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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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