Republic of the Philippines 1 2x

Department of Education + = 1?
2x 4
Region VII, Central Visayas a. 4 b. 3
Division of Bohol c.2 d.1
Calape District 11. Rewrite f(x) = 2x2 - 12x + 11 into the form
f(x) = a(x – h)² + k.
a. f( x) = 2 ( x - 3 )2 – 7
DIAGNOSTIC TEST b. f( x) = 2 ( x - 3 )2 + 7
MATHEMATICS 9 c. f( x) = 2 ( x + 3 )2 – 7
d. f( x) = 2 ( x + 3 )2 + 7
Directions: Read and analyze each item 12. The electrical voltage V varies jointly as the
carefully. Choose the correct answer and current I and the resistance R. This relationship
encircle the letter of your choice. is written as
kI
a. R = IV b. V =
R
1. Which of the following is the standard form of k
quadratic equations? c. V = kIR d. V =
IR
a. ax2 + bx + c < 0, a 0
13. Sketch the graph of f(x) = ( x – 1)2 – 5.
b. Ax + By + c = 0
a. b.
c. ax2 + bx + c = 0, a 0
d. y = mx + b
2. The roots of a quadratic equation are -4 and -5. 1 -1
Which of the following quadratic equations has
these roots? -5 -5
a. x2 + x - 20 = 0 b. x2 - x + 20 = 0
c. x + 9x + 20 = 0 d. x2 - 9x + 20 = 0
2
c. d.
3. What is the sum of the roots of the quadratic 5 5
equation 5x2 – 10x + 6 = 0?
a. - 2 b. 2 -1 1 -1 1
1 1
c. d. -
2 2
4. What is the discriminant of the quadratic
equation 3x2 – 2x - 5 = 0 ?
14. Given the expression ( 2 n ) 3/5, how will you
a. -64 b. -56
c. 56 d. 64 transform it into a radical expression?
5. What is the nature of the roots of a quadratic a. √
5
8 n3 b. √
3
8 n5
equation if the value of its discriminant is
negative?
c. √5 2 n3 d. √3 2 n5
a. The roots are not real. 15. What is √
4
16 x 8 y 4 equal to?
b. The roots are rational and not equal.
c. The roots are irrational and not equal. a. 4 x 2 y 2 b. 4 x 2y
d. The roots are rational and equal. c. 2 x 2y d. 2 x 2 y 2
6. Which of the following rational algebraic
equations is transformable to a quadratic
equation?
[
16. Which of the following is equal to (−3 x 3 y ) ]
0 −1
?

