Republic of the Philippines
Department of Education
Region IV-A CALABARZON
Division of Laguna
Santa Cruz
DIAGNOSTIC TEST IN MATHEMATICS 9
SY 2018-2019
Name: _________________________________
Score:_____________________
Grade and Section: _______________________
Date: ______________________
Directions: Read and analyze carefully each statement. Write the letter of the
correct answer.
1. Which from the following choices is an example of quadratic equation?
A. x + 3 = 0
B.
=1
D. x2 – 4x + 3 = 0
C. √𝑥 − 3 = 4
2. Solution set of the equation x2 + 3x – 28 = 0?
B. {4, 7}
B. {4, -7}
C. {-4, 7}
D. {-4, -7}
2
3. Describe the roots of the equation x – 6x + 9 = 0?
A. The roots are not real.
C. The roots are irrational and not
equal
B. The roots are rational and equal.
D. The roots are rational and not
equal.
4.If x2 – 4x + k = 0 and k is an element of real number, which statement is true about the
roots of the equation?
A. Roots are factors of 4
C. Roots are factors of k
B. 1 is the root of the equation
D. k is the root of the equation
5. Which of the following are the roots of the equation, +
A. ±
B.
±√
C. { 4 , -3}
= 1?
D.
±√
6. It takes Alvin 3 hours less than it takes Diane to finish a job. If they work together, they can
finish the same job in 2 hours. How long would it take Diane to finish the job alone?
A. 2 hours
B. 4 hours
C. 6 hours
D. 10 hours
7. Which of the following mathematical statements is a quadratic inequality?
A. h2 – 12h + 20 = 0
B. 5u2 – 6u + 12 ≤ 0
C. 7x - 8 > 0
D. r2 – 6r + 8 = 0
8. Solve the inequality x2 + 2x – 15 < 0.
A. (-3, 5)
B. (-5, 3)
C. [-5, 4]
D. [-3, 4)
9. A rectangular box is completely filled with dice. Each die has a volume of 1 cm3. The
length of the box is 3 cm greater than its width and its height is 5 cm. Suppose the box
holds at most 140 dice. What is the possible width of the box?
A. (-7, 4)
B. [-7, 4]
C. (-5, 3]
D. (4, 7)
10. Which is NOT a representation of QUADRATIC FUNCTION?
A. y = x2
B.
C. y = -4
D.
D.
11. Express the quadratic function f(x) = x2 + 6x + 4 in the form f(x) = a(x – h)2 + k.
A. f(x) = (x + 3)2 + 4 B. f(x) = (x - 6)2 – 5
C. f(x) = (x - 3)2 – 7 D. f(x) = (x + 3)2 – 5
12. Which of the following shows the graph of f(x) = -(x + 1)2 – 2?
A.
B.
C.
D.
13. The graph of y = (x – 3)2 + 1 is obtained by sliding the graph of y = (x – 2)2 + 3
A. 1 unit downward and 1 unit to the right
C. 2 units upward and 1 unit to the left
B. 3 units downward and 2 unit to the right
D. 2 units downward and 1 unit to the right
14. Quadratic function whose zeros are 2 and 1.
A. y = x2 – 3x - 2
B. y = x2 + 3x - 2
C. y = 3x2 – 4x + 6
D. y = x2 – 3x + 2
15. What is the largest area of a rectangular lot that can be enclosed by 100 meters fencing
material?
A. 225 sq. meters
B. 625 sq. meters
C. 100 sq. meters D. 1225 sq. meters
16. Which of the following situations illustrates a direct variation?
A. The number of hours to finish a job to the number of men working
B. The volume of water to the space that water did not occupy in a particular container
C. The area of the wall to the volume of paint used to cover it
D. The number of person sharing a pie to the size of slices of the pie
17. The circumference of a circle C varies directly as the measure of its radius r . Which
mathematical sentence is correct?
A. C = kr2
B. C = kr
C. C =
D. k = Cr
18. If “A” varies directly as “p” and A = 12 when p = 4, what is A when p = 6?
A. 14
B. 16
C. 18
D. 20
19. Simplest form of (3125-3)0104
A. -16
?
B. 25
C.
D. -
20. Which of the following expressions has rational exponents?
A. 5√
B. 10√
𝟓(𝟐𝒙 𝟏 𝒚𝟑 )𝟎
21. Simplify the expression𝟏𝟎𝒙
A.
𝟓 𝒚𝟔 𝒛 𝟖
.
…
C. √2 + √3 = √5 = D. √2
=2
C. 12
D. 23
C.
D.
C. √3
D. √3
.
B. 0
22. The expression 6 is the same as:
A. √6
B. √6
23. Which statement is FALSE:
A. √2 + 2√2 = 3√2
B. √2 + √2 = √2
(√32)2.
24. Write the simplified form of
A. 8 √2
B. 2√2
C. √64
25. Find the product of √7 + √2 and √7 − √2 in simplest form.
D. 6√2
A. 5
B. √49 − √4
C. 6
D. 2√7
26. Solution set of the radical equation √𝑥 + 3 = 3?
A. 0
B. 3
C. 6
D. {0, 3}
2
27. The volume of a cylinder is represented by V = 𝜋r h, where r is the radius of the base and
h is the height of the cylinder. If the volume of a cylinder is 175𝜋 cubic meters and the
height is 7 meters, what is the radius of the base?
A. 5 meters
B. 10 meters
C. 6 meters
D. 6.7 meters
28. Which of the following quadrilaterals is NOT parallelogram?
A. square
B. rhombus
C. trapezoid
D. rectangle
29. Which statement is not always true for a parallelogram ABCD?
A. / A ≅ / C
B. AC = BD
C. BC = AD
D. 𝛥ABC ≅ ΔCDA
30. Given the rhombus ABCD whose diagonals intersect at point O. If AO is twice the length
of BO and AB = 4√5, find OC.
A. 4
B. 12
C. 8
D. 16
31. Which of the following parallelograms has perpendicular diagonals?
I. Rectangle II. Square III. Rhombus
A. I only
B. II only
C. II and I
D. II and III
32. Given: ABCD is a parallelogram with / A = 3x – 2y, / B = 123°, and / D = x + 2y. Find x+y.
A. 45°
B. 84°
C. 79°
D. 57°
33. Find numerical ratio in simplest form of 3m – 2n : 3m if m : n = 4 : 3.
A. 2 : 5
B. 3 : 5
C. 1 : 2
D. 4 : 9
34. ΔCOD ~ ΔHOW because CD // HW, which of the following is not true?
A.
=
C.
=
=
=
B.
=
=
D.
=
=
H
W
D
O
C
35. Which of the following theorem is the simplest way to prove that the given pair of
triangles are similar?
A. SSS Similarity Theorem
D
N
B. SAS Similarity Theorem
C. AA Similarity Theorem
1 A2
D. Right Triangle Similarity Theorem
M
F
36. What is the perimeter of a 30-60-90 triangle whose shorter leg is 17 cm long?
A. 68√3 cm
B. 51 + 17√3 cm
C. 51 + 17√2 cm
D. 34 + 17√2 cm
37. Which statement is FALSE?
A. sin t =
C. tan t =
B. cos t =
D. sec t =
38. Cos 60° = ________________
A.
√
B.
C.
√
D. 1
39. Which figure correctly illustrates angle of depression labeled by the mark?
A.
B.
C.
D.
.
40. A surveyor sights two signs and the angle between the two lines of sight measures 49°. If
the first and the second signs are 65 m and 45 m away respectively from the surveyor, find
the distance between the two signs.
A. 49 meters
B. 60 meters
C. 45 meters
D. 87 meters