1. College Entrance Test Review
MATH SIMULATED TEST
College Entrance Test Review

2. 1. Party bread is cut into ¼ slices
1. Party bread is cut into ¼ slices. How many fourths are there in 24 pieces of bread?
A. 1/12
D. 72
B. 1/6
E. 96
C. 6
Fourths is NOT THE SAME as Fours.

3. 2. What part of is ? By Percentage-Rate-Base (PRB) method
We are looking for R (rate).

4. 2. (alternative solution)
¼ is less than 1/3. Eliminate choice E.
¼ is greater than 1/3 of 1/3. Eliminate choice A.

5. 2. Cont’n of solution 2
¼ is greater than half of 1/3. Eliminate choice C.
Looking at choice C, which is 3/8, we know that 3/8 is even less than ½. Eliminate choice B.
The option left is choice D.

6. 3. Which of the following is equal to
Make the exponent positive first.

7. 4. Pieces of wire are soldered together so as to form the edges of a cube, whose volume is 216 cubic inches. The number of inches of wire used is ____.

8. 5. If the slope of the line that contains the points (-6, -5) and (-2, x) is 3, then what is x?
slope – steepness of the line
Positive slope means the line
leans to the right.
Answer: E. 7
(-6, -5)

9. 5. If the slope of the line that contains the points (-6, -5) and (-2, x) is 3, then what is x?
Change to variable y,
for less confusion, since we are looking for the y coordinate.
Answer: E. 7

10. 6. What is the positive difference between the two solutions of
First solution:
Second solution:

11. 7. If and , for which values of x is h(x) – g(x) undefined?
Recall: Addition/ Subtraction of rational expressions
The expression above will be undefined if
Answer: A. x = -3 and x = 1

12. 8. A milk tea company has the following options for your drink below
8. A milk tea company has the following options for your drink below. A sample order is Jasmine flavor - Nata de coco - 25% sweet. In how many different ways can you order a drink?
Tea Flavors
Sinkers
Sweetness Level
Jasmine
Pearl
25% sweet
Almond
Nata De Coco
50% sweet
Wintermelon
Coffee Jelly
75% sweet
Green Tea
100% sweet
Fundamental Principle of Counting
Answer: B. 48

13. 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?
Answer: B. 8

14. 10. Solve for x: STRATEGY 1: WORK BACKWARDS.
Try plugging in each of the choices. 
The answer is B. 4
To check:
“To what power will you
raise 2 to get 8?”

15. The left side equals the right side.
Again, the answer is B. 4

16. From the Properties of Logarithms:
STRATEGY 2: Solve the log equation.
From the Properties of Logarithms:
The answer is B. 4

17. 11. If , what is the value of ? Answer: B. 15
Substitute p+3 as your x in the function f(x).
Substitute p as your x in the function f(x).
Answer: B. 15

18. 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.
Answer: D. 6

19. 13. A circle, whose diameter is 10cm, has a chord of length 8cm
13. A circle, whose diameter is 10cm, has a chord of length 8cm. What is the distance of the chord from the center of the circle?
Pythagorean Theorem

20. 14.

22. 15. Three circles are tangent externally to each other and have radii of 2 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?
Answer: D. 18

23. 16. A sphere’s radius is increased by 50%
16. A sphere’s radius is increased by 50%. The volume will then be increased by how many times the original?
Increasing by 50% means the new radius is 1.5times the original.

24. 17. Solve for x: Answer: D. +6 and +2
Quadratic Equation: Put all terms on one side of the equation.
Check if the expression is factorable.
Think of two factors of +12 whose sum is -8.
Answer: D. +6 and +2

25. 18. What is the domain of the function ?
Set of all possible X 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. For h(x) above, what values of x will make the denominator zero? Therefore, domain is ALL REAL NOS.

26. 19. Uncle gave to his children their allowance in the ratio 2:3:7
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
: : 7 ?
___ : ___ : 840
Answer: C.
240

27. 20. The sum of the ages of Lulu, Harvey and Camille is 45
20. The sum of the ages of Lulu, Harvey and Camille is 45. If Lulu is twice as old as Harvey and Harvey is thrice as old as Camille, how old is Lulu?
Lulu’s age: 6 times of Camille’s age. 6(4.5) = 27.
Not in the choices. BONUS

28. 21. What is the sixth term of an arithmetic sequence whose first term is 8 and whose common difference is 5?
8 ___ ___ ___ ___ ____
Answer: D. 33

29. 22. Liezel’s percent score in her physics test was 80%
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
Answer: C. 45

30. 23. In some circuits, the voltage E can be calculated by the formula , 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.

31. Answer: D. Solution 2: Solution 1:
Answer is correct, but not in the choices.
Answer: D.

32. 24. Simplify

33. (a) 50° (d) 80° (b) 60 ° (e) 85° (c) 70°
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°

34. “measure of angle K = 40”
Angle MJK = 50
Angle KJL = 50 also, because “KJ bisects angle J”
“Angle N is 20”
Angle L =
180 –( )

35. (a) (3, 0) (d) (0,1/3) (b) (0, 3) (e) (-18, 0) (c) ( , 0)
26. At which point does the graph of the function crss the x-axis? x-intecept  letting J(x)=0 Thus solve for x: 0= 6x x= 3. In point form, it will be (3,0).
(a) (3, 0)
(d) (0,1/3)
(b) (0, 3)
(e) (-18, 0)
(c) ( , 0)

36. 27. Solve for x in the following equation:
(a) x = - 3
(d) x = 0
(b) x = - 1
(e) x = 6
(c) x = -6/11

37. Ans: C. -6/11

38. 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?
Probability of getting a club =
Probability of getting a heart =