w+1 w+2 2 3 a. 1 b. –1
a. – =7 b. + =5
2 4 p p+ 1 1 −1
2 p−1 1 3 q 3 4 7 b. c. d.
c. + = d. + = 9 9
3 2 4 m−2 m+ 2 m
17. Which of the following is TRUE?
2
7. Find the solution set of x + 7x + 12 > 0. p
100
z
−5
−2
a. 3 and 4 b. -3 and 4 a. 100
=1 b. −7
=z
c. -3 and -4 d. 3 and -4 p z
8. It takes Manny 6 days more to paint a house m
23
n
1/ 3
2 /3
than Jimboy. If they work together, they can c. 23
=0 d. 1/ 3
=n
finish the same job in 4 days. How long would it m n
take Manny to finish the job alone?
a. 3 days b. 4 days 18. Which of the following is NOT TRUE about the
c. 10 days d. 12 days graph of y = - ( x + 2 )2 + 4?
9. The length of a tarpaulin is 3 ft. more than thrice a. the graph of y = x2 opens downward
its width and its area is 126 ft 2. What are the b. the graph of y = x2 moved 4 units upward
dimensions of the tarpaulin? from the origin
a. 7 ft x 6ft b. 10.5ft by 12ft c. the graph of y = x2 moved 2 units to the right
c. 9 ft by 14ft d. 21ft by 6ft from the origin
10. What is the value of x in the equation d. none of these
19. Consider 3 and -5 as the zeros of the function,
what is the equation of its function?
 a. Q(x) = x2 - 2x -15 c. Q(x) =x2 +2x +15 1 1
a. A = (6)(137) sin 8° b. A = (8)(137)
c. Q(x) = x2 + 8x -15 d. Q(x) =x2+2x-15 2 2
20. If 2 identical packages weigh 90 kg., how much sin 6°
will 20 of these packages weigh? 1 1
a. 315 kg b. 525 kg c. A = (6)(8) sin 137° d. 137 = (6)(8) sin A
2 2
c. 900 kg d. 1575 kg
32. Determine the correct formula for the tan ratio
21. Simplify and combine 9 √ 5 - 2 √ 5 - 4√ 3 + √ 3. of
a. 16 √ 15 b. 7 √ 5 - 3 √ 3 B.
a. tan B = length of side adjacent B
c. 4 √ 15 d. 11 √ 5 - 4 √ 3 length of the hypotenuse
b. tan B = length of side opposite to B
22. Which of the following statements is TRUE? length of side adjacent to B
a. Every square is a rectangle.
c. tan B = length of hypotenuse
c. Every rectangle is a square.
b. Every rhombus is a square. length of side opposite to B
d. Every parallelogram is a rhombus. d. tan B = length of side opposite to B
23. A quadrilateral with two pairs of adjacent, length of hypotenuse
congruent sides.
a. Square b. Rectangle 33. From triangle ACB, with right angle at C, if b = 15
c. Kite d. Trapezoid and c = 30, what is the measure of ∠B?
24. All of the following are properties of an a. 40o b. 30o
isosceles trapezoid EXCEPT: c. 60o d. 45o
a. Diagonals bisect each other. 34. A 10-foot ladder is placed so as to form an angle
c. Base angles are congruent. of 25° with the wall of a building. How far
b. Diagonals are congruent. is the ladder from the base of the building?
d. Opposite angles are supplementary. a. 4.1 ft. b.4.2ft.
25. MNOP is a parallelogram with MN =2x+3 and c. 4.4 ft. d. 4.5 ft.
OP = 4x-5. What is the value of x? 35. The angle from the horizontal to the line of sight of
a. 4 b. 11 the observer to the object above.
c. 16 d. 20 a. angle of depression
26. Which of the following is a proportion? b. angle of elevation
c. horizontal angle
a. 2 :3=5 :7 b. 6 :2=5: 4 d. oblique angle
c. 2 :1=1 :2 d. 3 :8=6 :16 36. What is used to solve x in the figure below?
27. This states that two triangles are similar if
two angles of one triangle are congruent a) sine b) cosine
to two angles of another triangle. cotangent
a. SSS Similarity Theorem 37. Find x using the law of
b. AA Similarity Theorem sines from the given
c. SAS Similarity Theorem figure. (sin 60˚ = 0.8660, sin 45˚ = 0.7071)
d. Right Triangle Similarity Theorem a. 8.90 cm
28. If a, b, and c represent three positive numbers b. 9.20 cm x 12cm
such that a 2−b2−c 2=35 and a :b : c=8 :5 :2, c. 9.80 cm
find the values of a, b, and c. d. 9 cm 60o 45o
a. a=8 ; b=5 ; c=2
8
b. a=60 ; b=20 ; c=10 38. In right triangle PQR, PQ = 12 cm and QR = 5 cm.
c. a=15 ; b=8 ; c=4 What is cot R?
d. a=25 ; b=10 ; c=8 12 5
29. A certain number is the same as the square a. b.
13 13
root of twice the number. What is the number?
a. 1 b. 2 c. 0 d. 3 5 12
c. d.
30. It is a theorem that states that the square 12 5
of the hypotenuse of a right triangle is 39. 39. Which Law would you use in finding the measure of
equal to the sum of the squares of the angle A?
a. cosine law
legs.
b. sine law
a. Mid-segment Theorem c. Pythagorean theorem
b. AA Similarity Theorem d. Trigonometric ratio
c. Pythagorean Theorem
d. SAS Similarity Theorem 40. The lengths of the sides of a triangle are 2cm, 3
31. Give the equation in finding the area of a cm, and 4 cm. Give the equation in determining
the measure of the angle opposite to the longest
triangle with two sides that measure 6 m side.
and 8 m with an included angle of 137°. a. 42 = 22 + 32 – 2(3)(4) cos X
b. 22 = 42 + 32 – 2(3)(4) cos X
c. 32 = 22 + 42 – 2(2)(4) cos X
d. 42 = 22 + 32 – 2(2)(3) cos X

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ANSWER KEY

MATH 9 DIAGNOSTIC TEST

1. C
2. C
3. B
4. D
5. A
6. B
7. C
8. D
9. A
10. D
11. _
12. C
13. A
14. A.
15. C
16. A
17. A
18. C
19. D
20. C
21. B
22. A
23. C
24. A
25.