EXAM FOR GRADE 9 MATHEMATICS

1. EXAMINATION IN
GRADE 9
MATHEMATICS
JULY 10, 2023
REPUBLIC OF THE PHILIPPINES
DEPARTMENT OF EDUCATION
REGION IV-A CALABARZON
DIVISION OF CAVITE
DISTRICT OF MARAGONDON
BUCAL NATIONAL INTEGRATED SCHOOL

2. INSTRUCTIONS
 This exam contains 30 questions and divided into 3
levels – easy, average, and difficult. Each level has a
corresponding point – 1 point for easy, 2 points for
average, and 3 points for difficult. This exam is an
open ended. You have 60 minutes or 1 hour to
answer all the questions. When the time is up, you
should pass your paper immediately and considered
all unanswered questions as wrong or zero point.

3. EASY [1 point]
LEVEL

4. Question #1:
What do you call a second-degree
polynomial equation that can be
written in the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0,
where a, b and c are real numbers
and 𝑎 ≠ 0?

5. Question #2:
The dimensions of a rectangle with an
area of 56 meters2 are (3x - 1) meters
by (x + 4) meters. What quadratic
equation in standard form represents
the situation?

6. Question #3:
In the quadratic equation
3x2 + 7x – 4 = 0, which is
the quadratic term?

7. Question #4:
How many real roots does
the quadratic equation 𝑥2 +
8𝑥 + 12 = 0 have?

8. Question #5:
Solve x (x– 5) = 36.

9. Question #6:
What are the dimensions of
the largest rectangular field
that can be enclosed by 80 m
of fencing wire?

10. Question #7:
If y varies directly as x and
y = 24 when x = 6, find the
constant of variation.

11. Question #8:
What is the result after
simplifying
2 3 + 4 3 - 5 3 ?

12. Question #9:
In rectangle KAYE, YO =
18 cm. Find the length of
diagonal AE.

13. Question #10:
What is the perimeter of a 30-
60-90 triangle whose shorter
leg is 5 inches long?

14. AVERAGE [2 points]
LEVEL

15. Question #11:
Find the roots of the
equation (x + 5)2 + (x – 2)2 =
37.

16. Question #12:
Express y = 3x2 – 4x + 1 in
the form y = a (x - h)2 + k form
and give the values of h and
k.

17. Question #13:
The maximum load m of a beam varies directly as
the breadth b and the square of the depth d and
inversely as the length l. If a beam 3.6 m long, 1.2
m wide, and 2.4 m deep can safely bear a load up
to 909 kg, find the maximum safe load for a beam
of the same material which is 3 m long, 6 m wide,
and 1.8 m deep.

18. Question #14:
Luis walks 5 kilometers due
east and 8 kilometers due
north. How far is he from the
starting point?

19. Question #15:
Given the trapezoid EFGH
with median IJ. If IJ = x, HG =
8 and EF = 12, what is the
value of x?

20. Question #16:
The ratio of the volumes of
two similar rectangular
prisms is 125:64. What is the
ratio of their base areas?

21. Question #17:
ABCD is a parallelogram. If AB is
8 cm long, BC is 5 cm and their
included angle measures 100°,
how long is diagonal AC?

22. Question #18:
In right triangle PQR, PQ =
12 cm and QR = 5 cm.
What is cos R?

23. Question #19:
A balloon is 50 m high. Its angle of
elevation from observer A is 45° and from
observer B it is 30°. What is the
maximum distance between the two
observers? Express your answer to the
nearest meter.

24. Question #20:
The expression 2(sin 30°) –
tan 45° is equal to
_____________.

25. DIFFICULT [3 points]
LEVEL

26. Question #21:
A farmer is tilling a square field with
an area of 900 m2. After 3 hrs, he
tilled
2
3
of the given area. If the area of
the square field measures 180 m2,
find the length of its side.

27. Question #22:
The perimeter of a parallelogram is 34
cm. If a diagonal is 1 cm less than its
length and 8 cm more than its width,
what are the dimensions of this
parallelogram?

28. Question #23:
Solve for the
indicated distance
across the lake.

29. Question #24:
Two points P and Q on the same side of a river are
12 m apart. A tree on the opposite side of the river
is directly opposite a point between P and Q. The
lines of sight of a tree across the river make angles
of 78° and 57°, respectively, with the line joining P
and Q. Find the distance from point Q to the tree.
Express your answer to the nearest meter.

30. Question #25:
Two ships leave the same port at the
same time. One ship sail on a course of
110° at 32 mi/h. The other sails on a
course of 230° at 40 mi/h. Find the
distance between them after 2 hours.
Express your answer to the nearest mile.

31. Question #26:
Triangle BCA is right-angled at C.
If c = 23 and b = 17, find ∠A, ∠B
and a. Express your answers up
to two decimal places.

32. Question #27:
According to a lighting specialist for an art gallery,
for best illumination of a piece of art, it is
recommended that a ceiling mounted light be 1.8
m from the piece of art and that the angle of
depression of the art piece be 38°. How far from
the wall should the light be placed so that the
recommendations of the specialist are met? Give
your answer to the nearest tenth of a meter.

33. Question #28:
Find the exact value of
(sec 30°) (cos 30°) – (tan
60°) (cot 60°)

34. Question #29:
After heavy winds brought by “Hanging Habagat”
damaged a house, workers placed an 8-m brace
against its side at a 45° angle. Then, at the same
spot on the ground, they placed a second longer
brace to make a 30° angle with the side of the
house. How long is the longer brace? Round your
answer to the nearest tenth of a meter.

35. Question #30:
An observer in a lighthouse 48.8 m above sea
level saw two vessels moving directly towards
the lighthouse. He observed that the angles
of depression are 42° and 35°. Find the
distance between the two vessels, assuming
that they are coming from the same side of
the tower.