Batch 2021 ALS A&E Test
Learning
Strand 3 – Mathematical and Problem-Solving Skills
Direction:
Choose the letter of the correct answer.
1. If Set A = {All the primary colors} and Set B
= {All the colors in the rainbow}, then A∩B =
A. {red, orange, yellow, green, blue,
indigo, violet}
B. {red, yellow, blue}
C. {orange, green, violet}
D. (indigo}
2. A number divided by three, minus
the same number multiplied by six, is one more than the number.
A. 3x – 6x = 1 - x
B. x/6 + 3x = x + 1
C. (6 – 3)/x = 1 + x
D. x + 1 = x/3 – 6x
3. The slope of a vertical line graph
is _______.
A. 0
B. positive
C. negative
D. infinite
4. The y-intercept of the function: 3x
+ 5y – 6 = 0 is ______.
A. 3
B. 5/6
C. 6/5
D. 2
5. A square with a side of 6 cm and a
rectangle with a width of 4 cm have the same area. What's the length of the
rectangle?
A. 4 cm
B. 6 cm
C. 9 cm
D. 10 cm
6. Fifteen more than three times a
number is the same as nine less than six times the number. What is the number?
A. 1/8
B. 2
C. 3
D. 8
7. The sum of the digits in a two-digit
number is seven. If the tens digit is three less than the ones digit, find the
number.
A. 25
B. 36
C. 47
D. 52
8. The area of a triangle is 30 units.
If its base is 5 units, then its altitude is ________.
A. 6 units
B. 9 units
C. 12 units
D. 15units
9. Manolo reads three-fifth of 75
pages of his lesson. How many more pages he need to complete the lesson?
A. 15
B. 30
C. 45
D. 60
10. The school canteen posted its
price list as follows:
Pancit ₱ 13.75
Spaghetti ₱ 20.50
Hamburger ₱ 24.75
Cheese sandwich ₱ 12.50
Fruit juice ₱ 10.00
Bottled water ₱ 8.00
Adele and her two friends ordered
one pancit, two spaghetti, one hamburger, two fruit juices, and one bottled
water. How much money did Adele give if she received a change of ₱42.50?
A. ₱107.50
B. ₱ 130.00
C. ₱ 150.00
D. ₱ 200.00
ANSWERS and SOLUTIONS
1. B
Set A = {red, yellow, blue}
Set B = {red, orange, yellow, green, blue, indigo, violet}
A∩B ={red, yellow, blue}
A∩B = A intersect B, which means what elements are COMMON to both A and B.
2. D
“A number divided by three, minus the same number multiplied by six, is one more than the number”?
Let x = the number
x + 1 = x/3 – 6x
3. D
The slope of a vertical line graph is infinite or undefined.
To find the y-intercept of a function, simply substitute 0 (zero) as the value of x and find y.
3x + 5y – 6 = 0
3(0) + 5y – 6 = 0
0 + 5y – 6 = 0
5y = 6 (Transposition)
5y/5 = 6/5
y = 6/5
5. C
Formula:
Area of a square (As) = s2 (s = length of side)
Area of a rectangle (Ar) = LW (L=length; W=width)
Since s = 6, As = 62 = 6 x 6= 36 cm2
Since W = 4 and As = Ar,
Ar = LW
36 = L4
36/4 = L4/4
9 cm = L
6. D
Let a = the number
3x + 15 = fifteen more than three times a number
= is the same as
6x – 9 = nine less than six times the number
3x + 15 = 6x – 9
3x + 15 – 15 - 6x = 6x – 9 – 6x – 15
-3x = -24
-3x/-3 = -24/-3
x = 8
Let t = tens digit
u = units digit
10t + u = the number
Given: t + u = 7 (Eq. 1)
t = u – 3 (Eq. 2)
Substitute Eq. 2 into Eq.
t + u = 7 (Eq. 1)
(u – 3) + u = 7
2u – 3 = 7
2u = 10
u = 5
Substitute 5 for u into Eq. 2
t = u – 3 (Eq. 2)
t = 5 – 3
t = 2
Substitute 5 for u and 3 for t to find our number.
10t + u = 10(2) + 5
20 + 5 = 25
Thus, our number is 25.
8. C
Area of a triangle (At) = ½bh,
where b = the base and h = height or the altitude.
Given: At = 30 units
b = 5 units
At = 1/2bh
30 = ½(5)h
2[30 = ½(5)h]
60 = 5h
60/5 = 5h/5
12 units = h
9. B
Let f = pages he already read
u = pages he needs to read
Given: f = 3/5(75) (Eq. 1)
f = 225/5
f = 45
f + u = 75 (Eq. 2)
45 + u = 75
45 + u – 45 = 75 – 45
u = 30
Thus, Manolo still needs to read 30 pages to complete the lesson.
10. C
Their order:
1 pancit = 13.75
2 Spaghetti 2(20.50) = 41.00
1 Hamburger = 24.75
2 Fruit juices 2(10) = 20.00
1 Bottled water = 8.00
Total Order =107.50
Let x = amount Adele gave
Given: 42.50 = Adele’s change
Equation:
x – 107.50 = 42.50
x – 107.50 + 107.50 = 42.50 + 107.50
x = 150
Thus, Adele gave ₱150.00
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