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  Algebra 1.   The first term in a sequence of number 2. Each even numbered term is 3 more than the previous term and each odd numbered term excluding the first is -1 times the previous term. What is the 45 th  term pf the sequence?  A1=2, A2=5, A=-5, A4=-2. . . . A45=2 2.   The number 0.06906907. . . is? Rational 3.   Which of the following is prime number? 17 4.   Positive integers greater than 1 and has no positive integers divisor than 1 and itself Prime number 5.   A basic property which states that a + b is equal to b + a Commutative law 6.   Which states the additive inverse property of real numbers? a + -a = 0 7.   The multiplicative inverse of x/3 is 3/x 8.   The identity element for addition is 0 9.   The terms of a sum may be grouped in any manner w/o affecting the result?  Associative Law 10.   What is the value of log 5 to the base 2 + log to the base 3 Log 2 5 + Log 3 5 = 3.79 11.   The equation whose roots are the reciprocal of the roots of the equation 2x2  –  3x  –  5 = 0 is Mode 5 3 a=2, b=-3, c=-5, x  1 =2/5, x  2 =-1 a=5, b=3, c=2, x  1 =5/2, x  2 =-1 12.   What is the sum of coefficient in the expansion of (x+y-z) 8? 0 (1+1-1) 8 =1  13.   It is the sum of finite and infinite of terms? Series 14.   Find the sum of the first 8 terms of the sequence whit general them: 2n-1. ∑()    15.   Evaluate the sum of the first n odd number 1+3+5+. . . . an. n 2   16.   Evaluate the sum of the first n odd number 2+4+6+. . . . an n(n+1) 2   17.   Find the sum from the 3 rd  to the 8 th  term of the sequence whose general term is 2^n + n? ∑(  )   18.   Evaluate the series 1+1+1/2!+1/3!+1/4!+. . . . 1+1+1/2!+1/3!+1/4!=2.72 19.   It is a sequence if numbers such that successive terns by a constant  Arithmetic progression 20.   9,3,1,1/3. . is a Geometric progression 21.   Find the 30 th  term of the a.p. 4,7,10, Mode 3 2  X = 1 2 Y = 4 7 30(yshift1,7,5),1,10) = 91 22.   A conference hall has 32 seats in the 1 st  row, 34 in the 2 nd  row 36 in the 3 rd  row and 48 in the 9 th  row. Find the total seating capacity if there are 50 seats each row from 11 th  to 20 th  row. Mode 3 2  X=1,2 Y=32,34  ∑(x(yshift1,7,5) 1,10) = 410 410 + 500 = 910 23.   Evaluate the expression x+3x+5x+. . . .+49x = 625 Mode 3 2   X=1,2 Y=1,3  ∑(x(yshift1,7,5)1,25) = 625   X =1 24.   Find the n term of the a.p. 4,7,10,. . . if the nth term is 25.  X=2 Y=7 25 xshift1,7,5 = 8 25.   In a potato race are placed 6 feet apart on a straight line the first being 6ft from the basket. A contestant starts from the basket and puts one potato at a time into the basket. Find the distance that he must ran in order to finish the race (6x2)+ (6x2x3)+(6x2x4)+(6x2x5)+(6x2x2)+ (6x2x6)+ (6x2x7)+(6x2x8)=432 26.   The 3 rd  term of a geometric progression is 45 and the 7 th  term is 3645 find the 1 st  term. Mode 3 6  X = 3,7 Y = 45,3645 1(y175) =5 27.   The number 28, x+2, 112 for a geometric progression. What is the 15 th  term of the sequence? Mode 3 6  X = 1,3 Y = 28,112 15(y175) = 458752 28.   The 3 rd  term of a geometric progression is 45 and the 7 th  term is 3645 find the sum of the 1 st  10 terms. Mode 3 6  X = 3,7 Y = 45,3645  ∑(x(yshift1,7,5)1,10) = 147670   29.   Solve the common ratio if the 5 th  term of a geometric progression is 162 and the 10 th  term is -39.366. Mode 3 6  X=1,5 Y=3,19 R = 2(yshift1,7,5)/1(yshift1,7,5) = -3  30.   What is the 8 th  term of the harmonic progression if the first and the fifth term are 1/3 and 1/19 Mode 3 2  X=1,5 Y=3,19 8(yshift1,7,5) =31 31.   Find the 8 th  term: 0.5, 0.167, and 0.1. . . Mode 3 2  X=1,2 Y=2,6 8(yshift1,7,5)=0 32.   A father is now 41 and his son is 9. After how many years will his age be just triple his sons age 41+x = 3(9+x) 33.   Two friend a and b are respectively 5 and 8 years old. In how many years will the ratio of their ages be 3:4? 5+4 =9, 8+4=12 ratio 3:4 34.   How many grams of nickel must be removed from 1500 grams of alloys having 5% nickel to make an alloy having 2% nickel? 0.05(1500)-x=0.02(1500-x)  X=36 35.   Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a drum srcinally containing 30 liters of 10% salt solution. What is the percent concentration in the mixture? 0.25(10)+(15)0.35+0.1(30)=55x  X=.2 36.   A certain pipe can fill a tank in 7 hours and another pipe can fill same tank in 5 hours. A drain pipe can empty the full content of tank in 25 hours. With all the three pipes open, how long will it takes to fill the tank? 1/7+1/5-1/25=1/T T=3.3 37.   Lorna can finish a job in 5 hours. Fe can do it in 4 hours. If Lorna worked for 2 hours and then Fe was asked to help her finish it, how long will Fe have to work with Lorna to finish the job? 1/5(2)+(1/5+1/4)=1/x  X=4/3
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