DIAGNOSTIC TEST IN MATH 8
Name: __________________________
Grade Level/ Section: _________________
Date:______________
Score:_____________
I-Multiple Choice. Read each item carefully and encircle the letter of the correct answer.
1. What is the side of a square garden if its area is x2 +4xy +4y?
A. x +2y
B. x+4y
C. x-2y
D. x- 4y
2. What values of will make x2 – k +9 a perfect square trinomial?
A. -3x
B. 3x
C. -6x
D. 6x
3. To maximize the use of the limited space of your house, you are designing 2 cube storage and at the same
time a stool box of different sizes. How will you represent the total volume of the two boxes in mathematical
expression?
A. x3- y3
B. x3 +y3
C. 2x3-y3
D. 2x3 +y3
4. Find the missing term: ____ (y + ___)= 3y2 + 24y +48 ?
A. 2, 4
B. 3, 4
C. 8, 4
D. 12, 2
5. The area of a square garden is 9a2 +12a +4 square units. Which expression represents the length of the side
of the garden?
A. (3a+2)units
B. (2a+3)units
C.(4a+9) units
D.(4a+13) units
6. What factoring technique did you used to find the length of the sides of the given area of a rectangle 4x2 -4x15?
A. Factoring by grouping.
B. Factoring general trinomial.
C. Factoring difference of two squares.
D. Factoring perfect square trinomial.
7. The product of two consecutive integers is 240. Which expression below will you use to assign the value of the
integers?
A. Let a be the first integer and a+1 be the second integer.
B. Let a be the first integer and a+1 be the second integer.
C. Let a+1 be the first integer and a+2 be the second integer
D. Let a+1 be the first integer and a– 2 be the second integer.
8. The length of a box is 3 less than twice the width. The height is 2 cm more than three times the width. The box
has a volume of 280 cm3 . Which of the following equation can be used to find the height of the box?
A. W(2L – 3) (3H + 2) = 280
B. W(2L + 3) (3H + 2) = 280
C. W(2W – 3) (3W + 2) = 280
D. W(2W + 3) (3W – 2) = 280
9. The base of a triangle is 4 cm less than the height. If the area is 48 cm2 , find the height and base of the
triangle.
A. base = 7 cm, height = 11cm
B. base = 8 cm, height = 12 cm
C. base = 9 cm, height = 13 cm
D. base = 10 cm, height = 14 cm
10. The distance traveled by a car is ( 6x2 -8x-8). The speed of the car is 6x-4.Find the time taken by the car for
the distance.
A. x-2
B. x+4
C. 2x-2
D. 2x+4
11. What expression is a ratio of two polynomials whose denominator is not equal to zero?
A. Expressions with Radicals
B. Negative Exponents
C. Polynomials
D. Rational Algebraic Expressions
𝑃
12. A rational algebraic expression is a ratio of two polynomials in symbol: 𝑄 ,where P and Q
are polynomials
and Q is _____________. What is the missing phrase that would make the statement true?
A. Equal to zero
B. Not equal to zero
C. Equal to the numerator
D. Not equal to the numerator
13. Which of the following illustrates a ratio of two polynomials?
1
A. 2
B.
2𝑥 −2
1
C.
√2𝑥+3
3𝑥
2𝑥+3
D. 3𝑥−2
14. What is the translation of the phrase “The product of p and q divided by three?
𝑝−3
𝑝𝑞
3
𝑝−𝑞
A. 𝑞
B. 3
C. 𝑝𝑞
D. 3
15. The denominator opf the rational algebraic expression should not be equal to zero. Is the statement correct?
A. Yes, because zero can make the rational algebraic expression undefined.
B. Yes, because the denominator of a rational algebraic expression cannotz have any value.
C. No, because zero is always the denominator of a rational algebraic expression.
D. No, because any value for the denominator opf a rational algebraic expression will do.
16. Which of the following is a system of linear inequalities in two variables?
2𝑥 + 5𝑦 = 7
𝑥 − 3𝑦 > 10
3𝑥 + 9𝑦 = −4
B. {
𝑥−2=8
A. {
𝑥 − 7𝑦 = 5
3𝑥 + 2𝑦 > 15
6𝑥 + 7𝑦 < 12
D. {
2𝑦 − 4𝑥 ≥ 9
C. {
2𝑥 − 4𝑦 < 10
17. Which ordered pair satisfies the system of linear inequalities in two variables {
?
𝑥 + 𝑦 ≥ −5
A. (-3, -3)
B. (9, 1)
C. (-6, 7)
D. (7, -4)
18. Which of the following is NOT a solution of the system of linear inequalities in two variables – 𝑥 + 4𝑦 ≥ -5 and
5𝑥 + 2𝑦 > 8?
