This document contains 10 multiple choice questions covering various math and statistics topics, including functions, geometry, probability, percentages, sequences, trigonometry, ellipses, and bank interest. It also contains 5 more difficult problems involving arithmetic sequences, trigonometric equations, modeling bacterial growth, finding distances on an ellipse, and comparing interest earned at different banks over 10 years. The questions range from easy to more challenging high school level math.

1. EASY (MULTIPLE CHOICE)
1. What is the range of the function:
𝑒2𝑥−1
2
?
-all positive numbers -all integers -all real numbers -all whole numbers
2. All the details below describe the graph of the function
(𝑥+2)3
2(𝑥+1)2 , EXCEPT:
-The graph has an oblique asymptote of 𝒚 = 𝟐𝒙
-The coordinates of the x-intercept is (-2, 0).
-There is no horizontal asymptote present in the graph.
-The function is undefined at x = -1
3. What do you call a polygon with 35 diagonals?
-Pentagon -Dodecagon -Nonagon - Decagon
4. The diagonal of the floor of a rectangular room is 7.50 m. The shorter side is 4.5 m. What is
the area of the room?
36 sq. m 27 sq. m. 58 sq. m 24 sq.m
5. The center of the ellipse 4𝑥2
+ 𝑦2
− 16𝑥 − 6𝑦 − 43 = 0 is at:
(2, 3) (3, 4) (2, -3) (-4, -3)
6. Solve for y: 𝑦 = ln
𝑒 𝑥
𝑒 𝑥−2
1 2 √2 e
7. If 𝑓( 𝑥) =
3𝑥−𝑎
5𝑥−𝑏
for any real positive number a and b. If 𝑓(0) = 0 and 𝑓(1) 𝑖𝑠 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑.
What is 𝑏 𝑎
?
0 1 1/5 125
8. Ms. Uson gave an exam and found that the average scores of the students is 50 witha standard
deviation 𝜎 = 8. She added 5 points to everyone’s score. What is now the new value of 𝜎?
5 13 3 8
9. The price of 8 calculators ranges from ₱200 to ₱1000. If their average price is ₱950, what is
the lowest possible price of any one of the calculators?
₱500 ₱550 ₱600 ₱650
10. Which of the following trigonometric functions equal to 1?
-
sec 𝑥
cos 𝑥
-sin 2
𝑥 − cos 2
𝑥 -𝐜𝐬𝐜 𝟐
𝒙 𝐭𝐚𝐧 𝟐
𝒙 −
𝟏
𝐜𝐨𝐭 𝟐 𝒙
-
tan 𝑥
cot 𝑥
−
sec 𝑥
cos 𝑥

2. AVERAGE
1. Suppose the function 𝑓( 𝑥) = √
1−𝑥
2
3
. Find the value of the inverse function when x =
√4
3
2
.
0
2. Let 𝐴𝐵̅̅̅̅ be a chord of circle C with radius 13 m. If the shortest distance of 𝐴𝐵̅̅̅̅ to the center C
is 5 m, what is the perimeter of ∆𝐴𝐵𝐶 ?
50 m
3. Throw a fair coin five times. What is the probability of getting three heads and two
tails?(Express answer in fraction)
5/16
4. A man sold 100 eggs. 80 of them were sold at a profit of 30%, while the rest were sold at a
loss of 40%. What is the percentage gain or loss on the whole stock?
16%
5. Find the value of k for which the equation 𝑥2
+ 𝑦2
+ 4𝑥 − 2𝑦 = 𝑘 represents a point circle.
-5
DIFFICULT
1. The sum of the first nine terms of an arithmetic sequence is 99. If the ninth term is 23, find
the sum of the first five terms of this sequence.
25
2. Find the angle 𝜃 (in degrees) where 2 tan 𝜃 + √3 sin 𝜃 sec2
𝜃 = 0, where 0° < 𝜃 < 180°
𝜽 = 𝟏𝟓𝟎°
3. The initial size of a culture of bacteria is 1000. After one hour, the bacteria population grows
to 8000. After how many hours will the population reach 25, 000? (express answer in two
decimal places)
1.55hrs
4. What is the distance (in cm) between the vertices of the following ellipse:
64𝑥2
+ 25𝑦2
+ 16𝑥 − 16𝑦 = 648 (express answer in 2 decimal places)
10.21 cm
5. Bong deposited ₱5 000 in a bank paying 5% annual interest compounded monthly. His friend
Harry deposited the same amount to a different bank paying 2.5% compounded quarterly.
After 10 years, how much money do Bong earn more than Harry?
(express answer in nearest peso)
1 820 pesos.