COMPILATION OF RELIABLE REVIEWER FOR LICENSURE EXAMINATION FOR TEACHER

General Education (MATH)

GEN-ED MATH
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1. Two buses leave the same station at 8:00 pm. One bus travels north at the rate of 30 kph and the other travels east at 40 kph. How many kilometers apart are the buses at 10 pm?
a. 140 km
b. 100 km
c. 70 km
d. 50 km
Solution: Use Pythagorean Theorem a² + b² =c²
a = 30x2 , b= 40x2 and c = unknown
a² + b² = c³
60² + 80² = c²
3600+ 6400 = c²
10000 = c²
√10000 = √c²
c = 100 , so the answer is B
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2. Calculate the mean absolute deviation of the following numbers: 60, 80, 100, 75 and 95
a. 12.4
b. 14.2
c. 16.1
d. 18.9
Solution:
60+80+100+75+95=410
410/5=82
60-82=-22=22
75-82=-7=7
80-82=-2=2
95-82=13=13
100-82=18=18
22+7+2+13+18= 62
Sum= 62
Count=5
Mean Absolute Deviation= 12.4 therefore the answer is A
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3. Which of the following is the factorization of the binomial X²-4
a. (x + 2)(x + 2)
b. (x – 2)²
c. x(x + 2x + 2)
d. (x + 2)(x - 2)
Solution :
x²-4 = x² - 2² = (x+2) (x-2) therefore the answer is D
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4. What value of x will satisfy the equation: 0.4(5x - 1470) = x?
a. 490
b. 2,130
c. 1470
d. 588
Solution :
multiply 0.4(5x - 1470) = x
2x - 588 = x
combine 2x-x = 588
like term x = 588 therefore the answer is D
5. Which of the following has the greatest value:
a. 3 + 32 + (3 + 3)2
b. 33
c. [(3 + 3)2]2
d. (3 + 3 + 3)2
Solution :
[(3+3)²]² =[ (9)²]² = (81)² = 6561 therefore the answer is C
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6. The average of 5 different counting numbers is 20. What is the highest possible value that one of the numbers can have?
a. 20
b. 40
c. 30
d. 90
Solution:
(1 +2 +3 +4 +90)/5 =20 Therefore The answer is D
Answer : 90
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7. Three brothers inherited a cash amount of P62,000 and they divided it among themselves in the ratio of 5:4:1. How much more is the largest share than the smallest share?
a. P75,000
b. P30,000
c. P24,800
Solution:
Add the ratio 5+4+1 =10
proceed to division 62000÷10 = 6200. Then multiply the ratios.
6200 × 5 = 31000(largest share)
6200 × 1 = 6200(smallest share) proceed to Subtraction 31000-6200 = 24,800 , therefore the answer is C
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8. What is the missing terms in the series 5, 20, 80, ___,1280, ___, 20, 480?
a. 50;210
b. 40;160
c. 35;135
d. 320;5120
Solution : The numbers above are being multiplied by 4
5×4 = 20
20 × 4 = 80
80 × 4 = 320
320 × 4 = 1280
1280 × 4 = 5120 therefore the answer is D
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9. At what rate per annum should P2400 be invested so that it will earn an interest of P800 in 8 years?
a. 6 ½ %
b. 5 ½ %
c. 4.17 %
d. 6 %
Solution : Simple interest=Principalrate time
*Since it is asking for rate per annum, we have to find first the interest earned per year so:
interest per year= P800/8
=P100
P100=P2400r1
P100/2400=r
r=0.0417
therefore the answer is C
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10. The area of a rectangle is (x2 + 2x - 8). If its length is x + 4, what is its width?
a. x + 2
b. x - 2
c. x + 1
d. x + 6
Solution:
Try and error
Rectangle Formula : A = LW
(x²+2x - 8) = x+4 (W) hahanap ka sa choices na pwede imultiply sa x+4 na magresult ng x² + 2x -8 at yun ay x-2 .
(x+4 )( x-2) = x² + 2x -8 therefore the answer is B
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11. What is the value of 12⅙ - 3 ⅜ - 5 ⅔ + 20 ¾?!
a. 21 1/8!
b. 22
c. 23 7/8
d. 21
Solution :
12⅙ - 3 ⅜ - 5 ⅔ + 20 ¾.
12 4/24 +20 18/24 = 32 22/24
-3 9/24 - 5 16/24= -8 25/24
32 22/24 borrow = 31 22/24 + 24/24 = 31 46/24
31 46/24 - 8 25/24
= 23 21/24 reduce into lowest term
= 23 7/8 therefore the answer is C
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12. The vertex angle of an isosceles triangle is 20°. What is the measure of one of the base angles?
a. 150°
b. 60°
c. 75°
d. 80°
Solution:
Remember that the total interior angle of a triangle is equal to 180°. 180 ° - 20° = 160° ÷ 2(angle) = 80° Therefore the answer is D
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13. Ana and Beth do a job together in three hours. Working alone, Ana does the job in 5 hours. How long will it take Beth to do the job alone?
a. 3 and 1/3 hours
b. 2 and 1/3 hours
c. 3 hours
d. 7 and 1/2 hours
Solution:
TW = Product / Sum
IW = Product / Difference
IW = 5(3)/5-3
= 15/2
= 7 1/2
therefore the answer is D.
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14. How much greater is the sum of the first 50 counting numbers greater than the sum of the first 100 counting numbers?
a. 110
b. 3,775
c. 3,155
d. 1200
Solution:
The sum of the first 50 counting numbers is 1275.
The sum of the first 100 counting numbers is 5050
then subtract 5050-1275 = 3775.
therefore the answer is B
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15. Which of the following has the largest value?
a. 85
b. 39
c. 65
d. 94
the answer is D
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16. A water tank contains 18 liters when it is 20% full. How many liters does it contain when 50% full?
a. 60
b. 30
c. 58
d. 45
Solution:
18/20=x/50 (cross multiply)
20x=(50)(18)
20x=900
x=900/20
x=45 Therefore the answer is D
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17. The edges of a rectangular solid have these measures: 1.5 feet by 1½ feet by 3 inches. What is its volume in cubic inches?
a. 324
b. 225
c. 972
d. 27
Solution :
Convert feet into inches, since the problem is to find the cubic inches.
1.5 feet x 12 inches = 18 inches
1 ½ or 1.5 x 12 inches = 18 inches then Multiply 18×18× 3 = 972 therefore the answer is C
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