AUEESS EQE REVIEWALGEBRA1. A diagram on which complex numbers are represented geometrically using Cartesian axes, the horizontal coordinate representing the real part of the number and the vertical coordinate the complex part.A. Argand Diagram B. Network DiagramC. Venn Diagram D. Euler Diagram2. What is the domain of the function defined by

( x )= 1

√9−x2 ?A. {x | –3 < x < 3} B. {x | x > 3}C. {x | –3 x 3} D. {x |x <–3 or x< 3}3. If x varies inversely as y and when x = 2, y = 5, what is the value of y2 when x = 1/3.A. 900 B. 1/900C. 30 D. 1/304. If A = [ 2 3

−1 1] and B = [ 3−4 ], then AB is equal to A. [−6−7] B. [−6 −7 ]

C. [6 94 −4] D. [ 6 −12

−3 −4 ]5. Simplify the imaginary number 2i2007

¿¿.A. –1 – i B. –1 + i C. 1 – i D. 1 + i

6. Determine m such that x3−5x2+7 x+m−5 is divisible by x – 4. A. –7 B. 0C. 5 D. 177. How many terms must the progression 3, 5, 7, … have in order for the sum to 2600?A. 47 B. 48C. 50 D. 528. Suppose log a3 = p and log a5 = r. Then log √a25+ loga227 terms of p and r is

A. 4r + 32

p B. 4r + 23

pC. 4r – 2

3p D. 4r – 3

2p

9. Evaluate (98 !)(99)100 !

.A. 99 B. 1/100C. 1/99 D. 9,90010. What is the range of y = sin x?A. (∞, +∞) B. [1, 1]C. [0, +∞) D. [1, 0]11. Given the logarithmic expression x = log 887, solve for x.A. 1 B. 8C. 7 D. 012. Troy is 19 years old and his father is 65 years old. In how many years will the father be three times as old as his son?A. 2 B. 4C. 8 D. 10

13. In a class of 40 students, 27 like Differential Calculus and 25 like Gen. Chemistry 1. How many students like both subjects?A. 8 B. 10C. 12 D. 1414. The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.A. 8/5 B. 13/5C. 5/13 D. 3/515. It takes 6 hours for vote counter A to count a bucket of votes. If vote counter B is assigned to help A with the count, it takes 4 hours. How long does it take vote counter B to count a bucket of votes alone?A. 8 hours B. 10 hoursC. 12 hours D. 24 hours16. Find the product of two numbers such that twice the first added to the second equals 19 and three times the first is 21 more than the second.A. 24 B. 32C. 18 D. 2017. One number is 5 less than the other. If their sum is 135, what are the numbers?A. 85, 50 B. 80, 55C. 70, 65 D. 75, 6018. Ten less than four times a certain number is 14. Determine the number.A. 6 B. 7C. 8 D. 9

19. If (3a¿¿2−4 b)5¿ is expanded, what is the sum of the numerical coefficients of the two middle terms?A. –720 B. 720C. 1440 D. –1440 20. Simplify (x−h)2−x2

h,whereh≠0.A. h B. 2x+h

hC. 2x D. h – 2x21. Simplify( ab+acab−ac

∙bb+c )( b

b−c ),where a≠0∧b≠±c.A. 0 B. 1

C. b2

(b−c )2D. b2

b2−c2

22. The product of the roots of √x+1+√x−1√x+1−√x−1

=1 and x–5=0 isA. 15 B. 10C. 5 D. – 1523. Solve for x in [ x 1

3 x ]= –2x.A. x∈ {–3, –1} B. x∈ {–3, 1}C. x∈ {3, 1} D. x∈ {3, –1}

24. Solve for U if U=√1−√1−√1−.. .A. 0.723 B. 0.618C. 0.852 D. 0.45325. Factor the expression x6 – 1 as completely as possible.A. (x+1)(x–1)(x4+x2–1)B. (x+1)(x–1)(x4–x2+1)C. (x+1)(x–1)(x4+2x2+1)D. (x+1)(x–1)(x4+x2+1)26. The roots of the equation (x–4)2(x+2) = (x+2)2(x–4) are:A. 4 & -2 only B. 1 onlyC. -2 & 4 only D. 1, -2 & 4 only27. Find A and B such that x+10

x2−4= Ax – 2

+ Bx+2 .A. A= –3, B= 2 B. A= –3, B= –2C. A= 3, B= –2 D. A= 3, B= 2

28. If 2x – 3y = x + y, then x2 : y2 =A. 1:4 B. 4:1

C. 1:16 D. 16:129. Peter`s age 13 years ago was 1/3 of his age 7 years hence. How old is Peter?A. 15 B. 20C. 23 D. 2730. In what ratio must a peanut costing P 240.00 per kg be mixed with a peanut costing P 340.00 per kg so that a profit of 20% is made by selling the mixture of P 360.00 per kg?A. 1:2 B. 3:2C. 2:3 D. 3:531. Find the mean proportion of 4 and 16.A. 8 B. 12C. 24 D. 7232. Find the geometric mean of 2 and 32.A. 8 B. 12C. 24 D. 7233. Orly can paint a house in 9 hours while Noe can paint the same house in 16 hours. They work together for 4 hours. After 4 hours. Noe left and Orly finished the job alone. How many more hours did it take Orly to finish the job? A. 2.75 hours B. 2.50 hoursC. 2.25 hours D. 3.0 hours34. If 3 is subtracted from the numerator of a certain fraction, the value of the fraction becomes 3/5. If 1 is subtracted from the denominator of the same fraction, it becomes 2/3. Find the original fraction.A. 35/55 B. 36/55C. 3/7 D. 32/4135. A father tells his son “I was your age now when you were born.” If the father is now 38 years old, how old was his son 2 years ago?A. 15 B. 17C. 19 D. 2136. Ed is three times as old as Mon. Three years ago, Ed was four times as old as Mon. The sum of their ages isA. 20 B. 24C. 28 D. 3637. Given log3 (x2−8 x )=2. Solve for x. A. -1 B. 9C. -1 and 9 D. 1 and -938. What expression is equivalent to log (x) – log (y + z)?A. log x + log y + log zB. log [x/(y+z)]

C. log x - log y - log zD. log y + log (x+z)39. If 16 is 4 more than 4x, find 5x-1.A. 14 B. 3C. 12 D. 540. What is the product of the roots of the quadratic equation 2x2 – 5x +8?A. ½ B. 4C. 5/2 D. 5

2 + 4i

FORMULASrth term of the binomial expansion (X+Y)nrth = nCr-1 X(n-r+1) Yr-1

Sum of the coefficients of the expansion (X+Y)nSum =(Coeff. Of X + coeff. Of Y)nSum of exponents of the expansion of (X+Y)n

Sum = n(n+1)Arithmetic Progression

nth term = a1+(n – 1)dSum of all terms= n2

(a1+an) = n2

[2a1+(n–1)d]Geometric Progression

nth term = a1rn-1Sum of all terms= a1(rn−1)

r−1 = a1(1−rn)

1−rInfinite Progression If r>1, Sum of all terms = ∞If r<1, Sum of all terms = a11−r