1.Glenn bought a car for Php600,000. The yearly depreciation of his car is
10% of its value at the start of the year. What is its value after 4 years?
A. Php437,400 B. Php438,000 C. Php393,660 D. Php378,000
2. During a free-fall, a skydiver jumps 16 feet, 48 feet, and 80 feet on the
first, second, and third fall, respectively. If he continues to jump at this
rate, how many feet will he have jumped during the tenth fall?
A. 304 B. 336 C. 314 928 D. 944 784
3. Twelve days before Valentine’s Day, Carl decided to give Nicole
flowers according to the Fibonacci sequence. On the first day, he sent
one red rose, on the second day, two red roses, and so on. How many
roses did Nicole receive during the tenth day?
A. 10 B. 55 C. 89 D. 144
4. A new square is formed by joining the midpoints of the consecutive
sides of a square 8 inches on a side. If the process is continued until
there are already six squares, find the sum of the areas of all squares
in square inches.
A. 96 B. 112 C. 124 D. 126
5.In President Sergio Osmeña High School, suspension of classes is
announced through text brigade. One stormy day, the principal
announces the suspension of classes to two teachers, each of whom
sends this message to two other teachers, and so on. Suppose that
text messages were sent in five rounds, counting the principal’s text
message as the first, how many text messages were sent in all?
A. 31 B. 32 C. 63 D. 64
Aling Puring's 24-hours convenience store opened eight months ago. The first month she made a profit of Php3,000. Each month thereafter, her profit averaged 20% greater than that of the previous month. How much profit did Aling Puring earn during her 8th month of business.
A. Php10,749.5424 C. Php10,729.5424
B. Php10,739.5424 D. Php10,719.5424
#1
600000*.9^4 = 393660
#2
16+32*9 = 304
#3
F12 = 89
#4
8*1/√2^5 = √2
#5
Assuming no one received more than one message
2+4+8+16+32 = 62
I suspect a typo in the problem.
#5
using the formula Sn=n/2(2a+(n-1)d)
S5=5/2(2(2)+(5-1)2)
S5=5/2(4+(4)2)
S5=5/2(4+8)
S5=5/2(12)
S5=5/2 x 12/1
S5=60/2 or 30+1= 31
S5=31
1. To find the value of the car after 4 years, we need to calculate the depreciation for each year and subtract it from the original value.
Year 1: 10% depreciation of Php600,000 = Php60,000
Value after Year 1: Php600,000 - Php60,000 = Php540,000
Year 2: 10% depreciation of Php540,000 = Php54,000
Value after Year 2: Php540,000 - Php54,000 = Php486,000
Year 3: 10% depreciation of Php486,000 = Php48,600
Value after Year 3: Php486,000 - Php48,600 = Php437,400
Year 4: 10% depreciation of Php437,400 = Php43,740
Value after Year 4: Php437,400 - Php43,740 = Php393,660
Therefore, the value of the car after 4 years is Php393,660.
Answer: C. Php393,660
2. To find the total distance the skydiver jumps during the tenth fall, we need to find the pattern in the distances jumped.
The distances jumped follow an arithmetic sequence with a common difference of 32 feet (48 - 16). Since each fall adds 32 feet to the previous one, we can find the distance jumped during the tenth fall by multiplying the common difference by 9 (since the tenth fall is 9 steps away from the first).
Distance during the tenth fall = 32 feet * 9 = 288 feet
To find the total distance jumped during the tenth fall, we add up the distances of all the jumps from the first to the tenth fall.
Total distance = Distance of first fall + Distance of second fall + ... + Distance of tenth fall
= 16 feet + 48 feet + 80 feet + ... + 288 feet
We can use the formula for the sum of an arithmetic series to calculate this. The formula is:
Sum = (n/2) * (first term + last term)
Using this formula, we can find the sum of the distances jumped.
Number of terms, n = 10
First term, a = 16
Last term, l = 288
Sum = (10/2) * (16 + 288)
= 5 * 304
= 1520 feet
Therefore, the skydiver would have jumped a total of 1520 feet during the tenth fall.
Answer: A. 1520 feet
3. The Fibonacci sequence starts with 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. Each term is the sum of the two previous terms.
To find out how many roses Nicole received during the tenth day, we need to look for the value of the tenth term in the Fibonacci sequence.
Tenth term = 55
Therefore, Nicole received 55 roses during the tenth day.
Answer: B. 55 roses
4. To find the sum of the areas of all squares, we need to calculate the area of each square and sum them up.
The original square has side length 8 inches, so its area is 8 inches * 8 inches = 64 square inches.
Each subsequent square is formed by joining the midpoints of the sides of the previous square. Each side length of the subsequent square is half of the previous square's side length.
So, the side lengths of the six squares are: 8 inches, 4 inches, 2 inches, 1 inch, 0.5 inches, and 0.25 inches.
The areas of the squares are: 64 square inches, 16 square inches, 4 square inches, 1 square inch, 0.25 square inches, and 0.0625 square inches.
To find the sum of the areas: 64 + 16 + 4 + 1 + 0.25 + 0.0625 = 85.3125 square inches.
Therefore, the sum of the areas of all six squares is 85.3125 square inches.
Answer: None of the given options.
5. The principal sends the initial text message to 2 teachers. Each of these 2 teachers sends the message to 2 other teachers, resulting in a total of 2 * 2 = 4 messages.
In the second round, each of the 4 teachers sends the message to 2 other teachers, resulting in 4 * 2 = 8 messages.
In the third round, each of the 8 teachers sends the message to 2 other teachers, resulting in 8 * 2 = 16 messages.
In the fourth round, each of the 16 teachers sends the message to 2 other teachers, resulting in 16 * 2 = 32 messages.
In the fifth and final round, each of the 32 teachers sends the message to 2 other teachers, resulting in 32 * 2 = 64 messages.
Adding up the messages sent in each round: 2 + 4 + 8 + 16 + 32 + 64 = 126 messages.
Therefore, a total of 126 text messages were sent.
Answer: None of the given options.
#1
600000*.9^4 = 393660
#2
16+(9)32 = 304
#3
1,2,3,5,8,13,21,34,55,?
34+55=89
#4
6/2 (2+(6-1)8)
3(2+40)=126
#5
5/2 (4(5-1)2) = 30
30 + 1 (the principals text) = 31