Download Answer: D. 18

MATH SIMULATED TEST
College Entrance Test Review
1. How many thirds are there in 6?
A. 1/18
B. ½
C. 2
D. 3
E. 18
1
3
6   6
3
1
1
thirds  ' s
3
 18
3
1
2. What part of
is ?
4
2
By PercentageRate-Base (PRB)
method
We are
R

looking for
R (rate).
1
R 2
3
4
P
B
1 3
1 4
2
   

2 4
2 3
3
2. (alternative solution)
3
4
1
2
Based on the
diagrams above,
1
2
3
is
of .
2
3
4
Again, the answer is:
2
D.
3
3. Which of the following is equal
1

to
1
3
 27 
 
 8 
?
Recall: y 3  3 y
Make the exponent positive first.
 27 
 
 8 
1

3
1
3
 8   3  8 
  


 27 
 27 
2
2
Answer: B. 

3
3
4. Pieces of wire are soldered together
so as to form the edges of a cube,
whose volume is 64 cubic inches. The
number of inches of wire used is ____.
Vcube  64 Wire  4 inches  12 edges
3
Vcube  e
64  e
4e
3
Wire 
48 inches
5. What is the slope of the line that
contains the points (-6, -5)
and (-2, 7)?
y
slope 
x

12
7 5

3

slope 

4
2  6
Answer:
E. 3
6. What is the positive difference
between the two solutions of
3  1  2q ?
First solution:
3  1  2q
2q  1  3
2q  2
2

q  1
3
Second solution:

1
3  1  2q
2q  1  3
2q  4
q 2
7. If
x2
x5
g
(
x
)

h(x) 
x3
x1 and
, for
which values of x is
h(x) – g(x) undefined?
Recall: Addition/ Subtraction of rational
expressions a c ad  cd
b

d

bd
The expression above will be undefined
if bd  0.
Answer: A. x = -3 and x = 1
8. The sum of two positive integers
is 121.Their difference is 25.
What is the smaller integer?
Let
x = first integer
121 - x = second integer
first integer - second integer  25
x  73
121  x  48
Answer: B. 48
x  121  x   25
x  121  x  25
2 x  25  121
2 x  146
9. An equilateral triangle has the same
perimeter as a square whose area is 36
cm2. What is the length of a side of the
equilateral triangle in cm?
Perimetertriangle  Perimetersquare
Areasquare  36
Areasquare  side
2
36  side
2
Perimetersquare  6  4 sides
Perimetersquare  24cm
2
Perimeter

24
cm
triangle
36  side
sidetriangle  8cm
6  sidesquare
Answer: B. 8
10. The sum of three consecutive
positive even integers is 90. What is
the largest integer?
3 consecutive even:
x, x  2, x  4
x  x  2  x  4  90
3x  6  90
3x  84
x  28
3 consecutive even:
28,30,32
Answer: C. 32
11. If f  x   5x  12 , what is the
value of f  p  3  f  p ?
Substitute p+3 as your x in the function f(x).
Substitute p as your x in the function f(x).
5  p  3  12    5  p   12 
5p  15  12  5p  12
5p  27
 5p  12
15
Answer: B. 15
12. How many prime numbers are
between 1 and 15?
between = 1 and 15 are not included
Moreover, 1 is NEITHER prime nor composite.
And 15 is composite.
2 3 4 5 6 7 8 9 10
11 12 13 14
Answer: D. 6
13. If a 4-meter tree casts a
shadow that is 12-m long, how tall
is an electric post that casts a
shadow 36-m long?
Ratio & Proportion
4
12
36
?
3
height of tree
:
shadow
4
?

