4. 3. In the expansion of (2𝑎 − 3𝑏)3
what is
the coefficient of 𝑎2
𝑏?
𝑎 + 𝑏 3 = 𝑎3 + 3𝑎2𝑏 + 3𝑎𝑏2 + 𝑏3
= 3 2𝑎 2
−3𝑏
-36
Solution:
Answer:
5. 4. The temperature of the boiling water decreased
from 100°C to 85°C a few minutes after it was
poured into a cup. By how many degrees
Fahrenheit did the water cool?
100°C - 85°C = 15 °C
590F
Solution:
Answer:
°F = 1.8(°C) + 32 = 1.8(15) + 32
6. 5. For the month of February, Roman spent
₱15000. He spent ₱8000 for rent, ₱4500 for
food, ₱2000 for utilities, and ₱500 for others.
In a pie graph representing Roman’s expenses,
what is the central angle of the region
representing the “other” expenses?
8. 6. In a movie theater, 55% of the moviegoers on
Monday are males. If there are 600 more males than
females, find the total number of moviegoers.
M:F=55:45 There is a difference of
10% which is equal to 600 males. So,
600/.1 = 6000
6000
Answer:
Solution:
9. 7. If 15% of x is 45, what is 20% of x?
45/.15 = 300
60
Solution:
Answer:
300 x .2 = 60
10. 8. The sum of three consecutive integers is
63. What is the lowest of the three
integers?
63/3 = 21 - the middle value
20
Answer:
Solution:
Then subtract 1 to the middle to get
the lowest integer.
11. 9. The circle in the figure below has the radius equal
to 3 cm. What is the ratio between the area and the
circumference of the circle?
A : C
3:2
Solution:
Answer:
𝝅𝒓𝟐
: 𝟐𝝅𝒓 Divide with their GCF
𝒓: 𝟐 Substitute the
value of r.
𝟑: 𝟐
12. 10. Four mangoes and 3 oranges cost Php 62.00. Four
mangoes and 5 oranges cost Php 88.00. How much does
one orange cost?
By subtracting 5 oranges and 4 mangoes to 3 oranges
and 4 mangoes, the result will be 5 – 3 = 2 oranges.
Thus, 2 oranges =88 – 62= Php 26 . Therefore, 1
orange is 26/2 = 13.
Php 13
Answer:
13. 11. Solve the inequality |x + 5| - 4 > 1.
{x/x > 0 or x < -10}
Answer:
Solution:
x+5 > 5
x > 0
x+5 < -5
x < -10
16. 14. If the length of a rectangle increased by 20% and the
width decreased by 30%, find the percentage by which its
area changes.
Decreased by 16%
Answer:
Solution:1.2 x 0.7 = 0.84
𝟏 − 𝟎. 𝟖𝟒 = 𝟎. 𝟏𝟔
17. 15. If each side of the square is increased by 20%, by
how many percent is the increase in the original area?
44%
Answer:
Solution:Let 1 be the length of the
side of the original square.
1.2 2
- 1 2
= 1.44 – 1
𝐶ℎ𝑎𝑛𝑔𝑒 𝑡𝑜 %.
= 0.44
18. 16. If the letters of the word MATHEMATICS are
repeatedly and consecutively written, what is the
2017th letter?
H
Answer:
Solution: 2017/11 = 183 remainder 4
The answer is the 4th letter.
19. 17. If 𝟏𝟐. 𝟖 × 𝟑. 𝟒 = 𝟒𝟑. 𝟓𝟐, what is
𝟎. 𝟏𝟐𝟖 × 𝟎. 𝟑𝟒?
0.04352
Answer:
Solution: Just count the number
of decimal places.
20. 18. The average of 11 positive
consecutive odd integers is 37. What
is the smallest number?
27
Answer:
Solution: The average is also the middle
number or the 6th number. The
lowest number has a difference of 2
x 5 = 10 to the lowest number.
21. 19. What is the product of
1
2
⋅
2
3
⋅
3
4
⋅
4
5
⋯
9
10
?
1
10
Answer:
Solution: Cancellation
22. Answer:
Solution: 65t + 75t = 350
2.5 hours
20. Two trains leave the same city at the
same time traveling in opposite directions.
