College Entrance Test Review MATH SIMULATED TEST College Entrance Test Review

1. How many thirds are there in 6? B. ½ E. 18 C. 2

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

2. (alternative solution) Based on the diagrams above,

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

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 ____.

5. What is the slope of the line that contains the points (-6, -5) and (-2, 7)? Answer: E. 3

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

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

8. The sum of two positive integers is 121. Their difference is 25 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 Answer: B. 48

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

10. The sum of three consecutive positive even integers is 90 10. The sum of three consecutive positive even integers is 90. What is the largest integer? 3 consecutive even: 3 consecutive even: Answer: C. 32

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

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

14.

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

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.

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

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.

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 2 : 3 : 7 ? ___ : ___ : 840 Answer: C. 240

20. The sum of the ages of Ged, Billy and Karla is 90 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? 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? 8 ___ ___ ___ ___ ____ Answer: D. 33

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

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.

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

24. Simplify

(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°

“measure of angle K = 40” Angle MJK = 50 Angle KJL = 50 also, because “KJ bisects angle J” “Angle N is 20” Angle L = 180 –( 20 + 100)

26. At which point does the graph of the function cross the x-axis? (b) (0, 3) (e) (-18, 0) (c) ( , 0)

27. Solve for x in the following equation: (a) x = - 4 (d) x = 2 (b) x = - 2 (e) x = 4 (c) x = 0

But 2 is not in the domain of the rational equation 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? Probability of getting a club = Probability of getting a heart =

29. Given the proportion , which of the following is FALSE about the proportion?

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

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

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

33. If , what is the value of k?

34. If 6x +12 = 9, what is the value for x2?

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

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

Intersection ; common to both solutions #37 Inequalities Intersection ; common to both solutions ANSWER: choice e. (-2, 3)

Answer: HYPOTENUSE = 2(70ft) =140ft # 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)

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

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

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

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

# 44

#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

# 46 note: For y-intercepts, include the operation before b. Linear Equation 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 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

>simplify and convert all to decimal # 50 Real Numbers >simplify and convert all to decimal 0.80 + 0.85 + 0.90 = 0.85 or 85% 3

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