A. (-3, -3)
B. (2,1)
C. (5,6)
D. (3,0)
19. Determine the ordered pair that satisfies the solution to the system of linear inequalities in two variables
4𝑥 − 2𝑦 ≤ 3 and 𝑦 − 2𝑥 ≤ 1.
A. (7, 8)
B. (−2, −5)
C. (3, −6)
D. (0, 4)
Use this situation to answer the questions in numbers 20 to21 :
Edwin sells pan de sal and pan de coco to earn money during vacation. Each pan de sal costs 𝑃2 and
each pan de coco costs 𝑃3. Edwin needs to earn at most 𝑃200 per day, so he needs to sell at least 20pieces of
pan de sal and at least 40 pieces of pan de coco. Assuming 𝑥 is the number of pan de sal and 𝑦 be the number of
pan de coco Edwin needs to sell.
20. Which of the following inequality represents the number of pan de sal that needs to be sold?
A. 𝑥 > 20
B. 𝑥 ≥ 20
C. 𝑥 < 20
D. 𝑥 ≤ 20
21. Which of the following inequality represents the number of pan de coco that Edwin needs to sell?
A. 𝑦 > 40
B. 𝑦 ≥ 40
C. 𝑦 < 40
D. 𝑦 ≤ 40
22. Which of the following statements is true?
A. Every relation is a function.
B. Every function is a relation.
C. Not all functions are relations.
D. All functions are not relations.
23. Which of the following relations is a function?
A. {(Mickey, mouse), (Bugs, Bunny), (Cosmo, Wanda)}
B. {(notebook, pen), (paper, pen), (pen, paper), (pen, notebook)}
C. {(January,1), (February,1), (March,1), (January,2), (February,2)}
D. {(trashcan, trash), (broom case, broomstick), (broom case, dustpan)}
24. In how many point(s) does a vertical line intersect the graph of a function?
A. at least one point
B. at exactly one point
C. more than one point
D. at exactly two points
25. Which of the following is an example of a one-to-one relation?
A. {(1, 1), (1, -1), (2, 2), (2, -2), (3, 3), (3, -3)}
B. {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7)}
C. {(q, 3), (r,3), (s, 5), (t,4), (u, 4), (v, 4), (w,5), (x, 5)}
D. {(a, p), (b, q), (c, r), (d, s), (e, t), (f, u), (g, w), (h, x)}
26. Which of the following terms are considered as building blocks of geometry?
A.Lines, Arrows, Points
B. Lines, Axioms, Corollaries
C.Lines, Points, Planes
D. Lines, Postulates, Theorems
27.If a point has no dimension and is represented by a dot, then which of the following suggests an idea of a
point?
A.The edge of a ruler
B.The knot of a rope
C.The wall of a room
D.The top of a desk
28.Which of the following describes a line?
A. A line has infinite length but has no width and thickness.
B. A line has length and width but has no thickness.
C. A line has no length but has width and thickness.
D. A line has no thickness, length, width, height and weight.
29.A plane is a flat surface comprising a set of points that extends infinitely in two dimensions. What are these
dimensions?
A. Depth and length
B. Length and height
C. Width and height
D. Width and length
30.Which of the following illustrates a line?
A..
B.
C.
D.
31.The following statements are true EXCEPT:
A.Exactly one plane contains two intersecting lines.
B.If two distinct planes intersect, then their intersection is a line.
C.If two points of a line are in a plane, then the line containing these points is on the plane.
D.Two points are contained in exactly one line
32. In the triangle, which is the median?
Y
X
W
Z
A. ̅̅̅̅̅
𝑋𝑊
B. ̅̅̅̅̅
𝑌𝑊
C. ̅̅̅̅
𝑌𝑍
D. ̅̅̅̅̅
𝑍𝑊
33. When can we say that two triangles are congruent?
A.If their corresponding parts are congruent.
B. If they are both isosceles.
C.If they are both right triangles.
D.If two of their sides are congruent.
34. Suppose ∆𝐴𝐵𝐶 is made to coincide with ∆𝑀𝑂𝑁 such as the vertices of ∆𝐴𝐵𝐶 fit exactly over the vertices of
∆𝑀𝑂𝑁 . What is the correspondence between vertices?
A. ∠𝐴 ↔ ∠𝑀, ∠𝐵 ↔ ∠𝑁, ∠𝑂 ↔ ∠𝐶
B. ∠𝐴 ↔ ∠𝑂, ∠𝐵 ↔ ∠𝑀, ∠𝑁 ↔ ∠𝐶
C. ∠𝐵 ↔ ∠𝑀, ∠𝑂 ↔ ∠𝑁, ∠𝐴 ↔ ∠𝐶
D. ∠𝐶 ↔ ∠𝑁, ∠𝐵 ↔ ∠𝑂, ∠𝐴 ↔ ∠𝑀
35. Two triangles are congruent if two angles and the included side of one triangle are congruent to two angles
and the included side of another triangle through what congruence postulate?
