complete the equation []x2+19x+12= (4x+3) (x+4).
a. 3 c. 6
b. 4 d. 9
2
31. Fill in the boxes to complete the equation [m]x -9x-9 = ([n]x+3) (x-3).
a. m=4, n=-4 c. m=-4, n=4
b. m=4, n=4 d. m=-4, n=-4
2
32. Factor 5x +x-18 completely.
a. (5x-6) (x+3) c. (5x+9) (x+2)
b. (5x-9) (x+2) d. (5x+6) (x-3)
33. A fraction whose numerator and denominator are polynomials.
a. rational expression c. trinomials
b. fraction d. none of the above
34. Find the value “a” in the expression 2a2/a-3 so that it will be undefined.
a. 0 c. -1
b. 2 d. 3
35. Simplify the rational expression 45a2b/30ab.
a. 3a/2 c. 3a/2b
b. 3a/b d. 3/a
36. Simplify the rational expression a2+7a/a+7.
a. –a c. a/7
b. -1 d. –a/7
2 3
37. Multiply and simplify (a /10) (5/a ).
a. 2a2 c. 5a2
2
b. a /2 d. a2/5
38. Multiply and simplify (8/14) (7/12).
a. 1/2 c. 1/3
b. 1 d. 3/4
39. Divide and simplify (7/6x) / (7/12x).
a. 7/3x c. 2
b. 2x d. 7x/3
40. Divide and simplify (4/5) / (3/10).
a. 8/3 c. 4/5
b. 3/8 d. 5/4
41. Find the sum of 5/3 + 3/8.
a. 8/13 c. 13/8
b. 4/13 d. 13/4
42. Find the difference of [(a2+8a-15) / (3a2-9a)] – [(4a+6) / (3a2-9)].
a. a+7/3a c. a+(7/3a)
b. (a+7)/3a d. a/7
43. Simplify [(3/4) + (1/2)] ÷ [(5/8) – (5/6)].
a. 5 c. 6
b. -5 d. -6
1
44. Simplify 1 .
1+ 1
1+
𝑎
a. a+1 𝑎+1
c. 2𝑎+1
b. 2a+1 2𝑎+1
d. 𝑎+1
𝑎
45. Simplify 𝑏 .
1−𝑎+𝑏
a. a c. b
b. a+b d. a-b
2
1+𝑎
46. Simplify 4 .
1− 2
𝑎
𝑎
a. c. a
𝑎−2
𝑎−2 d. 2a
b. 𝑎
𝑥 1 𝑥
47. Solve for “x” in the equation 5 + 4 = 2.

a. 6/5 c. 1/3
b. 5/6 d. 3
𝑦+3 4
48. Find the value of “y” in the equation 𝑦−1 = 𝑦−1.
a. 4 c. 2
b. -1 d. 1
49. Identify this equation -54 = -(5)4.
a. always true c. never be true
b. sometimes true d. none of the above
50. Identify the base in this notation “a4”.
a. a c. 4a
b. 4 d. a4
51. What rule does xm(xn) = xm+n emphasizes?
a. product rule of exponents c. second power rule of exponents
b. first power rule of exponents d. quotient rule
52. Simplify (c3d2)5.
a. c8d7 c. c2d3
b. c15d10 d. (cd)30
𝑥𝑚
53. What rule does 𝑥 𝑛 = 𝑥 𝑚−𝑛 emphasizes?
a. product rule of exponents c. second power rule of exponents
b. first power rule of exponents d. quotient rule
4𝑎4 𝑎3
54. Simplify 𝑎5 .
a. 4a4 c. 4a2
b. 4a3 d. 4a
55. Any number, excluding zero, raised to zero power is equal to ?.
a. 1 c. 0
b. -1 d. undefined
56. Simplify [(xmnp)]0 , if “x,m,n and p” are natural numbers.
a. 1 c. 0
b. -1 d. undefined
57. Solve for “x” in the equation p (p ) = p .
x x 5x-6

a. 4 c. 2
b. 3 d. 1
58. Solve for “y” in the equation 3y+2 = 81.
a. 4 c. 2
b. 3 d. 1
59. Solve for the value of “x” in the equation 9 = 243.
x

a. 2/5 c. 5/4
b. 4/5 d. 5/2
60. Find the value of “x” in the equation 2 =512.
2-3x

a. -7/3 c. -3/7
b. -7 d. -3