Pre Tests Algebra
Components
Fractions
1.
What is the sum of
2/3 and 3/7?
a) 1/2 b) 2/7 c) 22/21 d) 23/21
2.
What is 1 and 1/8th
divided by 2/5 ?
a) 4
½ b) 9/20
c) 45/16 d) 45/10
3.
What is the
5th power of -2?
a)
32 b) -25 c) -32
d) -64
4. Simplify (2/3 + Ύ) /(2/5 +
1)
a) 85/84 b) 84/85
c) 17/12 d)
29/5
5.
What is ½ +
1/3 + Ό ?
a) 1/12
b) 26/24 c) 3/8 d) 13/12
Exponents
1.
What is the
5th power of -2?
a) -32 b) -25
c) 32 d)
-64
2.
Simplify 2-3
a) -6
b) -8 c)
1/8 d)-1/8
3.
Simplify 253/2
a) 75/2
b) 125 c) 1250
d) 10
4.
True or
False: (a + b)2 = a2 + b2
5.
Simplify (23)2
a) 32
b) 64 c) 128 d) 1/8
6.
Simplify 108/(2*103)2
a) 2 x 103 b)
2x102 c) 250 d)
25
Expansions
1.
Expand (x +
2)3
a) x3
+ 8 b)
x3 + 2 c) x3
+2x2 + 2x+8 d) x3
+6x2 + 12x+8
2.
Expand (x-9)(x+9)x4
a) x6 +x5-9x4
+ 1 b) x6 +x5-18x4
c) x6 +x5-9x4
d) x6
-81x4
3.
Expand and
simplify ((x + a)3 x3)/a
a) x3 a3 b)x2 a2 c)3x2 + 3ax +a2 d) 3x2 + 3ax +a3
4.
What is the
coefficient of x6 in the expansion of (x + 1)7 ?
a)
7 b) 6
c) 49 d) 1
5.
What is (x2
a)(x2 + a) ?
a) x4 a4 b) x2
a2 c) x4 + a2 d) x4 a2
6.
What is the
5th row of Pascals Triangle?
a)
5 10 5
b)
1 5 10 10 5 1
c)
1 5 10
5 1
d)
1 5 25
5 1
Factoring
Please factor each polynomial as completely as possible
1.
x2
100
2.
x2
8x 9
3.
x4
-81
4.
x2
+ 10x + 25
5.
x4
+11x3 + 18x2
6.
x2
+ 9
Logs
1.
What is the base 10 log of 1000?
1.
What is the base 10 log of .001?
2.
True or False:
log(A/B) = log(A) log(B)
3.
True or False: log(A
+ B) = log(A) + log(B)
4.
Simplify 103log(2)
5.
If a quantity increases by a factor of 100, what does its log
increase by?
6.
If log(A) = x and log(B) = y, what
is the log(A2B3) ?
Series
1.
Simplify to a single number:
2. What is the sum of 1+2+3+4+ . . . + 100 ?
3.
What kind of series is the following:
1 +2+4+8+16+32+ . . . + 1024
a)
arithmetic
b) harmonic c) geometric d) Fibonacci ?
4. If it is given that
and 
what is
the value of the series 
??
5. What is the sum of the series
1+1/3+1/9+1/27+ . . . + 1/310 ?
6. What is the sum of the series
?