One is traveling at an average speed of
65 km per hour and the other is traveling
at an average speed of 75 km per hour.
In how many hours will they be 350 km
apart?
23. 21. Angelo can complete his school
project in x hours. What part of the
job can be completed by Angelo after
5 hours?
5/x
Answer:
Solution: W = rt = (1/x)(5)
24. 22. The average of the three numbers
is 44. If 1 is added to the first
number, 3 is added to the second
number, and 5 is added to the third,
what is the average of the new
number?
47
Answer:
Solution: [(1 + 3 + 5)/3] + 44
25. 23. What number is midway -22
and 10 on a number line?
-6
Answer:
Solution:(-22 + 10)/2
26. 24. Simplify
𝟒𝟎𝟎𝟎 × 𝟐𝟎𝟎𝟎𝟎
𝟎.𝟎𝟎𝟎𝟒
.
2 × 10𝟏𝟏
Answer:
Solution: Express the numbers first in
scientific notation.
4 × 103
× 2 × 104
4 × 10−4
28. 26. A truck was transferring
fertilizer. The first day, it
transferred 2/5 of the entire pile of
fertilizer. The second day it
transferred 3/4 of the remaining
fertilizer. There are 1200 kilograms of
fertilizer left. How much fertilizer was
there before the transferring?
29. 26. A truck was transferring fertilizer. The first day, it
transferred 2/5 of the entire pile of fertilizer. The second
day it transferred 3/4 of the remaining fertilizer. There are
1200 kilograms of fertilizer left. How much fertilizer was
there before the transferring?
8000 kg
Answer:
Solution: 1-2/5 = 3/5 remained on the first day
1200 ÷ 3/20
3/5 x (1-3/4) = 3/20 remained on the second
day
30. 27. If Rey takes 4x as long as Dave to do
the job and together they take 5 hrs how
long does it take for Rey to do the job?
25 hrs.
Answer:
Solution: From the given, we can say that only
1/5 of the job was done by Rey
when they work together in 5 hours
while Dave did 4/5 of the job,
4(1/5)
31. 28. What is the 8th term in the sequence
10,7, 4...?
-11
Answer:
Solution: Common difference is -3. Multiply it
with 5 since there are 3 given
numbers out of 8. Answer is -15.
Then add -15 to the third number
on the sequence.
32. 29. A shirt was bought for Php 420
at 85% discount. What is the
original price?
Php 2800
Answer:
Solution: 420/.15
34. 31. By how much would an exterior
angle of a triangle increase if each
of its corresponding remote interior
angle increased by 20°?
40°
Answer:
Solution:
An exterior angle is equal to
the sum of its two remote
interior angles.
35. 32. When a number is subtracted
from its additive inverse, the result
is 10. What is the number?
-5
Answer:
Solution: 5 – (-5) = 10
36. 33. Find the least positive integer
that leaves a remainder of 2 when
divided by 3 and 4 but gives an
exact quotient when divided by 5.
50
Answer:
Solution:
Multiples of 3: 12, 15, 18, 21, 24, 27, 30
Multiples of 4: 12, 16, 20, 24, 28, 32, 36
Multiples of 3 and 4: 12, 24, 36, 48
37. 34. Find x and y so that the
ordered data set has a median of
20 and a range of 65: 8, 10, 12,
14, 18, 19, x, 23, 25, 38, 55, y
x=21, y=73
Answer:
Solution: Y = 65+8 = 73
X = 20*2 – 19 = 21
39. 36. A salesman receives a basic salary of
Php 10,000 and a commission of 5% on all
sales. Find his total sales in a month when
he earned Php 25,000?
Php 300,000
Answer:
Solution: Php 25,000 – Php 10,000
Php 15,000/.05
40. 37. Find the LCM of 2040 and 900.
30600
Answer:
Solution: 2040 900
408 180
204 90
102 45
34 15
5
2
2
3
41. 38. The sum of two numbers is -1
and their product is -6, what is the
sum of their cubes?
-19
Answer:
Solution: Think of two factors -6 with the
sum of -1. So, its 2 and -3.
