1. MATH COMPREHENSIVE TEST
College Entrance Test Review
Young Einstein Learning Center
By Kristine Tan

2. 1. To write the sum as one fraction, we need to get the least common multiple (LCM) of the denominators. What is the LCM of 18 and 45?
A. 9
C. 45
B. 18
D. 90

3. 2. What is the sum of the expression:

4. 3. Which of the following equations is TRUE?
A. C.
B. D.

5. 4. Luke's shooting average in basketball is 80 %, which means that for every 100 attempts made, 80 shots went through the basket. During one practice session, if Luke attempted 40 shots, how many of these shots went through the basket?
A. 8
C. 32
B. 20
D. 36

6. 5. A roll of string costs P If the total length of the string is 7/8 of a meter, how much is a meter of string?
A. P8.00
C. P56.00
B. P49.00
D. P64.00
Solution 1:
Solution 2:

7. 6. What is the algebraic expression for the verbal phrase: Z less than the sum of X and Y
A. Z - X + Y
C. (X + Y) - Z
B. Z - (X - Y)
D. Z - (X + Y)

8. 7. Reduce to lowest terms. Follow PEMDAS! 
The denominator is not factorable anymore.
So the answer is B.

9. 8. If a, b > 0, then is the same as
We can only distribute the radical sign over MULTIPLICATION or DIVISION. The expression cannot be simplified further. But if the question was . then it will be simplified to

10. 9. Simplify the rational algebraic expression:
Factor out the common monomial.
Factor the perfect square trinomial below.

11. 10. The area of a rectangle is (x2 – 36)
10. The area of a rectangle is (x2 – 36). If its length is (x + 6), what is the expression for its width?
Difference of Two Squares.

12. 11. A mango tree that is 4 meters tall casts a shadow that is 12 meters long. If a bamboo tree casts an 18-meter shadow, how tall is the bamboo tree?
Ratio & Proportion ? 4 12 18

13. 12. A circle, whose diameter is 100cm, has a chord of length 80cm
12. A circle, whose diameter is 100cm, has a chord of length 80cm. What is the distance of the chord from the center of the circle?
Pythagorean Theorem

14. 13. If the four figures below were outdoor parks, and you wish to enclose these parks with rope, which park will need the longest rope? C.
B. D.
Largest Perimeter:
Peri = around
Meter = measure
Count the edges all
around. Most
number of square
edges is D.

15. 14. If the four figures were office floor spaces, and you wish to cover the floor in tiles, which office space will need the most number of tiles? C.
B. D.
Largest AREA
Count the NUMBER
OF SQUARES.
Most
number of squares
is C.

16. 15. Express the area of the shaded region in terms of r.

17. 16. What is the equation for volume V in terms of time t to describe the diagonal line?
A.      V = 200t + 5
B.      V = 40t +200
C.      D.
200
Volume 5
Time
Line leaning to the left  slope is negative
X-intercept: (5,0), Y-intercept: (0, 200)

18. We can use the slope-intercept form of a line.
m = slope
b = y-intercept
Substitute the point (5,0) for (x,y)
Answer:

19. 17. What is the slope of the line in the figure?4 -2

20. 18. Find the center and radius of the circle with the equation:
We use completing the square:
C. Center: (-4, 1), radius = 3

21. 19. The online stockbroker CitisecOnline spent P484,375 on x shares of Mang Inasal Stock at P15.50 per share and y shares of Meralco Stock at P62.50 per share. What is the linear equation that models this situation?
B x y = 484,375

22. 20. Find the equation of the line that passes through the point (-7, -2) and is perpendicular to the line whose equation is 2x - 6y + 1 = 0.
To get the slope of this line, transform 2x – 6y + 1 = 0 to the form y = mx + b.
Slope = 3

23. Since perpendicular, the slope of our unknown line:
Substitute the point (-7, -2) in y = mx +b.

24. the equation of the line is
Writing in the general form,

25. 21. Given the linear equation, solve for r:
Get rid of denominators: multiply both sides by 12.

26. 22. What are the roots of the quadratic equation y = x2 – 12x – 45?
To get the roots, we look for the values of x when y = 0.
Do factoring.
Therefore, the answer is
C. x = -3, x = 15.

27. 23. Find the solution set of the rational equation:
Multiply both sides by , which is just the same as
A. 10

28. 24. Solve for the solution set of the radical equation:
Plug in the choices.  See which value for m will make the equation true.
A. 0
C. 4
B. 2
D. Extraneous solution
Answer:
 True!

29. 25. In electrical engineering, we compute for the resulting load resistance in a parallel circuit using the formula:
Solve for R1.