Pre Tests – Algebra Components  with solutions

 

Fractions

A score of  4 or 5 is considered passing.

 

            1.  What is the sum of  2/3  and   3/7?     d)

 

                        a)  1/2       b) 2/7          c) 22/21        d) 23/21

 

2.      What is  1 and 1/8th divided by  2/5 ?  c)

a)  4 ½   b)  9/20   c) 45/16   d)  45/10  

 

3.      What is the 5th power of -2?   c)

a)  32    b) -25   c)  -32    d)  -64

 

4.   Simplify     (2/3 + Ύ) /(2/5 + 1)   a)

     a) 85/84    b)  84/85   c)  17/12   d)  29/5

 

5.      What is ½ + 1/3 + Ό ?    d)

a)  1/12     b) 26/24       c) 3/8       d) 13/12  

 

 

Exponents

A score of 5 or 6 is considered passing.

 

1.      What is the 5th power of -2?   a)

a)  -32    b) -25   c)  32    d)  -64

 

2.      Simplify 2-3     c)

a) -6    b)  -8   c)  1/8   d)-1/8

 

3.      Simplify  253/2    b) 

a)  75/2    b) 125   c)  1250   d) 10

 

4.      True or False:  (a + b)2 = a2  + b2  False

 

5.      Simplify  (23)2   b)

 

a) 32    b) 64   c) 128   d)  1/8

 

6.      Simplify   108/(2*103)2    d)

a)  2 x 103  b)  2x102  c)  250  d) 25

 

Expansions

 

A score of 4 or more is considered passing.

 

1.      Expand (x + 2)3    d)  

a)  x3 + 8   b)  x3 + 2  c) x3 +2x2 + 2x+8  d) x3 +6x2 + 12x+8 

 

2.      Expand  (x-9)(x+9)x4   d)

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    c)

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)

a)  7     b)  6   c) 49   d) 1

 

5.      What is (x2 – a)(x2 + a)  ?   d)

a)  x4 – a4   b)  x2 – a2   c)  x4 + a2   d) x4 –a2

 

6.      What is the 5th row of Pascal’s Triangle?    b)

a)    5   10   5

b)   1   5   10  10  5  1

c)   1   5   10    5   1

d)  1    5  25     5   1

 

Factoring

A score of 4 or more is required to pass this section.

 

            Please factor each polynomial as completely as possible

 

1.      x2 – 100   (x-10)(x+10)

2.      x2 – 8x – 9    (x – 9)(x+1)

3.      x4 -81     (x-3)(x+3)(x2 + 9)

4.      x2 + 10x + 25    (x+5)2

5.      x4 +11x3 + 18x2      x2(x+9)(x+2)

6.      x2 + 9   x2 + 9

 

Logs

A score of 5 or better is required to pass this section.

 

1.      What is the base 10 log of  1000?   3

2.      What is the base 10 log of  .001?   -3

3.      True or False:  log(A/B) = log(A) – log(B)  True

4.      True or False:  log(A + B) = log(A) + log(B)  False

5.      Simplify  103log(2)    8

6.      If a quantity increases by a factor of 100, what does its log increase by? 2

7.      If log(A) = x and log(B) = y, what is  the log(A2B3) ? 2x + 3y

 

 

Series

A score of 4 or more is required to pass this section.

 

1.      Simplify to a single number:

 

 

        2 + 5 + 10 + 17 = 34

 

1.      What is the sum of  1+2+3+4+ . . . + 100  ?  5050

2.      What kind of series is the following:

 

1 +2+4+8+16+32+ . . . + 1024

 

a)  arithmetic    b)  harmonic    c) geometric   d) Fibonacci     ?

           

3.      If it is given that

 

     and    

what is the value of the series       ??  3X + 2Y

4.      What is the sum of the series

 

1+1/3+1/9+1/27+ . . . + 1/310 ?    3( 1 – 1/311)/2

 

5.      What is the sum of the series

 

 ?    -1