𝟐𝟑
+ (−𝟑)𝟑
= -19
42. 39. Grace is 10 years old and his
mother is 20 years old. In how
many years will Grace age be 9/14
that of his mother?
8 years
Answer:
Solution: 10 + 𝑥
20 + 𝑥
=
9
14
14(10 + x) = 9(20 + x)
140 + 14x = 180 + 9x
5x = 40
x = 8
43. 40. A class of 40 students went on a
field trip where 75% of them joined the
hiking group,60% joined the biking group
and 40% joined both groups. How many
students did not join any of the two
groups?
2
Answer:
Solution: 40 - (0.75+0.6-0.4)(40)
44. 41. Find the value of 𝑎2
− 𝑎 if 𝑎 =
2+ 3
𝟒
.
−𝟏
𝟏𝟔
Answer:
Solution: 𝑎2 − 𝑎 = a(a-1)
46. 42.The product of 585 and a number
n is a square number. What is the
smallest value of n?
65
Answer:
Solution: 585 = 13 ⋅ 5 ⋅ 32
13 ⋅ 5 = 65
47. 43. In the rectangle below, the line MN cuts
the rectangle into two regions. Find x the
length of segment NB so that the area of the
quadrilateral MNBC is 40% of the total area of
the rectangle.
49. Solution:
0.4(20+x)(10) =
𝑥+15+𝐱
2
(10)
4(20+x) = 2x+15 (5)
80+4x = 10X +75
43. In the rectangle below, the line
MN cuts the rectangle into two
regions. Find x the length of segment
NB so that the area of the
quadrilateral MNBC is 40% of the
total area of the rectangle.
5/6 = X
50. 44. Mr. Rozario bought some apples and
oranges. The ratio of the number of apples
to the number of oranges are 2:5. He gave
3/4 of the apples to his sister and 34
oranges to his brother. The ratio of the
number of oranges to the number of apples
that he has now is 2:3.
How many apples and did Mr. Rozario buy?
How many oranges did Mr. Rozario buy?
51. 16 apples and 40 oranges
Answer:
Solution: 1
4
2𝑥 : 5𝑥 − 34 = 2: 3
3𝑥 = 2(10𝑥 − 68)
44. Mr. Rozario bought some apples and oranges. The ratio of the
number of apples to the number of oranges are 2:5. He gave 3/4 of the
apples to his sister and 34 oranges to his brother. The ratio of the
number of oranges to the number of apples that he has now is 2:3.
How many apples did Mr. Rozario buy?
How many oranges did Mr. Rozario buy?
𝑥
2
3 = 2 5𝑥 − 34
17𝑥 = 136
𝑥 = 8
2𝑥: 5𝑥
2 8 : 5(8)
Checking:
¼ of 16 = 4
40 – 34 = 6
4: 6 = 2:3
52. 45. The figure shows the dimensions of an
isosceles triangle in terms of x. What is the
area of the triangle?
48
Answer:
Solution:
2x – 2 = 3x -8
6 = x
𝐴 =
1
2
3𝑥 − 2 𝑥
2x - 2 3x - 8
x
𝑦0 𝑦0
3x - 2
53. 46. The data set consisting of 8 whole
numbers has mean, median and mode
that are all equal to 3. What is the
largest possible number in the data set
if the smallest number is 2?
6
Answer:
Solution: 2, 2, 2, 3, 3, 3, 3, __
54. 47. On a quiz, the mean of the scores
of five students is 13.6. If the highest
score is deleted, the mean of the four
remaining scores is 12.5. Find the
highest score.
18
Answer:
Solution: 13.6-12.5 = 1.1
1.1 x 5 = 5.5 12.5 + 5.5
55. 48. On a quiz, the mean of the scores
of five students is 13.6. If the highest
score is deleted, the mean of the four
remaining scores is 12.5. Find the
highest score.
18
Answer:
Solution: 13.6-12.5 = 1.1
1.1 x 5 = 5.5 12.5 + 5.5
56. 49. What is the smallest positive
integer that must be multiplied to
50 to get a perfect cube?
20
Answer:
Solution:
50 = 2 * 52