12 36
4  36
?
12
Answer:
B. 12 meters
14.
1
3
3
3
 1 
3
 1 1   3  3 

    
1
 3 3 
 1
     9 
 9
 1
 9
 9
 1

1

81
 9 
 9
9
80

9
80
Answer: A.
9
15. Three circles are
2 3
tangent externally to each 2
3
other and have radii of 2
4 4
inches, 3 inches, and 4
inches, respectively. How
many inches is the
perimeter of the triangle
formed by joining the
centers of the three
circles? 2  2  3  3  4  4  18
Answer: D. 18
16. A sphere’s radius is increased by
50%. The volume will then be
increased by how many times the
original?
3
4 3 
4 3
V


r
new


Vsphere  r
3
2


3
4  27 3 
  r 
3  8 
Increasing by 50% means the
new radius is 1.5times the
original.
3
1.5 or
2
 4 3  27
  r 
27
3
8


Answer: E.
8
17. Solve for x: x  12  8 x
2
Quadratic Equation:
Put all terms on one side of the equation.
x  8 x  12  0
2
Check if the expression is factorable.
Think of two factors of +12 whose sum is -8.
 x  6 x  2  0
x  6, x  2
Answer: D. +6 and +2
18. What is the domain of the
Set of all
5
x

15
function h  x   2
?
possible X
x 1
values such
that h(x)
will be a
real no.
h(x) is a rational function.
Recall:
Rational Functions: watch out for the
denominator. Denominator cannot be equal
to zero. Any number
 undefined
0
For h(x) above, what values of x will make the
denominator zero? None.
Therefore, domain is ALL REAL NOS.
19. Uncle gave to his children their
allowance in the ratio 2:3:7. If the
largest share is P840, how much is
the smallest share?
Partitive proportion
2
:
3
:
7
?
___
: ___ : 840
2
7

? 840
2  840
?
7
Answer: C.
240
20. The sum of the ages of Ged, Billy
and Karla is 90. If Ged is twice as old
as Billy and Billy is thrice as old as
Karla, how old is Ged?
G  B  K  90
G  2B  2  3K   6K
B  3K
6K  3K  K  90
10K  90
K 9
Ged’s age:
6 times of
Karla’s
age.
6(9) = 54.
Answer: D.
54
21. What is the sixth term of an
arithmetic sequence whose first
term is 8 and whose common
difference is 5?
13 ___
18 ___
23 ___
28 ____
33
8 ___
Answer: D.
33
22. Liezel’s percent score in her
physics test was 80%. She counted
her mistakes to be 9. What is the total
number of items in the test?
9 mistakes = 20% of the total number of items
Percentage
9
Base 

Rate
0.20
Base  45
Answer: C.
45
23. In some circuits, the voltage E can
be calculated by the formula ,
r

EIR 
n

where I = current in amperes, R =
resistance in ohms, r is a constant, and
n is the number of elements
connected to the circuit. Express n in
terms of the other variables.
r

E  IR  
n

Solution 1:
Ir
E  IR 
n
Solution 2:
E 
r
 R  
I 
n
E
r
R 
I
n
Ir Answer is
E  IR 
correct,
n
Ir
n
E  IR
but not in
the
choices.
n
r
E
R
I
Answer: D.
x
(
2)
x 
(
3)
x 
24. Simplify ()
6
23
 x  8x  9 x
6
 18 x
6
32
6
6
Answer: D.
18x
6
25. In the figure below, segment KJ
bisects angle J. The measure of angle K
is 40° and the measure of angle L is 20°.
What is the measure of angle N?
(a) 50° (d) 80°
(b) 60 ° (e) 85°
(c) 70°
“measure of angle K = 40”
Angle MJK = 50
Angle KJL = 50 also, because “KJ bisects angle
J”
“Angle N is 20”
40
Angle L =
180 –( 20 + 100)
60
20
50
50
26. At which point does the graph
of the function J(x)6x18
cross the x-axis?
(a) (3, 0) (d) (0,1/3)
(b) (0, 3) (e) (-18, 0)
(c) ( 1 , 0)
3
27. Solve for x in the following
equation:
2
5
2

 2
x 2 x 2 x 4
(a) x = - 4
(d) x = 2
(b) x = - 2
(e) x = 4
(c) x = 0
 x  2 x  2
2
5
2

 2
x  2 x  2

x 2 x 2 x 4
2  x  2   5 x  2   2
2 x  4  5x  4  2
2 x  4  5x  4  2
3x  8  2
6  3x
2x
But 2 is not in the domain of the rational
equation. It is an extraneous solution, which
is not in the choices. Therefore, BONUS. 
28. . If Bianca selects a card at
random from a deck of 52 cards,
what is the probability that she
selects a club or a heart?
1
13
Probability of getting a club =