39. 29. Given the proportion , which of the following is FALSE about the proportion?
By cross multiplication: JM=LK By cross multiplication: JM=LK

40. 30. Mr. Serrano earns P217,500 a year. How much is his quarterly salary?
A. P 108,750
D. P 21,750
B. P 72,500
E. P 18,125
C. P 54,375
Quarterly salary = P217,500 / 4

41. 31. What is the third term of a geometric sequence whose fourth term is 12 and whose common ratio is 3?
A. 4/9
D. 4
B. 4/3
E. 36
C. 3

42. 31. What is the third term of a geometric sequence whose fourth term is 12 and whose common ratio is 3?
___ ___ ___ ____
Answer: D. 4

43. You have 200 coins. You give them to your friends in such a way that each friend gets one coin and no two friends get the same number of coins. What is the largest number of friends that you could have?
Solution:
First friend  1 coins
Second friend  2 coins
Third friend  3 coins
So on..
The sequence can have a sum od 1+2+3… until what?
If N =19, sum of coins = 190 thus we still have 10 coins in excess.
Thus the 19th friend can have the excess receiving a total of 29
coins.
Answer: B. 19

44. 33. If , what is the value of k?

45. 34. If 2x +y = 13 and x+2y=11, what is the value for x+y?
Eq. 1: 2x+y=13
Eq. 2: x+2y=11
Solution 1: Using Elimination method
Eq. 1: 4x+2y=26
Eq. 2: x+2y=11
3x=15
X=5 therefore y=3.
Thus C. x+y = 8.

46. 34. If 2x +y = 13 and x+2y=11, what is the value for x+y?
Eq. 1: 2x+y=13
Eq. 2: x+2y=11
Solution 2:Using Substitution method
Eq 1: y=13-2x
Then
Eq . 2: x+2(13-2x) =11
x+26-4x=11
-3x=11-26
-3x= -15
x=5 thus y= Ans: C. x+y = 8

47. 35. The area of a square is 49x2. What is the length of a diagonal of the square?
The side = 7x. From the Theorem, the measure of the diagonal is

48. # 36
Radical Equation
> transpose -2 to have pure radical then
> then square both sides
Solution:
x2 + 7 = (x +1)2
x2 + 7 = x2 + 2x +1
6 = 2x
E. x=3

49. Intersection ; common to both solutions
#37
Inequalities
X> -2
X < 3
Intersection ; common to both solutions
ANSWER: choice E. (-2, 3)

50. Answer: HYPOTENUSE = 2(70ft) =140ft
# 38 ?
Trigonometry
>In a right triangle, the hypotenuse is twice the length of the side opposite the 30 degrees.
Answer: HYPOTENUSE = 2(70ft) =140ft
C ft
70 ft
30⁰

51. # 39 If M ∆ N = M-1 + N-1, what is the value of 1/2 ∆ 1/3
Defined Operations
the symbol is used to do the ff. operations
1) get the reciprocals
2) add them
ANSWER: = 5 (choice D)

52. NS: ¾ of the remainder = ¾ of ½
# 40
Fractions
>read the problem carefully.
NS: ¾ of the remainder = ¾ of ½
Ans. C. = 3/8

53. Exponential Function P(n) = Po * 2n P(7) = 250* 27 =32,000
# 41
Exponential Function
P(n) = Po * 2n
P(7) = 250* 27
=32,000

54. 1st + 2nd + 3rd + 4th + 5th + X = 85 6 5(84) + X = 85 E. X= 90%
# 42
1st + 2nd + 3rd + 4th + 5th + X = 85 6
5(84) + X = 85
E X= 90%

55. # 43 >Getting the LCM LCM(3,5,7) = 3*5*7= 105
Answer: E. multiples of 105

56. # 44

57. #45
Proportion
You need to count the number of ice cubes that will fit within the given dimensions of the container.
Dimensions: 8 deep X 4 wide X 5 high
to 4 pcs. x 2 pcs x 2 pcs = 16 cubes only

58. # 46 note: For y-intercepts, include the operation before b.
Linear Equation
y=mx+b
where slope m and y-intercept b
f(x) = 16x m1 =16 and b1 = -7
g(x) = 16x+5 m1 =16 and b1 = 5
For parallel lines, m1=m2 and b1 ≠ b2.
ANSWER: B
note: For y-intercepts, include the operation before b.

59. # 47 Absolute Value Inequalities Solve for x: Given /2x-5/ < -5.
Answer: NULL SET since no absolute value is LESS THAN zero, and so
there is no absolute value
Less than any negative number.
Ans: A. No Solution

60. # 48 Work Problem let x = time worked NS: X - X = 1 3 4 4X – 3X = 12
4X – 3X = 12
X=12 hrs.

61. # 49 Motion Problem >Important: total distance = 318 miles
Formula :distance = speed x time
NS: 3(s+6) + 3s = 318
s=50, therefore
faster car is 56 mph

62. # 50. James found the mean and standard deviation of the set of numbers: 3, 6, 2, 1, 7, 5. If he adds 5 to each number, which of the following will result?
New mean = Old mean + 5.

63. # 50. James found the mean and standard deviation of the set of numbers: 3, 6, 2, 1, 7, 5. If he adds 5 to each number, which of the following will result?
New SD = old mean.

64. # 50. James found the mean and standard deviation of the set of numbers: 3, 6, 2, 1, 7, 5. If he adds 5 to each number, which of the following will result?
A. The mean will be multiplied by 5.
B. The standard deviation will increase by 5.
C. The mean will not change.
D. The standard deviation will not change
E. Cannot be determined.

65. CONGRATULATIONS, THANK YOU, AND GOOD LUCK! 