A. ASA
B. SAS
C.SAA
D.SSS
36. Carlos concluded that the longest side in 𝛥𝑀𝐴𝑃 is 𝐴𝑃 ̅̅̅̅̅̅̅̅ after finding that the angle
opposite to 𝐴𝑃 ̅̅̅̅̅̅̅̅ is the largest angle. What theorem did Carlos use to make such
conclusion?
A. Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
B. Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠)
C. Hinge Theorem or SAS Triangle Inequality Theorem
D. Converse of Hinge Theorem or SSS Triangle Inequality
37. Liza, Kathryn, and Nadine were each given a 21-inch piece of stick. They were
instructed to create a triangle. Each stick was cut in their own chosen lengths as
follows: Liza - 6 𝑖𝑛, 7 𝑖𝑛, 8 𝑖𝑛; Kathryn - 4 𝑖𝑛, 6 𝑖𝑛, 11 𝑖𝑛; and Nadine - 3 𝑖𝑛, 5 𝑖𝑛, 13 𝑖𝑛.
Who among them was able to make a triangle?
A. Liza
B. Nadine
C. Kathryn
D. All of them
38. What theorem did you use in determining the longest and shortest side of ∆𝑇𝐼𝑃?
A. Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
B. Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠)
C. Hinge Theorem or SAS Triangle Inequality Theorem
D. Converse of Hinge Theorem or SSS Triangle Inequality Theorem
39. Which of the following lengths in cm are possible measures of the sides of a
triangle?
A. 1, 2, 3
B. 4, 5, 10
C. 5, 6, 7
D. 5, 9,15
40. Which of the following theorems will support your answer in number 4?
A. Exterior Angle Inequality Theorem
B. Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
C. Triangle Inequality Theorem 3 (𝑆1 + 𝑆2 > 𝑆3)
D. Converse of Hinge Theorem or SSS Triangle Inequality Theorem
For items 41 – 42, consider the figure at the right.
41.Which of the following statements is true?
A. 𝑚∠𝐾𝑁𝐼 = 𝑚∠𝑃𝐼𝑁.
B. 𝑚∠𝐾𝑁𝐼 > 𝑚∠𝑃𝐼𝑁.
C. 𝑚∠𝐾𝑁𝐼 < 𝑚∠𝑃𝐼𝑁.
D. Cannot be determined.
42.Which of the following statements is true?
A. 𝑚∠𝑁𝑃𝐼 = 𝑚∠𝐼𝑁𝐾.
C. 𝑚∠𝑁𝑃𝐼 < 𝑚∠𝐼𝑁𝐾.
B. 𝑚∠𝑁𝑃𝐼 > 𝑚∠𝐼𝑁𝐾.
D. Cannot be determined.
43. What theorem did you apply to answer item numbers 41 and 42?
A. Exterior Angle Inequality Theorem
B. Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
C. Triangle Inequality Theorem 3 (𝑆1 + 𝑆2 > 𝑆3)
D. Converse of Hinge Theorem or SSS Triangle Inequality Theorem
For items 44 – 45, consider the given ∆PET and ∆DOG below.
44.What can you conclude in the given figures?
A. |𝑃𝑇| = |𝐷𝐺|
B. |𝑃𝑇| > |𝐷𝐺|
C. |𝐷𝐺| < |𝑃𝑇|
D. |𝐷𝐺| > |𝑃𝑇|
45. .What theorem did you use to answer item number 9?
A. Exterior Angle Inequality Theorem
B. Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
C. Hinge Theorem or SAS Triangle Inequality Theorem
D. Converse of Hinge Theorem or SSS Triangle Inequality Theorem
For number 46-50 .Find all the possible outcomes of the following:
46. Picking a number from 1 to 4 and choosing the color red, green, or yellow.
A. 6
B. 9
C. 12
D. 24
47. You have a choice of 2 colors of pants, 3 colors of shirts, and 2 kinds of shoes. How many
different outfits can you wear?
A. 4
B. 13
C. 7
D. 12
48 . Christmas sweatshirts come in three sizes and six colors.
A. 18 outcomes
B. 9 outcomes
C. 24 outcomes
D. 36 outcomes
49. A number cube is rolled three times.
A. 36 outcomes
B. 216 outcomes
D. 66 outcomes
C. 18 outcomes
50. A number cube is rolled and a number card is drawn from cards numbered 1-14.
A. 146 outcomes
B. 14 outcomes
C. 84 outcomes
D. 20 outcomes
Prepared by:
JENELYN Y. TAGRA
Subject Teacher
Checked by:
GLORIA M. PARAGUYA
Principal III