52 4
1
13
Probability of getting a heart =

52 4
1 1 1
P(club or heart)   
4 4 2
29. Given the proportion ,
J
L

K M
which of the following is FALSE
about the proportion?
Answer: C.
J :M  L:K
30. Mr. Serrano earns P217,500 a
year. How much is his quarterly
salary?
A. P 108,750
B. P 72,500
C. P 54,375
D. P 21,750
E. P 18,125
Quarterly salary = P217,500 / 4
31. What is the third term of a geometric
sequence whose fourth term is 12 and
whose common ratio is 3?
A. 4/9
B. 4/3
C. 3
D. 4
E. 36
31. What is the third term of a
geometric sequence whose fourth
term is 12 and whose common
ratio is 3?
4
___
9
4
___
3
4
12
___ ____
Answer: D.
4
32. The sum of an odd number
and an even number is
(a) an even number.
(b) an odd number.
(c) a prime number.
(d) a composite number.
(e) divisible by 3.
4 k
33. If 27k 2   1 
,
 
3
what is the value of k?
3 k 2
3
 4 k 
3
3(k  2)  (4  k)
3k  6  4  k
Answer: C.
k  5
34. If 6x +12 = 9, what is the value
for x2?
6 x  12  9
6 x  3
1
x
2
1
x 
4
2
1
Answer: D.
4
35. The area of a square is 49x2.
What is the length of a diagonal of
the square?
The side = 7x.
From the 45-45-90 Theorem,
the measure of the diagonal is
7x 2
Answer: B.
7x 2
Radical Equation
# 36
> pure radical then square both sides.
>transpose -2 then square both sides
x
7
2x
1
2
Solution: x2 + 7 = (x +1)2
x2 + 7 = x2 + 2x +1
2x = 6
x=3
#37
Inequalities
Intersection ; common to both solutions
ANSWER: choice e. (-2, 3)
# 38
Trigonometry
>In a right triangle, the side opposite the 30
degrees is ½ the hypotenuse.
Answer: HYPOTENUSE = 2(70ft) =140ft
E. 140 ft
# 39
Defined Operations
the symbol is used to do the ff. operations
1) get the reciprocals
2) add them
ANSWER: 2 + 3 = 5 (choice D)
# 40
Fractions
>read the problem carefully.
NS: ¾ of the remainder = ¾ of ½
= 3/8
# 41
Exponential Equation
P(n)= Po * 2n
P(7) = 250* 27
=32,000
# 42
1st + 2nd + 3rd + 4th + 5th + X = 85
6
5(84) + X = 85
6
X= 90%
# 43
>Getting the LCM
LCM(3,5,7) = 3*5*7= 105
Answer: multiples of 105
# 44
8 x   3x  2y    6 x  9    x  y  
 8 x  8 x  3y  9
 8 x  8 x  3y  9
 3y  9
Answer: B. 3y  9
#45
Proportion
You need to reduce the dimensions of the
compartment in proportion to the ice cube
thus
from 8 deep X 4 wide X 5 high
to 4 deep x 2 wide x 2 high = 16 cubes only
Linear Equation
# 46
y=mx+b
where slope m and y-intercept b
For parallel lines, m1=m2 but b1 not=b2.
ANSWER: B
note: For y-intercepts, include the
operation before b.
# 47
Absolute Value Inequalities
Answer: NULL SET since no absolute value is
LESS THAN zero, and so
there is no absolute value
Less than any negative number.
# 48
Work Problem
let x = time worked
NS: X - X = 1
3
4
4X – 3X = 12
X=12 hrs.
# 49
Motion Problem
>Important: total distance = 318 miles
NS: 3(s+6) + 3s = 318
s=50, therefore
faster car is 56 mph
# 50
Real Numbers
>simplify and convert all to decimal
0.80 + 0.85 + 0.90 = 0.85 or 85%
3
CONGRATULATIONS,
THANK YOU,
AND GOOD LUCK! 