EASY (MULTIPLE CHOICE)
1. What is the range of the function 𝑓(𝑥) =
𝑒 2𝑥 −1
2
all positive numbers
all integers
all real numbers
all whole numbers
(𝑥+2)3
2. All the details below describe the graph of the function 𝑓(𝑥) = 2(𝑥+1)2 , ЕХСЕРТ:
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
Nonagon
Dodecagon
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.
58 sq. m.
27 sq. m.
24 sq. m.
2
2
5. The center of the ellipse 4𝑥 + 𝑦 − 16𝑥 − 6𝑦 − 43 = 0 is at:
(2, 3)
(2, -3)
(3, 4)
(-4, -3)
𝑒𝑥
6. Solve for y: 𝑓(𝑥) = 𝑙𝑛 𝑒 𝑥−2
√2
e
1
2
3𝑥−𝑎
7. If 𝑓(𝑥) = 5𝑥−𝑏 for any real positive number a and b. If f(0) = 0 and f(1) is undefined. What is bª?
0
1/5
1
125
8. Ms. Uson gave an exam and found that the average scores of the students is 50 with a standard deviation of 8. She
added 5 points to everyone's score. What is now the new value of the standard deviation?
5
3
13
8
9. The price of 8 calculators ranges from P200 to P1000. If their average price is P950, what is the lowest possible
price of any one of the calculators?
P500
P600
P550
P650
10. Which of the following trigonometric functions equal to 1?
𝑠𝑒𝑐𝑥
1
2
2
−𝑐𝑠𝑐
𝑥𝑡𝑎𝑛
𝑥
−
𝑐𝑜𝑠𝑥
𝑐𝑜𝑡 2 𝑥
2
2
𝑡𝑎𝑛
𝑥
𝑠𝑒𝑐𝑥
−𝑠𝑖𝑛 𝑥 − 𝑐𝑜𝑠 𝑥
−
𝑐𝑜𝑡 𝑥 𝑐𝑜𝑠𝑥
AVERAGE
3
1−𝑥
2
1. Suppose the function 𝑓(𝑥) = √
3
Find the value of the inverse function when 𝑥 =
√4
.
2
2. Let AB be a chord of circle C with radius 13 m. If the shortest distance of AB to the center C is 5 m, what is the
perimeter of ∆АВС?
3. Throw a fair coin five times. What is the probability of getting three heads and two tails? (Express answer in
fraction).
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?
5. Find the value of k for which the equation 𝑥 2 + 𝑦 2 + 4𝑥 − 2𝑦 = 𝑘 represents a point circle.
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.
2. Find the angle 𝜃 (in degrees) where 2𝑡𝑎𝑛𝜃 + √3𝑠𝑖𝑛𝜃𝑠𝑒𝑐 2 𝜃 = 0 , where 0° < 0 < 180°.
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)
4. What is the distance (in cm) between the vertices of the following ellipse: 64𝑥 2 + 25𝑦 2 + 16𝑥 − 16𝑦 = 648
(express answer in 2 decimal places)
5. Bong deposited P5 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)